TSTP Solution File: SWW315+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SWW315+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 00:13:41 EDT 2023
% Result : Theorem 28.73s 28.50s
% Output : CNFRefutation 28.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : SWW315+1 : TPTP v8.1.2. Released v5.2.0.
% 0.09/0.11 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.11/0.32 % Computer : n011.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sun Aug 27 19:33:55 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.17/0.56 start to proof:theBenchmark
% 28.12/28.33 %-------------------------------------------
% 28.12/28.33 % File :CSE---1.6
% 28.12/28.33 % Problem :theBenchmark
% 28.12/28.33 % Transform :cnf
% 28.12/28.33 % Format :tptp:raw
% 28.12/28.33 % Command :java -jar mcs_scs.jar %d %s
% 28.12/28.33
% 28.12/28.33 % Result :Theorem 22.760000s
% 28.12/28.33 % Output :CNFRefutation 22.760000s
% 28.12/28.33 %-------------------------------------------
% 28.12/28.34 %------------------------------------------------------------------------------
% 28.12/28.34 % File : SWW315+1 : TPTP v8.1.2. Released v5.2.0.
% 28.12/28.34 % Domain : Software Verification
% 28.12/28.34 % Problem : Hoare's Logic with Procedures 434976, 5000 axioms selected
% 28.12/28.34 % Version : Especial.
% 28.12/28.34 % English :
% 28.12/28.34
% 28.12/28.34 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 28.12/28.34 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 28.12/28.34 % Source : [Bla11]
% 28.12/28.34 % Names : hoare_434976.5000.p [Bla11]
% 28.12/28.34
% 28.12/28.34 % Status : Theorem
% 28.12/28.34 % Rating : 0.42 v8.1.0, 0.47 v7.5.0, 0.50 v7.4.0, 0.57 v7.3.0, 0.48 v7.2.0, 0.45 v7.1.0, 0.61 v7.0.0, 0.60 v6.4.0, 0.58 v6.2.0, 0.68 v6.1.0, 0.73 v6.0.0, 0.65 v5.5.0, 0.70 v5.4.0, 0.71 v5.3.0, 0.78 v5.2.0
% 28.12/28.34 % Syntax : Number of formulae : 5230 (1642 unt; 0 def)
% 28.12/28.34 % Number of atoms : 12838 (4418 equ)
% 28.12/28.34 % Maximal formula atoms : 13 ( 2 avg)
% 28.12/28.34 % Number of connectives : 8579 ( 971 ~; 148 |; 711 &)
% 28.12/28.34 % ( 892 <=>;5857 =>; 0 <=; 0 <~>)
% 28.12/28.34 % Maximal formula depth : 22 ( 6 avg)
% 28.12/28.34 % Maximal term depth : 19 ( 2 avg)
% 28.12/28.34 % Number of predicates : 152 ( 151 usr; 0 prp; 1-6 aty)
% 28.12/28.34 % Number of functors : 377 ( 377 usr; 48 con; 0-7 aty)
% 28.12/28.34 % Number of variables : 16688 (16532 !; 156 ?)
% 28.12/28.34 % SPC : FOF_THM_RFO_SEQ
% 28.12/28.34
% 28.12/28.34 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 28.12/28.34 % 2011-03-01 11:43:18
% 28.12/28.34 %------------------------------------------------------------------------------
% 28.12/28.34 %----Relevant facts (4985)
% 28.12/28.34 fof(fact_ext,axiom,
% 28.12/28.34 ! [V_g_2,V_f_2] :
% 28.12/28.34 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
% 28.12/28.34 => V_f_2 = V_g_2 ) ).
% 28.12/28.34
% 28.12/28.34 fof(fact_asm,axiom,
% 28.12/28.34 ! [V_G_2,V_tsa_2,T_b] :
% 28.12/28.34 ( 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))
% 28.12/28.34 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2) ) ).
% 28.12/28.34
% 28.12/28.34 fof(fact_weaken,axiom,
% 28.12/28.34 ! [V_tsa_2,V_ts_H_2,V_G_2,T_b] :
% 28.12/28.34 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_ts_H_2)
% 28.12/28.34 => ( 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))
% 28.12/28.34 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2) ) ) ).
% 28.12/28.34
% 28.12/28.34 fof(fact_cut,axiom,
% 28.12/28.34 ! [V_G_2,V_tsa_2,V_G_Ha_2,T_b] :
% 28.12/28.34 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_Ha_2,V_tsa_2)
% 28.12/28.34 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_G_Ha_2)
% 28.12/28.34 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2) ) ) ).
% 28.12/28.34
% 28.12/28.34 fof(fact_equalityI,axiom,
% 28.12/28.34 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 28.12/28.34 => V_A_2 = V_B_2 ) ) ).
% 28.12/28.34
% 28.12/28.34 fof(fact_order__refl,axiom,
% 28.12/28.34 ! [V_x,T_a] :
% 28.12/28.34 ( class_Orderings_Opreorder(T_a)
% 28.12/28.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ) ).
% 28.12/28.34
% 28.12/28.34 fof(fact_le__fun__def,axiom,
% 28.12/28.34 ! [V_g_2,V_f_2,T_b,T_c] :
% 28.12/28.34 ( class_Orderings_Oord(T_c)
% 28.12/28.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 28.12/28.34 <=> ! [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))) ) ) ).
% 28.12/28.34
% 28.12/28.34 fof(fact_le__funD,axiom,
% 28.12/28.34 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
% 28.12/28.34 ( class_Orderings_Oord(T_c)
% 28.12/28.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 28.12/28.34 => 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))) ) ) ).
% 28.12/28.34
% 28.12/28.34 fof(fact_le__funE,axiom,
% 28.12/28.34 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
% 28.12/28.34 ( class_Orderings_Oord(T_c)
% 28.12/28.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 28.12/28.34 => 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))) ) ) ).
% 28.12/28.34
% 28.12/28.34 fof(fact_subset__refl,axiom,
% 28.12/28.34 ! [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)) ).
% 28.12/28.34
% 28.12/28.34 fof(fact_set__eq__subset,axiom,
% 28.12/28.34 ! [T_b,V_B_2,V_A_2] :
% 28.12/28.34 ( V_A_2 = V_B_2
% 28.12/28.34 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 28.12/28.34
% 28.12/28.34 fof(fact_rev__predicate1D,axiom,
% 28.12/28.34 ! [V_Q_2,T_b,V_x_2,V_P_2] :
% 28.12/28.34 ( hBOOL(hAPP(V_P_2,V_x_2))
% 28.12/28.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_P_2),V_Q_2))
% 28.12/28.34 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ).
% 28.12/28.34
% 28.12/28.34 fof(fact_equalityD1,axiom,
% 28.12/28.34 ! [T_b,V_B_2,V_A_2] :
% 28.12/28.34 ( V_A_2 = V_B_2
% 28.12/28.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 28.12/28.34
% 28.12/28.34 fof(fact_equalityD2,axiom,
% 28.12/28.34 ! [T_b,V_B_2,V_A_2] :
% 28.12/28.34 ( V_A_2 = V_B_2
% 28.12/28.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 28.12/28.34
% 28.12/28.34 fof(fact_predicate1D,axiom,
% 28.12/28.34 ! [V_x_2,V_Q_2,V_P_2,T_b] :
% 28.12/28.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_P_2),V_Q_2))
% 28.12/28.34 => ( hBOOL(hAPP(V_P_2,V_x_2))
% 28.12/28.34 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ).
% 28.12/28.34
% 28.12/28.34 fof(fact_subset__trans,axiom,
% 28.12/28.34 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 28.12/28.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 28.12/28.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 28.12/28.35
% 28.12/28.35 fof(fact_linorder__le__cases,axiom,
% 28.12/28.35 ! [V_y,V_x,T_a] :
% 28.12/28.35 ( class_Orderings_Olinorder(T_a)
% 28.12/28.35 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 28.12/28.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 28.12/28.35
% 28.12/28.35 fof(fact_xt1_I6_J,axiom,
% 28.12/28.35 ! [V_z,V_x,V_y,T_a] :
% 28.12/28.35 ( class_Orderings_Oorder(T_a)
% 28.12/28.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 28.12/28.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 28.12/28.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ) ).
% 28.12/28.35
% 28.12/28.35 fof(fact_xt1_I5_J,axiom,
% 28.12/28.35 ! [V_x,V_y,T_a] :
% 28.12/28.35 ( class_Orderings_Oorder(T_a)
% 28.12/28.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 28.12/28.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 28.12/28.35 => V_x = V_y ) ) ) ).
% 28.12/28.35
% 28.12/28.35 fof(fact_order__trans,axiom,
% 28.12/28.35 ! [V_z,V_y,V_x,T_a] :
% 28.12/28.35 ( class_Orderings_Opreorder(T_a)
% 28.12/28.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 28.12/28.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 28.12/28.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ) ).
% 28.12/28.35
% 28.12/28.35 fof(fact_order__antisym,axiom,
% 28.12/28.35 ! [V_y,V_x,T_a] :
% 28.12/28.35 ( class_Orderings_Oorder(T_a)
% 28.12/28.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 28.12/28.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 28.12/28.35 => V_x = V_y ) ) ) ).
% 28.12/28.35
% 28.12/28.35 fof(fact_xt1_I4_J,axiom,
% 28.12/28.35 ! [V_c,V_a,V_b,T_a] :
% 28.12/28.35 ( class_Orderings_Oorder(T_a)
% 28.12/28.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 28.12/28.35 => ( V_b = V_c
% 28.12/28.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 28.12/28.35
% 28.12/28.35 fof(fact_ord__le__eq__trans,axiom,
% 28.12/28.35 ! [V_c,V_b,V_a,T_a] :
% 28.12/28.35 ( class_Orderings_Oord(T_a)
% 28.12/28.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 28.12/28.35 => ( V_b = V_c
% 28.12/28.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 28.12/28.35
% 28.12/28.35 fof(fact_xt1_I3_J,axiom,
% 28.12/28.35 ! [V_c,V_b,V_a,T_a] :
% 28.12/28.35 ( class_Orderings_Oorder(T_a)
% 28.12/28.35 => ( V_a = V_b
% 28.12/28.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b))
% 28.12/28.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 28.12/28.35
% 28.12/28.35 fof(fact_ord__eq__le__trans,axiom,
% 28.12/28.35 ! [V_c,V_b,V_a,T_a] :
% 28.12/28.35 ( class_Orderings_Oord(T_a)
% 28.12/28.35 => ( V_a = V_b
% 28.12/28.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 28.12/28.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 28.12/28.35
% 28.12/28.35 fof(fact_order__antisym__conv,axiom,
% 28.12/28.35 ! [V_x_2,V_y_2,T_b] :
% 28.12/28.35 ( class_Orderings_Oorder(T_b)
% 28.12/28.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
% 28.12/28.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 28.12/28.35 <=> V_x_2 = V_y_2 ) ) ) ).
% 28.12/28.35
% 28.12/28.35 fof(fact_order__eq__refl,axiom,
% 28.12/28.35 ! [V_y,V_x,T_a] :
% 28.12/28.35 ( class_Orderings_Opreorder(T_a)
% 28.12/28.35 => ( V_x = V_y
% 28.12/28.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 28.12/28.35
% 28.12/28.35 fof(fact_order__eq__iff,axiom,
% 28.12/28.35 ! [V_y_2,V_x_2,T_b] :
% 28.12/28.35 ( class_Orderings_Oorder(T_b)
% 28.12/28.35 => ( V_x_2 = V_y_2
% 28.12/28.35 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 28.12/28.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ).
% 28.12/28.35
% 28.12/28.35 fof(fact_linorder__linear,axiom,
% 28.12/28.35 ! [V_y,V_x,T_a] :
% 28.12/28.35 ( class_Orderings_Olinorder(T_a)
% 28.12/28.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 28.12/28.35 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 28.12/28.35
% 28.12/28.35 fof(fact_equalityE,axiom,
% 28.12/28.35 ! [T_b,V_B_2,V_A_2] :
% 28.12/28.35 ( V_A_2 = V_B_2
% 28.12/28.35 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.35 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 28.12/28.35
% 28.12/28.35 fof(fact_Powp__mono,axiom,
% 28.12/28.35 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.35 => 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))) ) ).
% 28.12/28.35
% 28.12/28.35 fof(fact_order__fun_I1_J,axiom,
% 28.12/28.35 ! [V_g_2,V_f_2,T_b,T_c] :
% 28.12/28.35 ( ( class_Orderings_Oorder(T_c)
% 28.12/28.35 & class_Enum_Oenum(T_b) )
% 28.12/28.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 28.12/28.35 <=> 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))) ) ) ).
% 28.12/28.35
% 28.12/28.35 fof(fact_Least__le,axiom,
% 28.12/28.35 ! [V_k_2,V_P_2,T_b] :
% 28.12/28.35 ( class_Orderings_Owellorder(T_b)
% 28.12/28.35 => ( hBOOL(hAPP(V_P_2,V_k_2))
% 28.12/28.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Orderings_Oord__class_OLeast(T_b,V_P_2)),V_k_2)) ) ) ).
% 28.12/28.35
% 28.12/28.35 fof(fact_le__funI,axiom,
% 28.12/28.35 ! [T_b,V_g_2,V_f_2,T_c] :
% 28.12/28.35 ( class_Orderings_Oord(T_c)
% 28.12/28.35 => ( ! [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)))
% 28.12/28.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) ) ) ).
% 28.12/28.35
% 28.12/28.35 fof(fact_inv__imagep__def,axiom,
% 28.12/28.35 ! [V_y_2,V_x_2,V_f_2,V_r_2,T_c,T_b] :
% 28.12/28.35 ( c_Predicate_Oinv__imagep(T_b,T_c,V_r_2,V_f_2,V_x_2,V_y_2)
% 28.12/28.35 <=> hBOOL(hAPP(hAPP(V_r_2,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ).
% 28.12/28.35
% 28.12/28.35 fof(fact_strict__mono__less__eq,axiom,
% 28.12/28.35 ! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
% 28.12/28.35 ( ( class_Orderings_Oorder(T_c)
% 28.12/28.35 & class_Orderings_Olinorder(T_b) )
% 28.12/28.35 => ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
% 28.12/28.35 => ( 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)))
% 28.12/28.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ) ).
% 28.12/28.35
% 28.12/28.35 fof(fact_greaterThan__subset__iff,axiom,
% 28.12/28.35 ! [V_y_2,V_x_2,T_b] :
% 28.12/28.35 ( class_Orderings_Olinorder(T_b)
% 28.12/28.35 => ( 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)))
% 28.12/28.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 28.12/28.35
% 28.12/28.35 fof(fact_lessThan__subset__iff,axiom,
% 28.12/28.35 ! [V_y_2,V_x_2,T_b] :
% 28.12/28.35 ( class_Orderings_Olinorder(T_b)
% 28.12/28.35 => ( 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)))
% 28.12/28.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ).
% 28.12/28.35
% 28.12/28.35 fof(fact_atLeast__subset__iff,axiom,
% 28.12/28.35 ! [V_y_2,V_x_2,T_b] :
% 28.12/28.35 ( class_Orderings_Oorder(T_b)
% 28.12/28.35 => ( 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)))
% 28.12/28.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 28.12/28.35
% 28.12/28.35 fof(fact_atMost__subset__iff,axiom,
% 28.12/28.35 ! [V_y_2,V_x_2,T_b] :
% 28.12/28.35 ( class_Orderings_Oorder(T_b)
% 28.12/28.35 => ( 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)))
% 28.12/28.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ).
% 28.12/28.35
% 28.12/28.35 fof(fact_SUP__subset,axiom,
% 28.12/28.35 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 28.12/28.35 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 28.12/28.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.35 => 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))) ) ) ).
% 28.12/28.35
% 28.12/28.35 fof(fact_INF__subset,axiom,
% 28.12/28.35 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 28.12/28.35 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 28.12/28.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.35 => 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))) ) ) ).
% 28.12/28.35
% 28.12/28.35 fof(fact_SUPR__apply,axiom,
% 28.12/28.35 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
% 28.12/28.35 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.12/28.35 => 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)) ) ).
% 28.12/28.35
% 28.12/28.35 fof(fact_INFI__apply,axiom,
% 28.12/28.35 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
% 28.12/28.35 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.12/28.35 => 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)) ) ).
% 28.12/28.35
% 28.12/28.35 fof(fact_greaterThan__eq__iff,axiom,
% 28.12/28.35 ! [V_y_2,V_x_2,T_b] :
% 28.12/28.35 ( class_Orderings_Olinorder(T_b)
% 28.12/28.35 => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2)
% 28.12/28.35 <=> V_x_2 = V_y_2 ) ) ).
% 28.12/28.35
% 28.12/28.35 fof(fact_lessThan__eq__iff,axiom,
% 28.12/28.35 ! [V_y_2,V_x_2,T_b] :
% 28.12/28.35 ( class_Orderings_Olinorder(T_b)
% 28.12/28.35 => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2)
% 28.12/28.35 <=> V_x_2 = V_y_2 ) ) ).
% 28.12/28.35
% 28.12/28.35 fof(fact_atLeast__eq__iff,axiom,
% 28.12/28.35 ! [V_y_2,V_x_2,T_b] :
% 28.12/28.35 ( class_Orderings_Olinorder(T_b)
% 28.12/28.35 => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2)
% 28.12/28.35 <=> V_x_2 = V_y_2 ) ) ).
% 28.12/28.35
% 28.12/28.35 fof(fact_atMost__eq__iff,axiom,
% 28.12/28.35 ! [V_y_2,V_x_2,T_b] :
% 28.12/28.35 ( class_Orderings_Olinorder(T_b)
% 28.12/28.35 => ( hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2)
% 28.12/28.35 <=> V_x_2 = V_y_2 ) ) ).
% 28.12/28.35
% 28.12/28.35 fof(fact_SUP__commute,axiom,
% 28.12/28.35 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
% 28.12/28.35 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.12/28.35 => 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))) ) ).
% 28.12/28.35
% 28.12/28.35 fof(fact_INF__commute,axiom,
% 28.12/28.35 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
% 28.12/28.35 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.12/28.35 => 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))) ) ).
% 28.12/28.35
% 28.12/28.35 fof(fact_all__code,axiom,
% 28.12/28.35 ! [V_P_2,T_b] :
% 28.12/28.35 ( class_Enum_Oenum(T_b)
% 28.12/28.35 => ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 28.12/28.35 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_P_2)) ) ) ).
% 28.12/28.35
% 28.12/28.35 fof(fact_enum__all,axiom,
% 28.12/28.35 ! [V_P_2,T_b] :
% 28.12/28.35 ( class_Enum_Oenum(T_b)
% 28.12/28.35 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_P_2))
% 28.12/28.35 <=> ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ).
% 28.12/28.35
% 28.12/28.35 fof(fact_LeastI__ex,axiom,
% 28.12/28.35 ! [V_P_2,T_b] :
% 28.12/28.35 ( class_Orderings_Owellorder(T_b)
% 28.12/28.35 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 28.12/28.35 => hBOOL(hAPP(V_P_2,c_Orderings_Oord__class_OLeast(T_b,V_P_2))) ) ) ).
% 28.12/28.35
% 28.12/28.35 fof(fact_strict__mono__eq,axiom,
% 28.12/28.35 ! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
% 28.12/28.35 ( ( class_Orderings_Oorder(T_c)
% 28.12/28.35 & class_Orderings_Olinorder(T_b) )
% 28.12/28.35 => ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
% 28.12/28.35 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 28.12/28.35 <=> V_x_2 = V_y_2 ) ) ) ).
% 28.12/28.35
% 28.12/28.35 fof(fact_INT__subset__iff,axiom,
% 28.12/28.35 ! [V_A_2,V_I_2,T_c,V_B_2,T_b] :
% 28.12/28.35 ( 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)))
% 28.12/28.35 <=> ! [B_x] :
% 28.12/28.35 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
% 28.12/28.35 => 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))) ) ) ).
% 28.12/28.35
% 28.12/28.35 fof(fact_UN__subset__iff,axiom,
% 28.12/28.35 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] :
% 28.12/28.35 ( 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))
% 28.12/28.35 <=> ! [B_x] :
% 28.12/28.35 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
% 28.12/28.35 => 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)) ) ) ).
% 28.12/28.35
% 28.12/28.35 fof(fact_LeastI,axiom,
% 28.12/28.35 ! [V_k_2,V_P_2,T_b] :
% 28.12/28.35 ( class_Orderings_Owellorder(T_b)
% 28.12/28.35 => ( hBOOL(hAPP(V_P_2,V_k_2))
% 28.12/28.35 => hBOOL(hAPP(V_P_2,c_Orderings_Oord__class_OLeast(T_b,V_P_2))) ) ) ).
% 28.12/28.35
% 28.12/28.35 fof(fact_le__INF__iff,axiom,
% 28.12/28.35 ! [V_M_2,V_A_2,T_c,V_u_2,T_b] :
% 28.12/28.35 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.12/28.35 => ( 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)))
% 28.12/28.36 <=> ! [B_x] :
% 28.12/28.36 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 28.12/28.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(V_M_2,B_x))) ) ) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_SUP__le__iff,axiom,
% 28.12/28.36 ! [V_u_2,V_M_2,V_A_2,T_c,T_b] :
% 28.12/28.36 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.12/28.36 => ( 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))
% 28.12/28.36 <=> ! [B_x] :
% 28.12/28.36 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 28.12/28.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,B_x)),V_u_2)) ) ) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_in__inv__imagep,axiom,
% 28.12/28.36 ! [V_y_2,V_x_2,V_f_2,V_r_2,T_c,T_b] :
% 28.12/28.36 ( c_Predicate_Oinv__imagep(T_b,T_c,V_r_2,V_f_2,V_x_2,V_y_2)
% 28.12/28.36 <=> hBOOL(hAPP(hAPP(V_r_2,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_Least__equality,axiom,
% 28.12/28.36 ! [V_x_2,V_P_2,T_b] :
% 28.12/28.36 ( class_Orderings_Oorder(T_b)
% 28.12/28.36 => ( hBOOL(hAPP(V_P_2,V_x_2))
% 28.12/28.36 => ( ! [B_y] :
% 28.12/28.36 ( hBOOL(hAPP(V_P_2,B_y))
% 28.12/28.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_y)) )
% 28.12/28.36 => c_Orderings_Oord__class_OLeast(T_b,V_P_2) = V_x_2 ) ) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_Pow__mono,axiom,
% 28.12/28.36 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.36 => 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))) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_Inter__anti__mono,axiom,
% 28.12/28.36 ! [V_A_2,V_B_2,T_b] :
% 28.12/28.36 ( 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))
% 28.12/28.36 => 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))) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_INF__leI,axiom,
% 28.12/28.36 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
% 28.12/28.36 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 28.12/28.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 28.12/28.36 => 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))) ) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_le__SUPI,axiom,
% 28.12/28.36 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
% 28.12/28.36 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 28.12/28.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 28.12/28.36 => 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))) ) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_atLeastLessThan__subset__iff,axiom,
% 28.12/28.36 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 28.12/28.36 ( class_Orderings_Olinorder(T_b)
% 28.12/28.36 => ( 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)))
% 28.12/28.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
% 28.12/28.36 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2))
% 28.12/28.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) ) ) ) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_Compl__greaterThan,axiom,
% 28.12/28.36 ! [V_k_2,T_b] :
% 28.12/28.36 ( class_Orderings_Olinorder(T_b)
% 28.12/28.36 => 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) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_Compl__atMost,axiom,
% 28.12/28.36 ! [V_k_2,T_b] :
% 28.12/28.36 ( class_Orderings_Olinorder(T_b)
% 28.12/28.36 => 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) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_atLeastatMost__subset__iff,axiom,
% 28.12/28.36 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 28.12/28.36 ( class_Orderings_Oorder(T_b)
% 28.12/28.36 => ( 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)))
% 28.12/28.36 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 28.12/28.36 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2))
% 28.12/28.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) ) ) ) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_Compl__lessThan,axiom,
% 28.12/28.36 ! [V_k_2,T_b] :
% 28.12/28.36 ( class_Orderings_Olinorder(T_b)
% 28.12/28.36 => 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) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_Compl__atLeast,axiom,
% 28.12/28.36 ! [V_k_2,T_b] :
% 28.12/28.36 ( class_Orderings_Olinorder(T_b)
% 28.12/28.36 => 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) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_Union__mono,axiom,
% 28.12/28.36 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.36 ( 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))
% 28.12/28.36 => 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))) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_equalityCE,axiom,
% 28.12/28.36 ! [V_c_2,T_b,V_B_2,V_A_2] :
% 28.12/28.36 ( V_A_2 = V_B_2
% 28.12/28.36 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 28.12/28.36 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) )
% 28.12/28.36 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 28.12/28.36 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_INF2__E,axiom,
% 28.12/28.36 ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 28.12/28.36 ( 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))
% 28.12/28.36 => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
% 28.12/28.36 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_INF2__D,axiom,
% 28.12/28.36 ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 28.12/28.36 ( 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))
% 28.12/28.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.12/28.36 => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2)) ) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_SUP2__I,axiom,
% 28.12/28.36 ! [T_d,T_c,V_c_2,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
% 28.12/28.36 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.12/28.36 => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
% 28.12/28.36 => 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)) ) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_subsetD,axiom,
% 28.12/28.36 ! [V_c_2,V_B_2,V_A_2,T_b] :
% 28.12/28.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 28.12/28.36 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_ComplI,axiom,
% 28.12/28.36 ! [V_A_2,V_c_2,T_b] :
% 28.12/28.36 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 28.12/28.36 => 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))) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_UnionI,axiom,
% 28.12/28.36 ! [V_A_2,V_C_2,V_X_2,T_b] :
% 28.12/28.36 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 28.12/28.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2))
% 28.12/28.36 => 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))) ) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_InterE,axiom,
% 28.12/28.36 ! [V_X_2,V_C_2,V_A_2,T_b] :
% 28.12/28.36 ( 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)))
% 28.12/28.36 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 28.12/28.36 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_InterD,axiom,
% 28.12/28.36 ! [V_X_2,V_C_2,V_A_2,T_b] :
% 28.12/28.36 ( 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)))
% 28.12/28.36 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 28.12/28.36 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_PowI,axiom,
% 28.12/28.36 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.36 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_UN__I,axiom,
% 28.12/28.36 ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 28.12/28.36 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.12/28.36 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
% 28.12/28.36 => 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))) ) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_SUP1__I,axiom,
% 28.12/28.36 ! [T_c,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
% 28.12/28.36 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.12/28.36 => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 28.12/28.36 => 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)) ) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_INT__D,axiom,
% 28.12/28.36 ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 28.12/28.36 ( 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)))
% 28.12/28.36 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
% 28.12/28.36 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_INT__E,axiom,
% 28.12/28.36 ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 28.12/28.36 ( 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)))
% 28.12/28.36 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2)))
% 28.12/28.36 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_INF1__E,axiom,
% 28.12/28.36 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 28.12/28.36 ( 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))
% 28.12/28.36 => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 28.12/28.36 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_INF1__D,axiom,
% 28.12/28.36 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 28.12/28.36 ( 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))
% 28.12/28.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.12/28.36 => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) ) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_UN__UN__flatten,axiom,
% 28.12/28.36 ! [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)) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_UN__simps_I9_J,axiom,
% 28.12/28.36 ! [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)) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_INT__simps_I9_J,axiom,
% 28.12/28.36 ! [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)) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_ball__UN,axiom,
% 28.12/28.36 ! [V_P_2,V_B_2,V_A_2,T_c,T_b] :
% 28.12/28.36 ( ! [B_x] :
% 28.12/28.36 ( 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)))
% 28.12/28.36 => hBOOL(hAPP(V_P_2,B_x)) )
% 28.12/28.36 <=> ! [B_x] :
% 28.12/28.36 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 28.12/28.36 => ! [B_xa] :
% 28.12/28.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(V_B_2,B_x)))
% 28.12/28.36 => hBOOL(hAPP(V_P_2,B_xa)) ) ) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_UN__extend__simps_I9_J,axiom,
% 28.12/28.36 ! [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) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_INT__extend__simps_I9_J,axiom,
% 28.12/28.36 ! [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) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_Union__Pow__eq,axiom,
% 28.12/28.36 ! [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 ).
% 28.12/28.36
% 28.12/28.36 fof(fact_INF1__iff,axiom,
% 28.12/28.36 ! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 28.12/28.36 ( 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))
% 28.12/28.36 <=> ! [B_x] :
% 28.12/28.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.12/28.36 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_SUP1__iff,axiom,
% 28.12/28.36 ! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 28.12/28.36 ( 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))
% 28.12/28.36 <=> ? [B_x] :
% 28.12/28.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.12/28.36 & hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_ComplE,axiom,
% 28.12/28.36 ! [V_A_2,V_c_2,T_b] :
% 28.12/28.36 ( 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)))
% 28.12/28.36 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_ComplD,axiom,
% 28.12/28.36 ! [V_A_2,V_c_2,T_b] :
% 28.12/28.36 ( 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)))
% 28.12/28.36 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_eq__mem__trans,axiom,
% 28.12/28.36 ! [V_A_2,T_b,V_b_2,V_a_2] :
% 28.12/28.36 ( V_a_2 = V_b_2
% 28.12/28.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 28.12/28.36 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_eqelem__imp__iff,axiom,
% 28.12/28.36 ! [V_A_2,T_b,V_y_2,V_x_2] :
% 28.12/28.36 ( V_x_2 = V_y_2
% 28.12/28.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.36 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_eqset__imp__iff,axiom,
% 28.12/28.36 ! [V_x_2,T_b,V_B_2,V_A_2] :
% 28.12/28.36 ( V_A_2 = V_B_2
% 28.12/28.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.36 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_Compl__eq__Compl__iff,axiom,
% 28.12/28.36 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.36 ( 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)
% 28.12/28.36 <=> V_A_2 = V_B_2 ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_eq__mem,axiom,
% 28.12/28.36 ! [V_y_2,V_x_2,T_b] :
% 28.12/28.36 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_fequal,V_y_2)))
% 28.12/28.36 <=> V_x_2 = V_y_2 ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_Compl__iff,axiom,
% 28.12/28.36 ! [V_A_2,V_c_2,T_b] :
% 28.12/28.36 ( 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)))
% 28.12/28.36 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_mem__def,axiom,
% 28.12/28.36 ! [V_A_2,V_x_2,T_b] :
% 28.12/28.36 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.36 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_double__complement,axiom,
% 28.12/28.36 ! [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 ).
% 28.12/28.36
% 28.12/28.36 fof(fact_Pow__top,axiom,
% 28.12/28.36 ! [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))) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_Union__upper,axiom,
% 28.12/28.36 ! [V_A_2,V_B_2,T_b] :
% 28.12/28.36 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 28.12/28.36 => 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))) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_Inter__lower,axiom,
% 28.12/28.36 ! [V_A_2,V_B_2,T_b] :
% 28.12/28.36 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 28.12/28.36 => 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)) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_Compl__INT,axiom,
% 28.12/28.36 ! [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)) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_Compl__UN,axiom,
% 28.12/28.36 ! [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)) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_Union__def,axiom,
% 28.12/28.36 ! [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))) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_INT__extend__simps_I8_J,axiom,
% 28.12/28.36 ! [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) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_UN__extend__simps_I8_J,axiom,
% 28.12/28.36 ! [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) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_INT__simps_I8_J,axiom,
% 28.12/28.36 ! [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)) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_UN__simps_I8_J,axiom,
% 28.12/28.36 ! [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)) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_Pow__iff,axiom,
% 28.12/28.36 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.36 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
% 28.12/28.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_PowD,axiom,
% 28.12/28.36 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.36 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
% 28.12/28.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_pred__equals__eq,axiom,
% 28.12/28.36 ! [V_S_2,V_R_2,T_b] :
% 28.12/28.36 ( 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)
% 28.12/28.36 <=> V_R_2 = V_S_2 ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_INT__iff,axiom,
% 28.12/28.36 ! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 28.12/28.36 ( 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)))
% 28.12/28.36 <=> ! [B_x] :
% 28.12/28.36 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 28.12/28.36 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_UN__iff,axiom,
% 28.12/28.36 ! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 28.12/28.36 ( 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)))
% 28.12/28.36 <=> ? [B_x] :
% 28.12/28.36 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 28.12/28.36 & hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_Sup__upper,axiom,
% 28.12/28.36 ! [V_A_2,V_x_2,T_b] :
% 28.12/28.36 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.12/28.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.36 => 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))) ) ) ).
% 28.12/28.36
% 28.12/28.36 fof(fact_Inf__lower,axiom,
% 28.12/28.36 ! [V_A_2,V_x_2,T_b] :
% 28.12/28.36 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.12/28.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.36 => 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)) ) ) ).
% 28.12/28.36
% 28.12/28.37 fof(fact_Inter__def,axiom,
% 28.12/28.37 ! [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))) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_Powp__Pow__eq,axiom,
% 28.12/28.37 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.37 ( 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))
% 28.12/28.37 <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_b),V_A_2))) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_Pow__INT__eq,axiom,
% 28.12/28.37 ! [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)) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_subset__Pow__Union,axiom,
% 28.12/28.37 ! [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)))) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_Compl__anti__mono,axiom,
% 28.12/28.37 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.37 => 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))) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_Compl__subset__Compl__iff,axiom,
% 28.12/28.37 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.37 ( 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)))
% 28.12/28.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_set__mp,axiom,
% 28.12/28.37 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 28.12/28.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.37 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_set__rev__mp,axiom,
% 28.12/28.37 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 28.12/28.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.37 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_in__mono,axiom,
% 28.12/28.37 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 28.12/28.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.37 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_pred__subset__eq,axiom,
% 28.12/28.37 ! [V_S_2,V_R_2,T_b] :
% 28.12/28.37 ( 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)))
% 28.12/28.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2)) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_UN__upper,axiom,
% 28.12/28.37 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
% 28.12/28.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.12/28.37 => 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))) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_INT__lower,axiom,
% 28.12/28.37 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
% 28.12/28.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.12/28.37 => 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))) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_Sup__le__iff,axiom,
% 28.12/28.37 ! [V_b_2,V_A_2,T_b] :
% 28.12/28.37 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.12/28.37 => ( 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))
% 28.12/28.37 <=> ! [B_x] :
% 28.12/28.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.12/28.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) ) ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_le__Inf__iff,axiom,
% 28.12/28.37 ! [V_A_2,V_b_2,T_b] :
% 28.12/28.37 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.12/28.37 => ( 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)))
% 28.12/28.37 <=> ! [B_x] :
% 28.12/28.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.12/28.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) ) ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_UN__Pow__subset,axiom,
% 28.12/28.37 ! [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)))) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_atMost__iff,axiom,
% 28.12/28.37 ! [V_k_2,V_i_2,T_b] :
% 28.12/28.37 ( class_Orderings_Oord(T_b)
% 28.12/28.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)))
% 28.12/28.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_k_2)) ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_atLeast__iff,axiom,
% 28.12/28.37 ! [V_k_2,V_i_2,T_b] :
% 28.12/28.37 ( class_Orderings_Oord(T_b)
% 28.12/28.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)))
% 28.12/28.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_k_2),V_i_2)) ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_fun__Compl__def,axiom,
% 28.12/28.37 ! [V_x_2,V_A_2,T_c,T_b] :
% 28.12/28.37 ( class_Groups_Ouminus(T_b)
% 28.12/28.37 => 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)) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_uminus__apply,axiom,
% 28.12/28.37 ! [V_x_2,V_A_2,T_c,T_b] :
% 28.12/28.37 ( class_Groups_Ouminus(T_b)
% 28.12/28.37 => 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)) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_ord_OgreaterThanAtMost__iff,axiom,
% 28.12/28.37 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
% 28.12/28.37 ( 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)))
% 28.12/28.37 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 28.12/28.37 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_ord_OatLeastLessThan__iff,axiom,
% 28.12/28.37 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
% 28.12/28.37 ( 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)))
% 28.12/28.37 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 28.12/28.37 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_ord_OgreaterThanLessThan__iff,axiom,
% 28.12/28.37 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_b] :
% 28.12/28.37 ( 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)))
% 28.12/28.37 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 28.12/28.37 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_ord_OatLeastAtMost__iff,axiom,
% 28.12/28.37 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_b] :
% 28.12/28.37 ( 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)))
% 28.12/28.37 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 28.12/28.37 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_ord_OgreaterThan__iff,axiom,
% 28.12/28.37 ! [V_k_2,V_less_2,V_i_2,T_b] :
% 28.12/28.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThan(T_b,V_less_2,V_k_2)))
% 28.12/28.37 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_ord_OlessThan__iff,axiom,
% 28.12/28.37 ! [V_k_2,V_less_2,V_i_2,T_b] :
% 28.12/28.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OlessThan(T_b,V_less_2,V_k_2)))
% 28.12/28.37 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_ord_OatLeast__iff,axiom,
% 28.12/28.37 ! [V_k_2,V_less__eq_2,V_i_2,T_b] :
% 28.12/28.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeast(T_b,V_less__eq_2,V_k_2)))
% 28.12/28.37 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_ord_OatMost__iff,axiom,
% 28.12/28.37 ! [V_k_2,V_less__eq_2,V_i_2,T_b] :
% 28.12/28.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatMost(T_b,V_less__eq_2,V_k_2)))
% 28.12/28.37 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_compl__mono,axiom,
% 28.12/28.37 ! [V_y,V_x,T_a] :
% 28.12/28.37 ( class_Lattices_Oboolean__algebra(T_a)
% 28.12/28.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 28.12/28.37 => 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))) ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_le__imp__neg__le,axiom,
% 28.12/28.37 ! [V_b,V_a,T_a] :
% 28.12/28.37 ( class_Groups_Oordered__ab__group__add(T_a)
% 28.12/28.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 28.12/28.37 => 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))) ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_SUP2__iff,axiom,
% 28.12/28.37 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 28.12/28.37 ( 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))
% 28.12/28.37 <=> ? [B_x] :
% 28.12/28.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.12/28.37 & hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_INF2__iff,axiom,
% 28.12/28.37 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 28.12/28.37 ( 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))
% 28.12/28.37 <=> ! [B_x] :
% 28.12/28.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.12/28.37 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_compl__eq__compl__iff,axiom,
% 28.12/28.37 ! [V_y_2,V_x_2,T_b] :
% 28.12/28.37 ( class_Lattices_Oboolean__algebra(T_b)
% 28.12/28.37 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)
% 28.12/28.37 <=> V_x_2 = V_y_2 ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_neg__equal__iff__equal,axiom,
% 28.12/28.37 ! [V_b_2,V_a_2,T_b] :
% 28.12/28.37 ( class_Groups_Ogroup__add(T_b)
% 28.12/28.37 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 28.12/28.37 <=> V_a_2 = V_b_2 ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_minus__equation__iff,axiom,
% 28.12/28.37 ! [V_b_2,V_a_2,T_b] :
% 28.12/28.37 ( class_Groups_Ogroup__add(T_b)
% 28.12/28.37 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_b_2
% 28.12/28.37 <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) = V_a_2 ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_equation__minus__iff,axiom,
% 28.12/28.37 ! [V_b_2,V_a_2,T_b] :
% 28.12/28.37 ( class_Groups_Ogroup__add(T_b)
% 28.12/28.37 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 28.12/28.37 <=> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_double__compl,axiom,
% 28.12/28.37 ! [V_x,T_a] :
% 28.12/28.37 ( class_Lattices_Oboolean__algebra(T_a)
% 28.12/28.37 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_minus__minus,axiom,
% 28.12/28.37 ! [V_a,T_a] :
% 28.12/28.37 ( class_Groups_Ogroup__add(T_a)
% 28.12/28.37 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_le__minus__iff,axiom,
% 28.12/28.37 ! [V_b_2,V_a_2,T_b] :
% 28.12/28.37 ( class_Groups_Oordered__ab__group__add(T_b)
% 28.12/28.37 => ( 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)))
% 28.12/28.37 <=> 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))) ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_minus__le__iff,axiom,
% 28.12/28.37 ! [V_b_2,V_a_2,T_b] :
% 28.12/28.37 ( class_Groups_Oordered__ab__group__add(T_b)
% 28.12/28.37 => ( 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))
% 28.12/28.37 <=> 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)) ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_neg__le__iff__le,axiom,
% 28.12/28.37 ! [V_a_2,V_b_2,T_b] :
% 28.12/28.37 ( class_Groups_Oordered__ab__group__add(T_b)
% 28.12/28.37 => ( 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)))
% 28.12/28.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_compl__le__compl__iff,axiom,
% 28.12/28.37 ! [V_y_2,V_x_2,T_b] :
% 28.12/28.37 ( class_Lattices_Oboolean__algebra(T_b)
% 28.12/28.37 => ( 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)))
% 28.12/28.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_InterI,axiom,
% 28.12/28.37 ! [V_A_2,V_C_2,T_b] :
% 28.12/28.37 ( ! [B_X] :
% 28.12/28.37 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2))
% 28.12/28.37 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X)) )
% 28.12/28.37 => 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))) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_UnionE,axiom,
% 28.12/28.37 ! [V_C_2,V_A_2,T_b] :
% 28.12/28.37 ( 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)))
% 28.12/28.37 => ~ ! [B_X] :
% 28.12/28.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X))
% 28.12/28.37 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_SUP2__E,axiom,
% 28.12/28.37 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 28.12/28.37 ( 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))
% 28.12/28.37 => ~ ! [B_x] :
% 28.12/28.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.12/28.37 => ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_INF2__I,axiom,
% 28.12/28.37 ! [T_d,T_c,V_c_2,V_b_2,V_B_2,V_A_2,T_b] :
% 28.12/28.37 ( ! [B_x] :
% 28.12/28.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.12/28.37 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) )
% 28.12/28.37 => 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)) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_ivl__disj__un_I13_J,axiom,
% 28.12/28.37 ! [V_u_2,V_l_2,T_b] :
% 28.12/28.37 ( class_Orderings_Olinorder(T_b)
% 28.12/28.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 28.12/28.37 => 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) ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_ivl__disj__un_I10_J,axiom,
% 28.12/28.37 ! [V_u_2,V_l_2,T_b] :
% 28.12/28.37 ( class_Orderings_Olinorder(T_b)
% 28.12/28.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 28.12/28.37 => 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) ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_INT__greatest,axiom,
% 28.12/28.37 ! [V_B_2,V_C_2,T_c,V_A_2,T_b] :
% 28.12/28.37 ( ! [B_x] :
% 28.12/28.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.12/28.37 => 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))) )
% 28.12/28.37 => 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))) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_INT__anti__mono,axiom,
% 28.12/28.37 ! [V_g_2,V_f_2,T_c,V_A_2,V_B_2,T_b] :
% 28.12/28.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 28.12/28.37 => ( ! [B_x] :
% 28.12/28.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.12/28.37 => 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))) )
% 28.12/28.37 => 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))) ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_UN__least,axiom,
% 28.12/28.37 ! [V_C_2,V_B_2,T_c,V_A_2,T_b] :
% 28.12/28.37 ( ! [B_x] :
% 28.12/28.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.12/28.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_B_2,B_x)),V_C_2)) )
% 28.12/28.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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_A_2),V_B_2)),V_C_2)) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_UN__mono,axiom,
% 28.12/28.37 ! [V_g_2,V_f_2,T_c,V_B_2,V_A_2,T_b] :
% 28.12/28.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.37 => ( ! [B_x] :
% 28.12/28.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.12/28.37 => 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))) )
% 28.12/28.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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_A_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_g_2))) ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_le__INFI,axiom,
% 28.12/28.37 ! [V_M_2,V_u_2,V_A_2,T_b,T_c] :
% 28.12/28.37 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 28.12/28.37 => ( ! [B_i] :
% 28.12/28.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_A_2))
% 28.12/28.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_u_2),hAPP(V_M_2,B_i))) )
% 28.12/28.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_u_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_M_2))) ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_sup1CI,axiom,
% 28.12/28.37 ! [T_b,V_A_2,V_x_2,V_B_2] :
% 28.12/28.37 ( ( ~ hBOOL(hAPP(V_B_2,V_x_2))
% 28.12/28.37 => hBOOL(hAPP(V_A_2,V_x_2)) )
% 28.12/28.37 => 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)) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_sup1E,axiom,
% 28.12/28.37 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 28.12/28.37 ( 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))
% 28.12/28.37 => ( ~ hBOOL(hAPP(V_A_2,V_x_2))
% 28.12/28.37 => hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_UnCI,axiom,
% 28.12/28.37 ! [V_A_2,V_B_2,V_c_2,T_b] :
% 28.12/28.37 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 28.12/28.37 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
% 28.12/28.37 => 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))) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_UnE,axiom,
% 28.12/28.37 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 28.12/28.37 ( 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)))
% 28.12/28.37 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 28.12/28.37 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_sup__apply,axiom,
% 28.12/28.37 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 28.12/28.37 ( class_Lattices_Olattice(T_b)
% 28.12/28.37 => 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)) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_sup__assoc,axiom,
% 28.12/28.37 ! [V_z,V_y,V_x,T_a] :
% 28.12/28.37 ( class_Lattices_Osemilattice__sup(T_a)
% 28.12/28.37 => 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)) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_inf__sup__aci_I6_J,axiom,
% 28.12/28.37 ! [V_z,V_y,V_x,T_a] :
% 28.12/28.37 ( class_Lattices_Olattice(T_a)
% 28.12/28.37 => 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)) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_sup_Oassoc,axiom,
% 28.12/28.37 ! [V_c,V_b,V_a,T_a] :
% 28.12/28.37 ( class_Lattices_Osemilattice__sup(T_a)
% 28.12/28.37 => 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)) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_sup__left__commute,axiom,
% 28.12/28.37 ! [V_z,V_y,V_x,T_a] :
% 28.12/28.37 ( class_Lattices_Osemilattice__sup(T_a)
% 28.12/28.37 => 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)) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_inf__sup__aci_I7_J,axiom,
% 28.12/28.37 ! [V_z,V_y,V_x,T_a] :
% 28.12/28.37 ( class_Lattices_Olattice(T_a)
% 28.12/28.37 => 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)) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_sup_Oleft__commute,axiom,
% 28.12/28.37 ! [V_c,V_a,V_b,T_a] :
% 28.12/28.37 ( class_Lattices_Osemilattice__sup(T_a)
% 28.12/28.37 => 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)) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_sup__left__idem,axiom,
% 28.12/28.37 ! [V_y,V_x,T_a] :
% 28.12/28.37 ( class_Lattices_Osemilattice__sup(T_a)
% 28.12/28.37 => 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) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_inf__sup__aci_I8_J,axiom,
% 28.12/28.37 ! [V_y,V_x,T_a] :
% 28.12/28.37 ( class_Lattices_Olattice(T_a)
% 28.12/28.37 => 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) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_sup_Oleft__idem,axiom,
% 28.12/28.37 ! [V_b,V_a,T_a] :
% 28.12/28.37 ( class_Lattices_Osemilattice__sup(T_a)
% 28.12/28.37 => 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) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_sup__commute,axiom,
% 28.12/28.37 ! [V_y,V_x,T_a] :
% 28.12/28.37 ( class_Lattices_Osemilattice__sup(T_a)
% 28.12/28.37 => 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) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_inf__sup__aci_I5_J,axiom,
% 28.12/28.37 ! [V_y,V_x,T_a] :
% 28.12/28.37 ( class_Lattices_Olattice(T_a)
% 28.12/28.37 => 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) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_sup_Ocommute,axiom,
% 28.12/28.37 ! [V_b,V_a,T_a] :
% 28.12/28.37 ( class_Lattices_Osemilattice__sup(T_a)
% 28.12/28.37 => 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) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_sup__fun__def,axiom,
% 28.12/28.37 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 28.12/28.37 ( class_Lattices_Olattice(T_b)
% 28.12/28.37 => 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)) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_sup__idem,axiom,
% 28.12/28.37 ! [V_x,T_a] :
% 28.12/28.37 ( class_Lattices_Osemilattice__sup(T_a)
% 28.12/28.37 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_sup_Oidem,axiom,
% 28.12/28.37 ! [V_a,T_a] :
% 28.12/28.37 ( class_Lattices_Osemilattice__sup(T_a)
% 28.12/28.37 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_sup1I2,axiom,
% 28.12/28.37 ! [V_A_2,T_b,V_x_2,V_B_2] :
% 28.12/28.37 ( hBOOL(hAPP(V_B_2,V_x_2))
% 28.12/28.37 => 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)) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_sup1I1,axiom,
% 28.12/28.37 ! [V_B_2,T_b,V_x_2,V_A_2] :
% 28.12/28.37 ( hBOOL(hAPP(V_A_2,V_x_2))
% 28.12/28.37 => 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)) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_ball__Un,axiom,
% 28.12/28.37 ! [V_P_2,V_B_2,V_A_2,T_b] :
% 28.12/28.37 ( ! [B_x] :
% 28.12/28.37 ( 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)))
% 28.12/28.37 => hBOOL(hAPP(V_P_2,B_x)) )
% 28.12/28.37 <=> ( ! [B_x] :
% 28.12/28.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.12/28.37 => hBOOL(hAPP(V_P_2,B_x)) )
% 28.12/28.37 & ! [B_x] :
% 28.12/28.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 28.12/28.37 => hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_bex__Un,axiom,
% 28.12/28.37 ! [V_P_2,V_B_2,V_A_2,T_b] :
% 28.12/28.37 ( ? [B_x] :
% 28.12/28.37 ( 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)))
% 28.12/28.37 & hBOOL(hAPP(V_P_2,B_x)) )
% 28.12/28.37 <=> ( ? [B_x] :
% 28.12/28.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.12/28.37 & hBOOL(hAPP(V_P_2,B_x)) )
% 28.12/28.37 | ? [B_x] :
% 28.12/28.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 28.12/28.37 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_Un__assoc,axiom,
% 28.12/28.37 ! [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)) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_Un__left__commute,axiom,
% 28.12/28.37 ! [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)) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_Un__left__absorb,axiom,
% 28.12/28.37 ! [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) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_Un__commute,axiom,
% 28.12/28.37 ! [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) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_Un__absorb,axiom,
% 28.12/28.37 ! [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 ).
% 28.12/28.37
% 28.12/28.37 fof(fact_Union__Un__distrib,axiom,
% 28.12/28.37 ! [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)) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_le__supE,axiom,
% 28.12/28.37 ! [V_x,V_b,V_a,T_a] :
% 28.12/28.37 ( class_Lattices_Osemilattice__sup(T_a)
% 28.12/28.37 => ( 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))
% 28.12/28.37 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 28.12/28.37 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_sup__mono,axiom,
% 28.12/28.37 ! [V_d,V_b,V_c,V_a,T_a] :
% 28.12/28.37 ( class_Lattices_Osemilattice__sup(T_a)
% 28.12/28.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 28.12/28.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 28.12/28.37 => 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))) ) ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_sup__least,axiom,
% 28.12/28.37 ! [V_z,V_x,V_y,T_a] :
% 28.12/28.37 ( class_Lattices_Osemilattice__sup(T_a)
% 28.12/28.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 28.12/28.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 28.12/28.37 => 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)) ) ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_le__supI,axiom,
% 28.12/28.37 ! [V_b,V_x,V_a,T_a] :
% 28.12/28.37 ( class_Lattices_Osemilattice__sup(T_a)
% 28.12/28.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 28.12/28.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 28.12/28.37 => 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)) ) ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_sup__absorb1,axiom,
% 28.12/28.37 ! [V_x,V_y,T_a] :
% 28.12/28.37 ( class_Lattices_Osemilattice__sup(T_a)
% 28.12/28.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 28.12/28.37 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_sup__absorb2,axiom,
% 28.12/28.37 ! [V_y,V_x,T_a] :
% 28.12/28.37 ( class_Lattices_Osemilattice__sup(T_a)
% 28.12/28.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 28.12/28.37 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_le__supI2,axiom,
% 28.12/28.37 ! [V_a,V_b,V_x,T_a] :
% 28.12/28.37 ( class_Lattices_Osemilattice__sup(T_a)
% 28.12/28.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 28.12/28.37 => 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))) ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_le__supI1,axiom,
% 28.12/28.37 ! [V_b,V_a,V_x,T_a] :
% 28.12/28.37 ( class_Lattices_Osemilattice__sup(T_a)
% 28.12/28.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 28.12/28.37 => 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))) ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_le__sup__iff,axiom,
% 28.12/28.37 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 28.12/28.37 ( class_Lattices_Osemilattice__sup(T_b)
% 28.12/28.37 => ( 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))
% 28.12/28.37 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 28.12/28.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_le__iff__sup,axiom,
% 28.12/28.37 ! [V_y_2,V_x_2,T_b] :
% 28.12/28.37 ( class_Lattices_Osemilattice__sup(T_b)
% 28.12/28.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 28.12/28.37 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = V_y_2 ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_sup__ge2,axiom,
% 28.12/28.37 ! [V_x,V_y,T_a] :
% 28.12/28.37 ( class_Lattices_Osemilattice__sup(T_a)
% 28.12/28.37 => 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))) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_inf__sup__ord_I4_J,axiom,
% 28.12/28.37 ! [V_x,V_y,T_a] :
% 28.12/28.37 ( class_Lattices_Olattice(T_a)
% 28.12/28.37 => 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))) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_sup__ge1,axiom,
% 28.12/28.37 ! [V_y,V_x,T_a] :
% 28.12/28.37 ( class_Lattices_Osemilattice__sup(T_a)
% 28.12/28.37 => 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))) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_inf__sup__ord_I3_J,axiom,
% 28.12/28.37 ! [V_y,V_x,T_a] :
% 28.12/28.37 ( class_Lattices_Olattice(T_a)
% 28.12/28.37 => 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))) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_UnI2,axiom,
% 28.12/28.37 ! [V_A_2,V_B_2,V_c_2,T_b] :
% 28.12/28.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 28.12/28.37 => 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))) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_UnI1,axiom,
% 28.12/28.37 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 28.12/28.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 28.12/28.37 => 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))) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_Un__iff,axiom,
% 28.12/28.37 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 28.12/28.37 ( 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)))
% 28.12/28.37 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 28.12/28.37 | hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_Un__mono,axiom,
% 28.12/28.37 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
% 28.12/28.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 28.12/28.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
% 28.12/28.37 => 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))) ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_Un__least,axiom,
% 28.12/28.37 ! [V_B_2,V_C_2,V_A_2,T_b] :
% 28.12/28.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 28.12/28.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 28.12/28.37 => 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)) ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_Un__absorb2,axiom,
% 28.12/28.37 ! [V_A_2,V_B_2,T_b] :
% 28.12/28.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 28.12/28.37 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_Un__absorb1,axiom,
% 28.12/28.37 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.37 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_subset__Un__eq,axiom,
% 28.12/28.37 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.37 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_Un__upper2,axiom,
% 28.12/28.37 ! [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))) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_Un__upper1,axiom,
% 28.12/28.37 ! [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))) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_Un__Pow__subset,axiom,
% 28.12/28.37 ! [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)))) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_sup__Un__eq,axiom,
% 28.12/28.37 ! [V_x_2,V_S_2,V_R_2,T_b] :
% 28.12/28.37 ( 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))
% 28.12/28.37 <=> 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))) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_UN__Un__distrib,axiom,
% 28.12/28.37 ! [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)) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_UN__Un,axiom,
% 28.12/28.37 ! [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)) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_INT__simps_I7_J,axiom,
% 28.12/28.37 ! [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)) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_INT__simps_I6_J,axiom,
% 28.12/28.37 ! [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) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_INT__extend__simps_I7_J,axiom,
% 28.12/28.37 ! [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)) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_Un__INT__distrib,axiom,
% 28.12/28.37 ! [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)) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_INT__extend__simps_I6_J,axiom,
% 28.12/28.37 ! [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)) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_Un__INT__distrib2,axiom,
% 28.12/28.37 ! [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))) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_ivl__disj__un_I17_J,axiom,
% 28.12/28.37 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 28.12/28.37 ( class_Orderings_Olinorder(T_b)
% 28.12/28.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 28.12/28.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 28.12/28.37 => 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) ) ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_UN__absorb,axiom,
% 28.12/28.37 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
% 28.12/28.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2))
% 28.12/28.37 => 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) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_ivl__disj__un_I21_J,axiom,
% 28.12/28.37 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 28.12/28.37 ( class_Orderings_Olinorder(T_b)
% 28.12/28.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 28.12/28.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 28.12/28.37 => 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) ) ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_ivl__disj__un_I8_J,axiom,
% 28.12/28.37 ! [V_u_2,V_l_2,T_b] :
% 28.12/28.37 ( class_Orderings_Olinorder(T_b)
% 28.12/28.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 28.12/28.37 => 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) ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_ivl__disj__un_I14_J,axiom,
% 28.12/28.37 ! [V_u_2,V_l_2,T_b] :
% 28.12/28.37 ( class_Orderings_Olinorder(T_b)
% 28.12/28.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 28.12/28.37 => 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) ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_Un__Inter,axiom,
% 28.12/28.37 ! [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)) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_ivl__disj__un_I11_J,axiom,
% 28.12/28.37 ! [V_u_2,V_l_2,T_b] :
% 28.12/28.37 ( class_Orderings_Olinorder(T_b)
% 28.12/28.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 28.12/28.37 => 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) ) ) ).
% 28.12/28.37
% 28.12/28.37 fof(fact_ivl__disj__un_I9_J,axiom,
% 28.12/28.37 ! [V_u_2,V_l_2,T_b] :
% 28.12/28.37 ( class_Orderings_Olinorder(T_b)
% 28.12/28.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 28.12/28.37 => 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) ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_SUP__leI,axiom,
% 28.12/28.38 ! [V_u_2,V_M_2,V_A_2,T_b,T_c] :
% 28.12/28.38 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 28.12/28.38 => ( ! [B_i] :
% 28.12/28.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_A_2))
% 28.12/28.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_M_2,B_i)),V_u_2)) )
% 28.12/28.38 => 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_M_2)),V_u_2)) ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_ivl__disj__un_I22_J,axiom,
% 28.12/28.38 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 28.12/28.38 ( class_Orderings_Olinorder(T_b)
% 28.12/28.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 28.12/28.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 28.12/28.38 => 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) ) ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Inter__greatest,axiom,
% 28.12/28.38 ! [V_C_2,V_A_2,T_b] :
% 28.12/28.38 ( ! [B_X] :
% 28.12/28.38 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2))
% 28.12/28.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),B_X)) )
% 28.12/28.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Union__least,axiom,
% 28.12/28.38 ! [V_C_2,V_A_2,T_b] :
% 28.12/28.38 ( ! [B_X] :
% 28.12/28.38 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2))
% 28.12/28.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) )
% 28.12/28.38 => 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)),V_C_2)) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_INF1__I,axiom,
% 28.12/28.38 ! [T_c,V_b_2,V_B_2,V_A_2,T_b] :
% 28.12/28.38 ( ! [B_x] :
% 28.12/28.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.12/28.38 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) )
% 28.12/28.38 => 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)) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_INT__I,axiom,
% 28.12/28.38 ! [V_B_2,V_b_2,T_c,V_A_2,T_b] :
% 28.12/28.38 ( ! [B_x] :
% 28.12/28.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.12/28.38 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,B_x))) )
% 28.12/28.38 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_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))) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_SUP1__E,axiom,
% 28.12/28.38 ! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 28.12/28.38 ( 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))
% 28.12/28.38 => ~ ! [B_x] :
% 28.12/28.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.12/28.38 => ~ hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_UN__E,axiom,
% 28.12/28.38 ! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 28.12/28.38 ( 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)))
% 28.12/28.38 => ~ ! [B_x] :
% 28.12/28.38 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 28.12/28.38 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Inf__greatest,axiom,
% 28.12/28.38 ! [V_z_2,V_A_2,T_b] :
% 28.12/28.38 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.12/28.38 => ( ! [B_x] :
% 28.12/28.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.12/28.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),B_x)) )
% 28.12/28.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2))) ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_ivl__disj__un_I20_J,axiom,
% 28.12/28.38 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 28.12/28.38 ( class_Orderings_Olinorder(T_b)
% 28.12/28.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 28.12/28.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 28.12/28.38 => 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) ) ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Sup__least,axiom,
% 28.12/28.38 ! [V_z_2,V_A_2,T_b] :
% 28.12/28.38 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.12/28.38 => ( ! [B_x] :
% 28.12/28.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.12/28.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_z_2)) )
% 28.12/28.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)),V_z_2)) ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Sup__fin_Oidem,axiom,
% 28.12/28.38 ! [V_x,T_a] :
% 28.12/28.38 ( class_Lattices_Olattice(T_a)
% 28.12/28.38 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Un__Union__image,axiom,
% 28.12/28.38 ! [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))) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_subsetI,axiom,
% 28.12/28.38 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.38 ( ! [B_x] :
% 28.12/28.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.12/28.38 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) )
% 28.12/28.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Inter__Un__subset,axiom,
% 28.12/28.38 ! [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)))) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_image__uminus__atLeast,axiom,
% 28.12/28.38 ! [V_x_2,T_b] :
% 28.12/28.38 ( class_Groups_Oordered__ab__group__add(T_b)
% 28.12/28.38 => 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)) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_image__uminus__atMost,axiom,
% 28.12/28.38 ! [V_x_2,T_b] :
% 28.12/28.38 ( class_Groups_Oordered__ab__group__add(T_b)
% 28.12/28.38 => 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)) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_image__uminus__greaterThan,axiom,
% 28.12/28.38 ! [V_x_2,T_b] :
% 28.12/28.38 ( class_Groups_Oordered__ab__group__add(T_b)
% 28.12/28.38 => 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)) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_image__uminus__lessThan,axiom,
% 28.12/28.38 ! [V_x_2,T_b] :
% 28.12/28.38 ( class_Groups_Oordered__ab__group__add(T_b)
% 28.12/28.38 => 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)) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_INT__cong,axiom,
% 28.12/28.38 ! [T_c,V_D_2,V_C_2,T_b,V_B_2,V_A_2] :
% 28.12/28.38 ( V_A_2 = V_B_2
% 28.12/28.38 => ( ! [B_x] :
% 28.12/28.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 28.12/28.38 => hAPP(V_C_2,B_x) = hAPP(V_D_2,B_x) )
% 28.12/28.38 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_D_2) ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_sup__compl__top,axiom,
% 28.12/28.38 ! [V_x,T_a] :
% 28.12/28.38 ( class_Lattices_Oboolean__algebra(T_a)
% 28.12/28.38 => 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) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_UNIV__I,axiom,
% 28.12/28.38 ! [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)))) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_inf1E,axiom,
% 28.12/28.38 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 28.12/28.38 ( 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))
% 28.12/28.38 => ~ ( hBOOL(hAPP(V_A_2,V_x_2))
% 28.12/28.38 => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_inf1I,axiom,
% 28.12/28.38 ! [T_b,V_B_2,V_x_2,V_A_2] :
% 28.12/28.38 ( hBOOL(hAPP(V_A_2,V_x_2))
% 28.12/28.38 => ( hBOOL(hAPP(V_B_2,V_x_2))
% 28.12/28.38 => 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)) ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_image__eqI,axiom,
% 28.12/28.38 ! [T_b,V_A_2,T_c,V_x_2,V_f_2,V_b_2] :
% 28.12/28.38 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 28.12/28.38 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 28.12/28.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_IntE,axiom,
% 28.12/28.38 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 28.12/28.38 ( 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)))
% 28.12/28.38 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 28.12/28.38 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_IntI,axiom,
% 28.12/28.38 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 28.12/28.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 28.12/28.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 28.12/28.38 => 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))) ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_rangeI,axiom,
% 28.12/28.38 ! [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))))) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_range__eqI,axiom,
% 28.12/28.38 ! [T_c,T_b,V_x_2,V_f_2,V_b_2] :
% 28.12/28.38 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 28.12/28.38 => 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))))) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_inf__apply,axiom,
% 28.12/28.38 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 28.12/28.38 ( class_Lattices_Olattice(T_b)
% 28.12/28.38 => 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)) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_inf__assoc,axiom,
% 28.12/28.38 ! [V_z,V_y,V_x,T_a] :
% 28.12/28.38 ( class_Lattices_Osemilattice__inf(T_a)
% 28.12/28.38 => 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)) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_inf__sup__aci_I2_J,axiom,
% 28.12/28.38 ! [V_z,V_y,V_x,T_a] :
% 28.12/28.38 ( class_Lattices_Olattice(T_a)
% 28.12/28.38 => 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)) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_inf_Oassoc,axiom,
% 28.12/28.38 ! [V_c,V_b,V_a,T_a] :
% 28.12/28.38 ( class_Lattices_Osemilattice__inf(T_a)
% 28.12/28.38 => 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)) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_inf__eq__top__iff,axiom,
% 28.12/28.38 ! [V_y_2,V_x_2,T_b] :
% 28.12/28.38 ( class_Lattices_Obounded__lattice__top(T_b)
% 28.12/28.38 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_b)
% 28.12/28.38 <=> ( V_x_2 = c_Orderings_Otop__class_Otop(T_b)
% 28.12/28.38 & V_y_2 = c_Orderings_Otop__class_Otop(T_b) ) ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_inf__left__commute,axiom,
% 28.12/28.38 ! [V_z,V_y,V_x,T_a] :
% 28.12/28.38 ( class_Lattices_Osemilattice__inf(T_a)
% 28.12/28.38 => 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)) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_inf__sup__aci_I3_J,axiom,
% 28.12/28.38 ! [V_z,V_y,V_x,T_a] :
% 28.12/28.38 ( class_Lattices_Olattice(T_a)
% 28.12/28.38 => 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)) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_inf_Oleft__commute,axiom,
% 28.12/28.38 ! [V_c,V_a,V_b,T_a] :
% 28.12/28.38 ( class_Lattices_Osemilattice__inf(T_a)
% 28.12/28.38 => 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)) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_inf__left__idem,axiom,
% 28.12/28.38 ! [V_y,V_x,T_a] :
% 28.12/28.38 ( class_Lattices_Osemilattice__inf(T_a)
% 28.12/28.38 => 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) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_inf__sup__aci_I4_J,axiom,
% 28.12/28.38 ! [V_y,V_x,T_a] :
% 28.12/28.38 ( class_Lattices_Olattice(T_a)
% 28.12/28.38 => 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) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_inf_Oleft__idem,axiom,
% 28.12/28.38 ! [V_b,V_a,T_a] :
% 28.12/28.38 ( class_Lattices_Osemilattice__inf(T_a)
% 28.12/28.38 => 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) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_inf__commute,axiom,
% 28.12/28.38 ! [V_y,V_x,T_a] :
% 28.12/28.38 ( class_Lattices_Osemilattice__inf(T_a)
% 28.12/28.38 => 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) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_inf__sup__aci_I1_J,axiom,
% 28.12/28.38 ! [V_y,V_x,T_a] :
% 28.12/28.38 ( class_Lattices_Olattice(T_a)
% 28.12/28.38 => 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) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_inf_Ocommute,axiom,
% 28.12/28.38 ! [V_b,V_a,T_a] :
% 28.12/28.38 ( class_Lattices_Osemilattice__inf(T_a)
% 28.12/28.38 => 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) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_inf__fun__def,axiom,
% 28.12/28.38 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 28.12/28.38 ( class_Lattices_Olattice(T_b)
% 28.12/28.38 => 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)) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_inf__idem,axiom,
% 28.12/28.38 ! [V_x,T_a] :
% 28.12/28.38 ( class_Lattices_Osemilattice__inf(T_a)
% 28.12/28.38 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_inf_Oidem,axiom,
% 28.12/28.38 ! [V_a,T_a] :
% 28.12/28.38 ( class_Lattices_Osemilattice__inf(T_a)
% 28.12/28.38 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_inf__top__right,axiom,
% 28.12/28.38 ! [V_x,T_a] :
% 28.12/28.38 ( class_Lattices_Obounded__lattice__top(T_a)
% 28.12/28.38 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_inf__top__left,axiom,
% 28.12/28.38 ! [V_x,T_a] :
% 28.12/28.38 ( class_Lattices_Obounded__lattice__top(T_a)
% 28.12/28.38 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Inf__fin_Oidem,axiom,
% 28.12/28.38 ! [V_x,T_a] :
% 28.12/28.38 ( class_Lattices_Olattice(T_a)
% 28.12/28.38 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_inf1D2,axiom,
% 28.12/28.38 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 28.12/28.38 ( 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))
% 28.12/28.38 => hBOOL(hAPP(V_B_2,V_x_2)) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_inf1D1,axiom,
% 28.12/28.38 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 28.12/28.38 ( 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))
% 28.12/28.38 => hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Int__assoc,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_range__composition,axiom,
% 28.12/28.38 ! [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)))) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Int__left__commute,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Int__left__absorb,axiom,
% 28.12/28.38 ! [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) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Int__commute,axiom,
% 28.12/28.38 ! [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) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Int__absorb,axiom,
% 28.12/28.38 ! [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 ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Int__UNIV__right,axiom,
% 28.12/28.38 ! [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 ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Int__UNIV__left,axiom,
% 28.12/28.38 ! [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 ).
% 28.12/28.38
% 28.12/28.38 fof(fact_top__apply,axiom,
% 28.12/28.38 ! [V_x_2,T_c,T_b] :
% 28.12/28.38 ( class_Orderings_Otop(T_b)
% 28.12/28.38 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Otop__class_Otop(T_b) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_image__Int__subset,axiom,
% 28.12/28.38 ! [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)))) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_image__image,axiom,
% 28.12/28.38 ! [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) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_image__Pow__surj,axiom,
% 28.12/28.38 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
% 28.12/28.38 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_B_2
% 28.12/28.38 => 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) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Pow__Int__eq,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Union__UNIV,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Pow__UNIV,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Sup__UNIV,axiom,
% 28.12/28.38 ! [T_b] :
% 28.12/28.38 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.12/28.38 => 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) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_rev__image__eqI,axiom,
% 28.12/28.38 ! [T_c,V_f_2,V_b_2,V_A_2,V_x_2,T_b] :
% 28.12/28.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.38 => ( V_b_2 = hAPP(V_f_2,V_x_2)
% 28.12/28.38 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_imageI,axiom,
% 28.12/28.38 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 28.12/28.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.38 => 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))) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_image__iff,axiom,
% 28.12/28.38 ! [V_A_2,V_f_2,T_c,V_z_2,T_b] :
% 28.12/28.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 28.12/28.38 <=> ? [B_x] :
% 28.12/28.38 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 28.12/28.38 & V_z_2 = hAPP(V_f_2,B_x) ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Union__Int__subset,axiom,
% 28.12/28.38 ! [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)))) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_le__infE,axiom,
% 28.12/28.38 ! [V_b,V_a,V_x,T_a] :
% 28.12/28.38 ( class_Lattices_Osemilattice__inf(T_a)
% 28.12/28.38 => ( 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)))
% 28.12/28.38 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 28.12/28.38 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_inf__mono,axiom,
% 28.12/28.38 ! [V_d,V_b,V_c,V_a,T_a] :
% 28.12/28.38 ( class_Lattices_Osemilattice__inf(T_a)
% 28.12/28.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 28.12/28.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 28.12/28.38 => 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))) ) ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_inf__greatest,axiom,
% 28.12/28.38 ! [V_z,V_y,V_x,T_a] :
% 28.12/28.38 ( class_Lattices_Osemilattice__inf(T_a)
% 28.12/28.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 28.12/28.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 28.12/28.38 => 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))) ) ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_le__infI,axiom,
% 28.12/28.38 ! [V_b,V_a,V_x,T_a] :
% 28.12/28.38 ( class_Lattices_Osemilattice__inf(T_a)
% 28.12/28.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 28.12/28.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 28.12/28.38 => 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))) ) ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_inf__absorb2,axiom,
% 28.12/28.38 ! [V_x,V_y,T_a] :
% 28.12/28.38 ( class_Lattices_Osemilattice__inf(T_a)
% 28.12/28.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 28.12/28.38 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_inf__absorb1,axiom,
% 28.12/28.38 ! [V_y,V_x,T_a] :
% 28.12/28.38 ( class_Lattices_Osemilattice__inf(T_a)
% 28.12/28.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 28.12/28.38 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_le__infI2,axiom,
% 28.12/28.38 ! [V_a,V_x,V_b,T_a] :
% 28.12/28.38 ( class_Lattices_Osemilattice__inf(T_a)
% 28.12/28.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 28.12/28.38 => 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)) ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_le__infI1,axiom,
% 28.12/28.38 ! [V_b,V_x,V_a,T_a] :
% 28.12/28.38 ( class_Lattices_Osemilattice__inf(T_a)
% 28.12/28.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 28.12/28.38 => 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)) ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_le__inf__iff,axiom,
% 28.12/28.38 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 28.12/28.38 ( class_Lattices_Osemilattice__inf(T_b)
% 28.12/28.38 => ( 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)))
% 28.12/28.38 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 28.12/28.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_le__iff__inf,axiom,
% 28.12/28.38 ! [V_y_2,V_x_2,T_b] :
% 28.12/28.38 ( class_Lattices_Osemilattice__inf(T_b)
% 28.12/28.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 28.12/28.38 <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = V_x_2 ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_inf__le2,axiom,
% 28.12/28.38 ! [V_y,V_x,T_a] :
% 28.12/28.38 ( class_Lattices_Osemilattice__inf(T_a)
% 28.12/28.38 => 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)) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_inf__sup__ord_I2_J,axiom,
% 28.12/28.38 ! [V_y,V_x,T_a] :
% 28.12/28.38 ( class_Lattices_Olattice(T_a)
% 28.12/28.38 => 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)) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_inf__le1,axiom,
% 28.12/28.38 ! [V_y,V_x,T_a] :
% 28.12/28.38 ( class_Lattices_Osemilattice__inf(T_a)
% 28.12/28.38 => 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)) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_inf__sup__ord_I1_J,axiom,
% 28.12/28.38 ! [V_y,V_x,T_a] :
% 28.12/28.38 ( class_Lattices_Olattice(T_a)
% 28.12/28.38 => 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)) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_image__mono,axiom,
% 28.12/28.38 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
% 28.12/28.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.38 => 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))) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_subset__image__iff,axiom,
% 28.12/28.38 ! [V_A_2,V_f_2,T_c,V_B_2,T_b] :
% 28.12/28.38 ( 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)))
% 28.12/28.38 <=> ? [B_AA] :
% 28.12/28.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_AA),V_A_2))
% 28.12/28.38 & V_B_2 = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),B_AA) ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_image__Un,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_sup__inf__distrib2,axiom,
% 28.12/28.38 ! [V_x,V_z,V_y,T_a] :
% 28.12/28.38 ( class_Lattices_Odistrib__lattice(T_a)
% 28.12/28.38 => 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)) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_inf__sup__distrib2,axiom,
% 28.12/28.38 ! [V_x,V_z,V_y,T_a] :
% 28.12/28.38 ( class_Lattices_Odistrib__lattice(T_a)
% 28.12/28.38 => 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)) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_sup__inf__distrib1,axiom,
% 28.12/28.38 ! [V_z,V_y,V_x,T_a] :
% 28.12/28.38 ( class_Lattices_Odistrib__lattice(T_a)
% 28.12/28.38 => 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)) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_inf__sup__distrib1,axiom,
% 28.12/28.38 ! [V_z,V_y,V_x,T_a] :
% 28.12/28.38 ( class_Lattices_Odistrib__lattice(T_a)
% 28.12/28.38 => 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)) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_sup__inf__absorb,axiom,
% 28.12/28.38 ! [V_y,V_x,T_a] :
% 28.12/28.38 ( class_Lattices_Olattice(T_a)
% 28.12/28.38 => 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 ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_inf__sup__absorb,axiom,
% 28.12/28.38 ! [V_y,V_x,T_a] :
% 28.12/28.38 ( class_Lattices_Olattice(T_a)
% 28.12/28.38 => 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 ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_IntD2,axiom,
% 28.12/28.38 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 28.12/28.38 ( 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)))
% 28.12/28.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_IntD1,axiom,
% 28.12/28.38 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 28.12/28.38 ( 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)))
% 28.12/28.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Int__iff,axiom,
% 28.12/28.38 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 28.12/28.38 ( 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)))
% 28.12/28.38 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 28.12/28.38 & hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Int__mono,axiom,
% 28.12/28.38 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
% 28.12/28.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 28.12/28.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
% 28.12/28.38 => 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))) ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Int__greatest,axiom,
% 28.12/28.38 ! [V_B_2,V_A_2,V_C_2,T_b] :
% 28.12/28.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2))
% 28.12/28.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2))
% 28.12/28.38 => 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))) ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Int__absorb1,axiom,
% 28.12/28.38 ! [V_A_2,V_B_2,T_b] :
% 28.12/28.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 28.12/28.38 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Int__absorb2,axiom,
% 28.12/28.38 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.38 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Int__lower2,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Int__lower1,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Un__Int__crazy,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Un__Int__distrib2,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Int__Un__distrib2,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Un__Int__distrib,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Int__Un__distrib,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_subset__UNIV,axiom,
% 28.12/28.38 ! [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)))) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Un__UNIV__right,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Un__UNIV__left,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Int__Inter__image,axiom,
% 28.12/28.38 ! [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))) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_UN__extend__simps_I10_J,axiom,
% 28.12/28.38 ! [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) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_image__UN,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_UN__simps_I10_J,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_INT__extend__simps_I10_J,axiom,
% 28.12/28.38 ! [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) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_INT__simps_I10_J,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_inf__Int__eq,axiom,
% 28.12/28.38 ! [V_x_2,V_S_2,V_R_2,T_b] :
% 28.12/28.38 ( 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))
% 28.12/28.38 <=> 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))) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_UN__simps_I5_J,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_UN__simps_I4_J,axiom,
% 28.12/28.38 ! [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) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_UN__extend__simps_I5_J,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Int__UN__distrib,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_UN__extend__simps_I4_J,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Int__UN__distrib2,axiom,
% 28.12/28.38 ! [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))) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_image__Pow__mono,axiom,
% 28.12/28.38 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.38 ( 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))
% 28.12/28.38 => 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))) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_INT__Int__distrib,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_INTER__UNIV__conv_I1_J,axiom,
% 28.12/28.38 ! [V_B_2,V_A_2,T_c,T_b] :
% 28.12/28.38 ( 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)
% 28.12/28.38 <=> ! [B_x] :
% 28.12/28.38 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 28.12/28.38 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_INTER__UNIV__conv_I2_J,axiom,
% 28.12/28.38 ! [V_B_2,V_A_2,T_b,T_c] :
% 28.12/28.38 ( 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))
% 28.12/28.38 <=> ! [B_x] :
% 28.12/28.38 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 28.12/28.38 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_top__greatest,axiom,
% 28.12/28.38 ! [V_x,T_a] :
% 28.12/28.38 ( class_Orderings_Otop(T_a)
% 28.12/28.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_sup__top__right,axiom,
% 28.12/28.38 ! [V_x,T_a] :
% 28.12/28.38 ( class_Lattices_Obounded__lattice__top(T_a)
% 28.12/28.38 => 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) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_sup__top__left,axiom,
% 28.12/28.38 ! [V_x,T_a] :
% 28.12/28.38 ( class_Lattices_Obounded__lattice__top(T_a)
% 28.12/28.38 => 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) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_distrib__sup__le,axiom,
% 28.12/28.38 ! [V_z,V_y,V_x,T_a] :
% 28.12/28.38 ( class_Lattices_Olattice(T_a)
% 28.12/28.38 => 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)))) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_distrib__inf__le,axiom,
% 28.12/28.38 ! [V_z,V_y,V_x,T_a] :
% 28.12/28.38 ( class_Lattices_Olattice(T_a)
% 28.12/28.38 => 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)))) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_compl__sup,axiom,
% 28.12/28.38 ! [V_y,V_x,T_a] :
% 28.12/28.38 ( class_Lattices_Oboolean__algebra(T_a)
% 28.12/28.38 => 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)) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_compl__inf,axiom,
% 28.12/28.38 ! [V_y,V_x,T_a] :
% 28.12/28.38 ( class_Lattices_Oboolean__algebra(T_a)
% 28.12/28.38 => 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)) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_image__uminus__atLeastAtMost,axiom,
% 28.12/28.38 ! [V_y_2,V_x_2,T_b] :
% 28.12/28.38 ( class_Groups_Oordered__ab__group__add(T_b)
% 28.12/28.38 => 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)) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Un__Int__assoc__eq,axiom,
% 28.12/28.38 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 28.12/28.38 ( 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))
% 28.12/28.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Compl__Un,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Compl__Int,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Compl__partition2,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Compl__partition,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_UNION__eq__Union__image,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Union__image__eq,axiom,
% 28.12/28.38 ! [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) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_INT__absorb,axiom,
% 28.12/28.38 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
% 28.12/28.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2))
% 28.12/28.38 => 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) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_INTER__eq__Inter__image,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Inter__image__eq,axiom,
% 28.12/28.38 ! [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) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_INT__Un,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_SUP__UN__eq,axiom,
% 28.12/28.38 ! [V_x_2,V_r_2,T_c,T_b] :
% 28.12/28.38 ( 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))
% 28.12/28.38 <=> 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))) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_INF__INT__eq,axiom,
% 28.12/28.38 ! [V_x_2,V_r_2,T_c,T_b] :
% 28.12/28.38 ( 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))
% 28.12/28.38 <=> 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))) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_image__Union,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Inter__Un__distrib,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Int__Union2,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Int__Union,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_image__uminus__greaterThanAtMost,axiom,
% 28.12/28.38 ! [V_y_2,V_x_2,T_b] :
% 28.12/28.38 ( class_Groups_Oordered__ab__group__add(T_b)
% 28.12/28.38 => 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)) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_image__uminus__atLeastLessThan,axiom,
% 28.12/28.38 ! [V_y_2,V_x_2,T_b] :
% 28.12/28.38 ( class_Groups_Oordered__ab__group__add(T_b)
% 28.12/28.38 => 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)) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_compl__sup__top,axiom,
% 28.12/28.38 ! [V_x,T_a] :
% 28.12/28.38 ( class_Lattices_Oboolean__algebra(T_a)
% 28.12/28.38 => 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) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_surj__Compl__image__subset,axiom,
% 28.12/28.38 ! [V_A_2,V_f_2,T_b,T_c] :
% 28.12/28.38 ( 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))
% 28.12/28.38 => 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)))) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Cantors__paradox,axiom,
% 28.12/28.38 ! [V_A_2,T_b] :
% 28.12/28.38 ~ ? [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) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Least__mono,axiom,
% 28.12/28.38 ! [V_S_2,V_f_2,T_b,T_c] :
% 28.12/28.38 ( ( class_Orderings_Oorder(T_c)
% 28.12/28.38 & class_Orderings_Oorder(T_b) )
% 28.12/28.38 => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
% 28.12/28.38 => ( ? [B_x] :
% 28.12/28.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 28.12/28.38 & ! [B_xa] :
% 28.12/28.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_S_2))
% 28.12/28.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) ) )
% 28.12/28.38 => 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))) ) ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_compl__unique,axiom,
% 28.12/28.38 ! [V_y,V_x,T_a] :
% 28.12/28.38 ( class_Lattices_Oboolean__algebra(T_a)
% 28.12/28.38 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a)
% 28.12/28.38 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a)
% 28.12/28.38 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_image__ident,axiom,
% 28.12/28.38 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ).
% 28.12/28.38
% 28.12/28.38 fof(fact_imageE,axiom,
% 28.12/28.38 ! [V_A_2,V_f_2,T_c,V_b_2,T_b] :
% 28.12/28.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 28.12/28.38 => ~ ! [B_x] :
% 28.12/28.38 ( V_b_2 = hAPP(V_f_2,B_x)
% 28.12/28.38 => ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_image__subsetI,axiom,
% 28.12/28.38 ! [V_B_2,V_f_2,T_c,V_A_2,T_b] :
% 28.12/28.38 ( ! [B_x] :
% 28.12/28.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.12/28.38 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,B_x)),V_B_2)) )
% 28.12/28.38 => 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)) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_ivl__disj__int_I5_J,axiom,
% 28.12/28.38 ! [V_u_2,V_l_2,T_b] :
% 28.12/28.38 ( class_Orderings_Oorder(T_b)
% 28.12/28.38 => 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)) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_ivl__disj__int_I3_J,axiom,
% 28.12/28.38 ! [V_u_2,V_l_2,T_b] :
% 28.12/28.38 ( class_Orderings_Oorder(T_b)
% 28.12/28.38 => 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)) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_ivl__disj__int_I7_J,axiom,
% 28.12/28.38 ! [V_u_2,V_l_2,T_b] :
% 28.12/28.38 ( class_Orderings_Oorder(T_b)
% 28.12/28.38 => 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)) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_ivl__disj__int_I8_J,axiom,
% 28.12/28.38 ! [V_u_2,V_l_2,T_b] :
% 28.12/28.38 ( class_Orderings_Oorder(T_b)
% 28.12/28.38 => 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)) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_top1I,axiom,
% 28.12/28.38 ! [V_x_2,T_b] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_x_2)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_emptyE,axiom,
% 28.12/28.38 ! [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)))) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_empty__subsetI,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_UNIV__not__empty,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_bot__fun__def,axiom,
% 28.12/28.38 ! [V_x_2,T_c,T_b] :
% 28.12/28.38 ( class_Orderings_Obot(T_b)
% 28.12/28.38 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_bot__apply,axiom,
% 28.12/28.38 ! [V_x_2,T_c,T_b] :
% 28.12/28.38 ( class_Orderings_Obot(T_b)
% 28.12/28.38 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Union__empty,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Sup__empty,axiom,
% 28.12/28.38 ! [T_b] :
% 28.12/28.38 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.12/28.38 => 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) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_all__not__in__conv,axiom,
% 28.12/28.38 ! [V_A_2,T_b] :
% 28.12/28.38 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.12/28.38 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_ex__in__conv,axiom,
% 28.12/28.38 ! [V_A_2,T_b] :
% 28.12/28.38 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.12/28.38 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_empty__iff,axiom,
% 28.12/28.38 ! [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)))) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_equals0D,axiom,
% 28.12/28.38 ! [V_a_2,T_b,V_A_2] :
% 28.12/28.38 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.38 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_subset__empty,axiom,
% 28.12/28.38 ! [V_A_2,T_b] :
% 28.12/28.38 ( 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))))
% 28.12/28.38 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_empty__is__image,axiom,
% 28.12/28.38 ! [V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.38 ( 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)
% 28.12/28.38 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_image__empty,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_image__is__empty,axiom,
% 28.12/28.38 ! [V_A_2,V_f_2,T_b,T_c] :
% 28.12/28.38 ( 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))
% 28.12/28.38 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Un__empty__left,axiom,
% 28.12/28.38 ! [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 ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Un__empty__right,axiom,
% 28.12/28.38 ! [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 ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Un__empty,axiom,
% 28.12/28.38 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.38 ( 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))
% 28.12/28.38 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.38 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Int__empty__left,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Int__empty__right,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_disjoint__iff__not__equal,axiom,
% 28.12/28.38 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.38 ( 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))
% 28.12/28.38 <=> ! [B_x] :
% 28.12/28.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.12/28.38 => ! [B_xa] :
% 28.12/28.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_B_2))
% 28.12/28.38 => B_x != B_xa ) ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Compl__empty__eq,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Compl__UNIV__eq,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_empty,axiom,
% 28.12/28.38 ! [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))) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_hoare__derivs_Oequations_I1_J,axiom,
% 28.12/28.38 ! [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))) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Pow__not__empty,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Inter__UNIV,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Inter__empty,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_monoD,axiom,
% 28.12/28.38 ! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
% 28.12/28.38 ( ( class_Orderings_Oorder(T_c)
% 28.12/28.38 & class_Orderings_Oorder(T_b) )
% 28.12/28.38 => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
% 28.12/28.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 28.12/28.38 => 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))) ) ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_bot__empty__eq,axiom,
% 28.12/28.38 ! [V_x_2,T_b] :
% 28.12/28.38 ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_x_2))
% 28.12/28.38 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_bot__least,axiom,
% 28.12/28.38 ! [V_x,T_a] :
% 28.12/28.38 ( class_Orderings_Obot(T_a)
% 28.12/28.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_SUP__const,axiom,
% 28.12/28.38 ! [V_M_2,T_b,V_A_2,T_c] :
% 28.12/28.38 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 28.12/28.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.38 => 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 ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_UNION__empty__conv_I2_J,axiom,
% 28.12/28.38 ! [V_B_2,V_A_2,T_b,T_c] :
% 28.12/28.38 ( 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))
% 28.12/28.38 <=> ! [B_x] :
% 28.12/28.38 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 28.12/28.38 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_UN__constant,axiom,
% 28.12/28.38 ! [V_c_2,T_c,T_b,V_A_2] :
% 28.12/28.38 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.38 => 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)) )
% 28.12/28.38 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.38 => 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 ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_UN__empty2,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_UNION__empty__conv_I1_J,axiom,
% 28.12/28.38 ! [V_B_2,V_A_2,T_c,T_b] :
% 28.12/28.38 ( 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)
% 28.12/28.38 <=> ! [B_x] :
% 28.12/28.38 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 28.12/28.38 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_INF__const,axiom,
% 28.12/28.38 ! [V_M_2,T_b,V_A_2,T_c] :
% 28.12/28.38 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 28.12/28.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.38 => 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 ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_INT__empty,axiom,
% 28.12/28.38 ! [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)) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_INT__constant,axiom,
% 28.12/28.38 ! [V_c_2,T_c,T_b,V_A_2] :
% 28.12/28.38 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.38 => 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)) )
% 28.12/28.38 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.38 => 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 ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_sup__bot__left,axiom,
% 28.12/28.38 ! [V_x,T_a] :
% 28.12/28.38 ( class_Lattices_Obounded__lattice__bot(T_a)
% 28.12/28.38 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_sup__bot__right,axiom,
% 28.12/28.38 ! [V_x,T_a] :
% 28.12/28.38 ( class_Lattices_Obounded__lattice__bot(T_a)
% 28.12/28.38 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_sup__eq__bot__iff,axiom,
% 28.12/28.38 ! [V_y_2,V_x_2,T_b] :
% 28.12/28.38 ( class_Lattices_Obounded__lattice__bot(T_b)
% 28.12/28.38 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_b)
% 28.12/28.38 <=> ( V_x_2 = c_Orderings_Obot__class_Obot(T_b)
% 28.12/28.38 & V_y_2 = c_Orderings_Obot__class_Obot(T_b) ) ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_inf__bot__left,axiom,
% 28.12/28.38 ! [V_x,T_a] :
% 28.12/28.38 ( class_Lattices_Obounded__lattice__bot(T_a)
% 28.12/28.38 => 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) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_inf__bot__right,axiom,
% 28.12/28.38 ! [V_x,T_a] :
% 28.12/28.38 ( class_Lattices_Obounded__lattice__bot(T_a)
% 28.12/28.38 => 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) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_Inf__UNIV,axiom,
% 28.12/28.38 ! [T_b] :
% 28.12/28.38 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.12/28.38 => 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) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_strict__mono__mono,axiom,
% 28.12/28.38 ! [V_f_2,T_b,T_c] :
% 28.12/28.38 ( ( class_Orderings_Oorder(T_c)
% 28.12/28.38 & class_Orderings_Oorder(T_b) )
% 28.12/28.38 => ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
% 28.12/28.38 => c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2) ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_atLeastatMost__empty__iff2,axiom,
% 28.12/28.38 ! [V_b_2,V_a_2,T_b] :
% 28.12/28.38 ( class_Orderings_Oorder(T_b)
% 28.12/28.38 => ( 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)
% 28.12/28.38 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 28.12/28.38
% 28.12/28.38 fof(fact_atLeastatMost__empty__iff,axiom,
% 28.12/28.38 ! [V_b_2,V_a_2,T_b] :
% 28.12/28.38 ( class_Orderings_Oorder(T_b)
% 28.12/28.39 => ( 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))
% 28.12/28.39 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_atLeastLessThan__empty,axiom,
% 28.12/28.39 ! [V_a_2,V_b_2,T_b] :
% 28.12/28.39 ( class_Orderings_Oorder(T_b)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
% 28.12/28.39 => 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)) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_ivl__disj__int_I11_J,axiom,
% 28.12/28.39 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 28.12/28.39 ( class_Orderings_Oorder(T_b)
% 28.12/28.39 => 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)) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_subset__Compl__self__eq,axiom,
% 28.12/28.39 ! [V_A_2,T_b] :
% 28.12/28.39 ( 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)))
% 28.12/28.39 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Compl__disjoint,axiom,
% 28.12/28.39 ! [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)) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Compl__disjoint2,axiom,
% 28.12/28.39 ! [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)) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_greaterThanAtMost__empty,axiom,
% 28.12/28.39 ! [V_k_2,V_l_2,T_b] :
% 28.12/28.39 ( class_Orderings_Oorder(T_b)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
% 28.12/28.39 => 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)) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Inf__empty,axiom,
% 28.12/28.39 ! [T_b] :
% 28.12/28.39 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.12/28.39 => 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) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Union__disjoint,axiom,
% 28.12/28.39 ! [V_A_2,V_C_2,T_b] :
% 28.12/28.39 ( 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))
% 28.12/28.39 <=> ! [B_x] :
% 28.12/28.39 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_C_2))
% 28.12/28.39 => 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)) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Pow__bottom,axiom,
% 28.12/28.39 ! [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))) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_ivl__disj__int_I14_J,axiom,
% 28.12/28.39 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 28.12/28.39 ( class_Orderings_Oorder(T_b)
% 28.12/28.39 => 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)) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_mono__Un,axiom,
% 28.12/28.39 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.39 ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),V_f_2)
% 28.12/28.39 => 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)))) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_mono__Int,axiom,
% 28.12/28.39 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.39 ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),V_f_2)
% 28.12/28.39 => 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)))) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_UN__simps_I3_J,axiom,
% 28.12/28.39 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 28.12/28.39 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.39 => 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)) )
% 28.12/28.39 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.39 => 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)) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_UN__simps_I2_J,axiom,
% 28.12/28.39 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 28.12/28.39 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.39 => 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)) )
% 28.12/28.39 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.39 => 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) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_UN__extend__simps_I3_J,axiom,
% 28.12/28.39 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 28.12/28.39 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.39 => 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 )
% 28.12/28.39 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.39 => 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)) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_UN__extend__simps_I2_J,axiom,
% 28.12/28.39 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 28.12/28.39 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.39 => 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 )
% 28.12/28.39 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.39 => 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)) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_INT__extend__simps_I2_J,axiom,
% 28.12/28.39 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 28.12/28.39 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.39 => 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 )
% 28.12/28.39 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.39 => 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)) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_INT__extend__simps_I1_J,axiom,
% 28.12/28.39 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 28.12/28.39 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.39 => 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 )
% 28.12/28.39 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.39 => 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)) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_INT__simps_I1_J,axiom,
% 28.12/28.39 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 28.12/28.39 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.39 => 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)) )
% 28.12/28.39 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.39 => 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) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_INT__simps_I2_J,axiom,
% 28.12/28.39 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 28.12/28.39 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.39 => 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)) )
% 28.12/28.39 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.39 => 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)) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_mono__sup,axiom,
% 28.12/28.39 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
% 28.12/28.39 ( ( class_Lattices_Osemilattice__sup(T_c)
% 28.12/28.39 & class_Lattices_Osemilattice__sup(T_b) )
% 28.12/28.39 => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
% 28.12/28.39 => 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)))) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_mono__inf,axiom,
% 28.12/28.39 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
% 28.12/28.39 ( ( class_Lattices_Osemilattice__inf(T_c)
% 28.12/28.39 & class_Lattices_Osemilattice__inf(T_b) )
% 28.12/28.39 => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
% 28.12/28.39 => 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)))) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_inf__compl__bot,axiom,
% 28.12/28.39 ! [V_x,T_a] :
% 28.12/28.39 ( class_Lattices_Oboolean__algebra(T_a)
% 28.12/28.39 => 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) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_compl__inf__bot,axiom,
% 28.12/28.39 ! [V_x,T_a] :
% 28.12/28.39 ( class_Lattices_Oboolean__algebra(T_a)
% 28.12/28.39 => 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) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_compl__top__eq,axiom,
% 28.12/28.39 ! [T_a] :
% 28.12/28.39 ( class_Lattices_Oboolean__algebra(T_a)
% 28.12/28.39 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_compl__bot__eq,axiom,
% 28.12/28.39 ! [T_a] :
% 28.12/28.39 ( class_Lattices_Oboolean__algebra(T_a)
% 28.12/28.39 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_disjoint__eq__subset__Compl,axiom,
% 28.12/28.39 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.39 ( 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))
% 28.12/28.39 <=> 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))) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_ivl__disj__int_I15_J,axiom,
% 28.12/28.39 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 28.12/28.39 ( class_Orderings_Oorder(T_b)
% 28.12/28.39 => 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)) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_ivl__disj__int_I4_J,axiom,
% 28.12/28.39 ! [V_u_2,V_l_2,T_b] :
% 28.12/28.39 ( class_Orderings_Oorder(T_b)
% 28.12/28.39 => 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)) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_ivl__disj__int_I2_J,axiom,
% 28.12/28.39 ! [V_u_2,V_l_2,T_b] :
% 28.12/28.39 ( class_Orderings_Oorder(T_b)
% 28.12/28.39 => 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)) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_ivl__disj__int_I16_J,axiom,
% 28.12/28.39 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 28.12/28.39 ( class_Orderings_Oorder(T_b)
% 28.12/28.39 => 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)) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_iso__tuple__UNIV__I,axiom,
% 28.12/28.39 ! [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)))) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_ivl__disj__un_I5_J,axiom,
% 28.12/28.39 ! [V_u_2,V_l_2,T_b] :
% 28.12/28.39 ( class_Orderings_Olinorder(T_b)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 28.12/28.39 => 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) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_ivl__disj__un_I6_J,axiom,
% 28.12/28.39 ! [V_u_2,V_l_2,T_b] :
% 28.12/28.39 ( class_Orderings_Olinorder(T_b)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 28.12/28.39 => 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) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_coinduct3__mono__lemma,axiom,
% 28.12/28.39 ! [V_B_2,V_X_2,V_f_2,T_c,T_b] :
% 28.12/28.39 ( class_Orderings_Oorder(T_b)
% 28.12/28.39 => ( c_Orderings_Oorder__class_Omono(T_b,tc_fun(T_c,tc_HOL_Obool),V_f_2)
% 28.12/28.39 => 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)) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_ivl__disj__int_I6_J,axiom,
% 28.12/28.39 ! [V_u_2,V_l_2,T_b] :
% 28.12/28.39 ( class_Orderings_Oorder(T_b)
% 28.12/28.39 => 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)) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_ivl__disj__int_I1_J,axiom,
% 28.12/28.39 ! [V_u_2,V_l_2,T_b] :
% 28.12/28.39 ( class_Orderings_Oorder(T_b)
% 28.12/28.39 => 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)) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_ivl__disj__int_I10_J,axiom,
% 28.12/28.39 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 28.12/28.39 ( class_Orderings_Oorder(T_b)
% 28.12/28.39 => 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)) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_ivl__disj__un_I1_J,axiom,
% 28.12/28.39 ! [V_l_2,T_b] :
% 28.12/28.39 ( class_Orderings_Olinorder(T_b)
% 28.12/28.39 => 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) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_INT__simps_I4_J,axiom,
% 28.12/28.39 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 28.12/28.39 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.39 => 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)) )
% 28.12/28.39 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.39 => 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)) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_atMost__Int__atLeast,axiom,
% 28.12/28.39 ! [V_n_2,T_b] :
% 28.12/28.39 ( class_Orderings_Oorder(T_b)
% 28.12/28.39 => 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))) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_insertCI,axiom,
% 28.12/28.39 ! [V_b_2,V_B_2,V_a_2,T_b] :
% 28.12/28.39 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 28.12/28.39 => V_a_2 = V_b_2 )
% 28.12/28.39 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_insertE,axiom,
% 28.12/28.39 ! [V_A_2,V_b_2,V_a_2,T_b] :
% 28.12/28.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
% 28.12/28.39 => ( V_a_2 != V_b_2
% 28.12/28.39 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_DiffE,axiom,
% 28.12/28.39 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 28.12/28.39 ( 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)))
% 28.12/28.39 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 28.12/28.39 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_DiffI,axiom,
% 28.12/28.39 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 28.12/28.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 28.12/28.39 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 28.12/28.39 => 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))) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Diff__insert,axiom,
% 28.12/28.39 ! [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)))) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Diff__insert2,axiom,
% 28.12/28.39 ! [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) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_insert__Diff__single,axiom,
% 28.12/28.39 ! [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) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_insert__Diff__if,axiom,
% 28.12/28.39 ! [V_A_2,V_B_2,V_x_2,T_b] :
% 28.12/28.39 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 28.12/28.39 => 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) )
% 28.12/28.39 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 28.12/28.39 => 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)) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_insert__Diff1,axiom,
% 28.12/28.39 ! [V_A_2,V_B_2,V_x_2,T_b] :
% 28.12/28.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 28.12/28.39 => 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) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_diff__eq__diff__eq,axiom,
% 28.12/28.39 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 28.12/28.39 ( class_Groups_Oab__group__add(T_b)
% 28.12/28.39 => ( 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)
% 28.12/28.39 => ( V_a_2 = V_b_2
% 28.12/28.39 <=> V_c_2 = V_d_2 ) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_minus__apply,axiom,
% 28.12/28.39 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 28.12/28.39 ( class_Groups_Ominus(T_b)
% 28.12/28.39 => 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)) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_fun__diff__def,axiom,
% 28.12/28.39 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 28.12/28.39 ( class_Groups_Ominus(T_b)
% 28.12/28.39 => 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)) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_insert__code,axiom,
% 28.12/28.39 ! [V_x_2,V_A_2,V_y_2,T_b] :
% 28.12/28.39 ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2))
% 28.12/28.39 <=> ( V_y_2 = V_x_2
% 28.12/28.39 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Diff__idemp,axiom,
% 28.12/28.39 ! [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) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_insert__commute,axiom,
% 28.12/28.39 ! [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)) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_insert__absorb2,axiom,
% 28.12/28.39 ! [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) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_insert__Diff,axiom,
% 28.12/28.39 ! [V_A_2,V_a_2,T_b] :
% 28.12/28.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.12/28.39 => 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 ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Diff__insert__absorb,axiom,
% 28.12/28.39 ! [V_A_2,V_x_2,T_b] :
% 28.12/28.39 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.39 => 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 ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_diff__eq__diff__less__eq,axiom,
% 28.12/28.39 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 28.12/28.39 ( class_Groups_Oordered__ab__group__add(T_b)
% 28.12/28.39 => ( 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)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 28.12/28.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2)) ) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_single__Diff__lessThan,axiom,
% 28.12/28.39 ! [V_k_2,T_b] :
% 28.12/28.39 ( class_Orderings_Oorder(T_b)
% 28.12/28.39 => 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))) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_minus__diff__eq,axiom,
% 28.12/28.39 ! [V_b,V_a,T_a] :
% 28.12/28.39 ( class_Groups_Oab__group__add(T_a)
% 28.12/28.39 => 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) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_DiffD2,axiom,
% 28.12/28.39 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 28.12/28.39 ( 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)))
% 28.12/28.39 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_DiffD1,axiom,
% 28.12/28.39 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 28.12/28.39 ( 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)))
% 28.12/28.39 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Diff__iff,axiom,
% 28.12/28.39 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 28.12/28.39 ( 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)))
% 28.12/28.39 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 28.12/28.39 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_insert__absorb,axiom,
% 28.12/28.39 ! [V_A_2,V_a_2,T_b] :
% 28.12/28.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.12/28.39 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = V_A_2 ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_insertI2,axiom,
% 28.12/28.39 ! [V_b_2,V_B_2,V_a_2,T_b] :
% 28.12/28.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 28.12/28.39 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_insert__ident,axiom,
% 28.12/28.39 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 28.12/28.39 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.39 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 28.12/28.39 => ( 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)
% 28.12/28.39 <=> V_A_2 = V_B_2 ) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_insert__iff,axiom,
% 28.12/28.39 ! [V_A_2,V_b_2,V_a_2,T_b] :
% 28.12/28.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
% 28.12/28.39 <=> ( V_a_2 = V_b_2
% 28.12/28.39 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_insertI1,axiom,
% 28.12/28.39 ! [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))) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Diff__cancel,axiom,
% 28.12/28.39 ! [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)) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Diff__empty,axiom,
% 28.12/28.39 ! [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 ).
% 28.12/28.39
% 28.12/28.39 fof(fact_empty__Diff,axiom,
% 28.12/28.39 ! [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)) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_singleton__inject,axiom,
% 28.12/28.39 ! [V_b_2,V_a_2,T_b] :
% 28.12/28.39 ( 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)))
% 28.12/28.39 => V_a_2 = V_b_2 ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_doubleton__eq__iff,axiom,
% 28.12/28.39 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 28.12/28.39 ( 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))))
% 28.12/28.39 <=> ( ( V_a_2 = V_c_2
% 28.12/28.39 & V_b_2 = V_d_2 )
% 28.12/28.39 | ( V_a_2 = V_d_2
% 28.12/28.39 & V_b_2 = V_c_2 ) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_insert__not__empty,axiom,
% 28.12/28.39 ! [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)) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_empty__not__insert,axiom,
% 28.12/28.39 ! [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) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_double__diff,axiom,
% 28.12/28.39 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 28.12/28.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 28.12/28.39 => 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 ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Diff__mono,axiom,
% 28.12/28.39 ! [V_B_2,V_D_2,V_C_2,V_A_2,T_b] :
% 28.12/28.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_D_2),V_B_2))
% 28.12/28.39 => 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))) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Diff__subset,axiom,
% 28.12/28.39 ! [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)) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Un__Diff,axiom,
% 28.12/28.39 ! [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)) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Un__Diff__cancel2,axiom,
% 28.12/28.39 ! [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) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Un__Diff__cancel,axiom,
% 28.12/28.39 ! [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) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Diff__Int2,axiom,
% 28.12/28.39 ! [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) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Diff__Int__distrib2,axiom,
% 28.12/28.39 ! [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)) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Int__Diff,axiom,
% 28.12/28.39 ! [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)) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Diff__Int__distrib,axiom,
% 28.12/28.39 ! [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)) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_insert__mono,axiom,
% 28.12/28.39 ! [V_a_2,V_D_2,V_C_2,T_b] :
% 28.12/28.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))
% 28.12/28.39 => 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))) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_subset__insertI2,axiom,
% 28.12/28.39 ! [V_b_2,V_B_2,V_A_2,T_b] :
% 28.12/28.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.39 => 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))) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_subset__insertI,axiom,
% 28.12/28.39 ! [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))) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_image__insert,axiom,
% 28.12/28.39 ! [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)) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Un__insert__left,axiom,
% 28.12/28.39 ! [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)) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Un__insert__right,axiom,
% 28.12/28.39 ! [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)) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_insert__inter__insert,axiom,
% 28.12/28.39 ! [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)) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_hoare__derivs_Oinsert,axiom,
% 28.12/28.39 ! [V_tsa_2,V_t_2,V_G_2,T_b] :
% 28.12/28.39 ( 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))))
% 28.12/28.39 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2)
% 28.12/28.39 => 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)) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_subset__insert__iff,axiom,
% 28.12/28.39 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 28.12/28.39 ( 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)))
% 28.12/28.39 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.39 => 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)) )
% 28.12/28.39 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_diff__single__insert,axiom,
% 28.12/28.39 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 28.12/28.39 ( 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))
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.39 => 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))) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_UN__simps_I6_J,axiom,
% 28.12/28.39 ! [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) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_UN__extend__simps_I6_J,axiom,
% 28.12/28.39 ! [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)) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_INT__simps_I5_J,axiom,
% 28.12/28.39 ! [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)) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_INT__extend__simps_I5_J,axiom,
% 28.12/28.39 ! [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)) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_diff__eq,axiom,
% 28.12/28.39 ! [V_y,V_x,T_a] :
% 28.12/28.39 ( class_Lattices_Oboolean__algebra(T_a)
% 28.12/28.39 => 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)) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_singletonE,axiom,
% 28.12/28.39 ! [V_a_2,V_b_2,T_b] :
% 28.12/28.39 ( 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)))))
% 28.12/28.39 => V_b_2 = V_a_2 ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_singleton__iff,axiom,
% 28.12/28.39 ! [V_a_2,V_b_2,T_b] :
% 28.12/28.39 ( 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)))))
% 28.12/28.39 <=> V_b_2 = V_a_2 ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_insert__subset,axiom,
% 28.12/28.39 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 28.12/28.39 ( 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))
% 28.12/28.39 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 28.12/28.39 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_subset__insert,axiom,
% 28.12/28.39 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 28.12/28.39 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.39 => ( 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)))
% 28.12/28.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_insert__image,axiom,
% 28.12/28.39 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 28.12/28.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.39 => 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) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Diff__UNIV,axiom,
% 28.12/28.39 ! [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)) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Int__insert__left__if1,axiom,
% 28.12/28.39 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 28.12/28.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 28.12/28.39 => 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)) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Int__insert__right__if1,axiom,
% 28.12/28.39 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 28.12/28.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.12/28.39 => 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)) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Int__insert__left__if0,axiom,
% 28.12/28.39 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 28.12/28.39 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 28.12/28.39 => 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) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Int__insert__right__if0,axiom,
% 28.12/28.39 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 28.12/28.39 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.12/28.39 => 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) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Int__insert__left,axiom,
% 28.12/28.39 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 28.12/28.39 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 28.12/28.39 => 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)) )
% 28.12/28.39 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 28.12/28.39 => 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) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Int__insert__right,axiom,
% 28.12/28.39 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 28.12/28.39 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.12/28.39 => 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)) )
% 28.12/28.39 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.12/28.39 => 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) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Diff__triv,axiom,
% 28.12/28.39 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.39 ( 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))
% 28.12/28.39 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Diff__disjoint,axiom,
% 28.12/28.39 ! [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)) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_image__diff__subset,axiom,
% 28.12/28.39 ! [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)))) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_subset__singletonD,axiom,
% 28.12/28.39 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.39 ( 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)))))
% 28.12/28.39 => ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.39 | 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))) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Diff__subset__conv,axiom,
% 28.12/28.39 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 28.12/28.39 ( 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))
% 28.12/28.39 <=> 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))) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Diff__partition,axiom,
% 28.12/28.39 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.39 => 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 ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_insert__is__Un,axiom,
% 28.12/28.39 ! [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) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Un__Diff__Int,axiom,
% 28.12/28.39 ! [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 ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Diff__Un,axiom,
% 28.12/28.39 ! [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)) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Diff__Int,axiom,
% 28.12/28.39 ! [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)) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_ivl__diff,axiom,
% 28.12/28.39 ! [V_m_2,V_n_2,V_i_2,T_b] :
% 28.12/28.39 ( class_Orderings_Olinorder(T_b)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_n_2))
% 28.12/28.39 => 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) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_atLeastAtMost__singleton_H,axiom,
% 28.12/28.39 ! [V_b_2,V_a_2,T_b] :
% 28.12/28.39 ( class_Orderings_Oorder(T_b)
% 28.12/28.39 => ( V_a_2 = V_b_2
% 28.12/28.39 => 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))) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_atLeastAtMost__singleton__iff,axiom,
% 28.12/28.39 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 28.12/28.39 ( class_Orderings_Oorder(T_b)
% 28.12/28.39 => ( 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)))
% 28.12/28.39 <=> ( V_a_2 = V_b_2
% 28.12/28.39 & V_b_2 = V_c_2 ) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_atLeastAtMost__singleton,axiom,
% 28.12/28.39 ! [V_a_2,T_b] :
% 28.12/28.39 ( class_Orderings_Oorder(T_b)
% 28.12/28.39 => 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))) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Sup__singleton,axiom,
% 28.12/28.39 ! [V_a_2,T_b] :
% 28.12/28.39 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.12/28.39 => 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 ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Sup__insert,axiom,
% 28.12/28.39 ! [V_A_2,V_a_2,T_b] :
% 28.12/28.39 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.12/28.39 => 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)) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Compl__eq__Diff__UNIV,axiom,
% 28.12/28.39 ! [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) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Compl__Diff__eq,axiom,
% 28.12/28.39 ! [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) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Diff__Compl,axiom,
% 28.12/28.39 ! [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) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Diff__eq,axiom,
% 28.12/28.39 ! [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)) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Inf__singleton,axiom,
% 28.12/28.39 ! [V_a_2,T_b] :
% 28.12/28.39 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.12/28.39 => 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 ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Inf__insert,axiom,
% 28.12/28.39 ! [V_A_2,V_a_2,T_b] :
% 28.12/28.39 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.12/28.39 => 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)) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Union__insert,axiom,
% 28.12/28.39 ! [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)) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Un__eq__Union,axiom,
% 28.12/28.39 ! [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))))) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Pow__empty,axiom,
% 28.12/28.39 ! [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))) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Inter__insert,axiom,
% 28.12/28.39 ! [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)) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Int__eq__Inter,axiom,
% 28.12/28.39 ! [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))))) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_UN__insert__distrib,axiom,
% 28.12/28.39 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
% 28.12/28.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2))
% 28.12/28.39 => 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)) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_image__constant__conv,axiom,
% 28.12/28.39 ! [V_c_2,T_c,T_b,V_A_2] :
% 28.12/28.39 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.39 => 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)) )
% 28.12/28.39 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.39 => 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))) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_UN__extend__simps_I1_J,axiom,
% 28.12/28.39 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
% 28.12/28.39 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.39 => 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))) )
% 28.12/28.39 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.39 => 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)) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_UN__singleton,axiom,
% 28.12/28.39 ! [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 ).
% 28.12/28.39
% 28.12/28.39 fof(fact_UN__simps_I1_J,axiom,
% 28.12/28.39 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
% 28.12/28.39 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.39 => 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)) )
% 28.12/28.39 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.39 => 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)) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_INT__insert__distrib,axiom,
% 28.12/28.39 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
% 28.12/28.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2))
% 28.12/28.39 => 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)) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_UN__insert,axiom,
% 28.12/28.39 ! [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)) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_UN__simps_I7_J,axiom,
% 28.12/28.39 ! [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)) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_UN__extend__simps_I7_J,axiom,
% 28.12/28.39 ! [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)) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_INT__insert,axiom,
% 28.12/28.39 ! [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)) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_greaterThanLessThan__empty,axiom,
% 28.12/28.39 ! [V_k_2,V_l_2,T_b] :
% 28.12/28.39 ( class_Orderings_Oorder(T_b)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
% 28.12/28.39 => 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)) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_image__uminus__greaterThanLessThan,axiom,
% 28.12/28.39 ! [V_y_2,V_x_2,T_b] :
% 28.12/28.39 ( class_Groups_Oordered__ab__group__add(T_b)
% 28.12/28.39 => 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)) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Sup__binary,axiom,
% 28.12/28.39 ! [V_b_2,V_a_2,T_b] :
% 28.12/28.39 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.12/28.39 => 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) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Inf__binary,axiom,
% 28.12/28.39 ! [V_b_2,V_a_2,T_b] :
% 28.12/28.39 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.12/28.39 => 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) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_image__constant,axiom,
% 28.12/28.39 ! [V_c_2,T_c,V_A_2,V_x_2,T_b] :
% 28.12/28.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.39 => 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))) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_INT__simps_I3_J,axiom,
% 28.12/28.39 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 28.12/28.39 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.39 => 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)) )
% 28.12/28.39 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.39 => 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) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_INT__extend__simps_I3_J,axiom,
% 28.12/28.39 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 28.12/28.39 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.39 => 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) )
% 28.12/28.39 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.39 => 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)) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_image__eq__UN,axiom,
% 28.12/28.39 ! [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)))) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_INT__extend__simps_I4_J,axiom,
% 28.12/28.39 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 28.12/28.39 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.39 => 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 )
% 28.12/28.39 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.39 => 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)) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Pow__insert,axiom,
% 28.12/28.39 ! [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))) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_ivl__disj__int_I12_J,axiom,
% 28.12/28.39 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 28.12/28.39 ( class_Orderings_Oorder(T_b)
% 28.12/28.39 => 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)) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_ivl__disj__int_I13_J,axiom,
% 28.12/28.39 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 28.12/28.39 ( class_Orderings_Oorder(T_b)
% 28.12/28.39 => 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)) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_ivl__disj__un_I2_J,axiom,
% 28.12/28.39 ! [V_u_2,T_b] :
% 28.12/28.39 ( class_Orderings_Olinorder(T_b)
% 28.12/28.39 => 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) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_ivl__disj__int_I9_J,axiom,
% 28.12/28.39 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 28.12/28.39 ( class_Orderings_Oorder(T_b)
% 28.12/28.39 => 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)) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_the__elem__eq,axiom,
% 28.12/28.39 ! [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 ).
% 28.12/28.39
% 28.12/28.39 fof(fact_fun__upd__image,axiom,
% 28.12/28.39 ! [V_y_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 28.12/28.39 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.39 => 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)))))) )
% 28.12/28.39 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.39 => 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) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_Inter__subset,axiom,
% 28.12/28.39 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.39 ( ! [B_X] :
% 28.12/28.39 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2))
% 28.12/28.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_X),V_B_2)) )
% 28.12/28.39 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
% 28.12/28.39 => 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)) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_ivl__disj__un_I19_J,axiom,
% 28.12/28.39 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 28.12/28.39 ( class_Orderings_Olinorder(T_b)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 28.12/28.39 => 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) ) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_ivl__disj__un_I4_J,axiom,
% 28.12/28.39 ! [V_u_2,V_l_2,T_b] :
% 28.12/28.39 ( class_Orderings_Olinorder(T_b)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 28.12/28.39 => 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) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_ivl__disj__un_I18_J,axiom,
% 28.12/28.39 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 28.12/28.39 ( class_Orderings_Olinorder(T_b)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
% 28.12/28.39 => 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) ) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_ivl__disj__un_I3_J,axiom,
% 28.12/28.39 ! [V_u_2,V_l_2,T_b] :
% 28.12/28.39 ( class_Orderings_Olinorder(T_b)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 28.12/28.39 => 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) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_coinduct__set,axiom,
% 28.12/28.39 ! [V_X_2,V_a_2,V_f_2,T_b] :
% 28.12/28.39 ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
% 28.12/28.39 => ( 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)))))
% 28.12/28.39 => 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))) ) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_def__coinduct__set,axiom,
% 28.12/28.39 ! [V_X_2,V_a_2,V_f_2,T_b,V_A_2] :
% 28.12/28.39 ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 28.12/28.39 => ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
% 28.12/28.39 => ( 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))))
% 28.12/28.39 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_fun__upd__triv,axiom,
% 28.12/28.39 ! [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 ).
% 28.12/28.39
% 28.12/28.39 fof(fact_order__less__irrefl,axiom,
% 28.12/28.39 ! [V_x,T_a] :
% 28.12/28.39 ( class_Orderings_Opreorder(T_a)
% 28.12/28.39 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_linorder__neq__iff,axiom,
% 28.12/28.39 ! [V_y_2,V_x_2,T_b] :
% 28.12/28.39 ( class_Orderings_Olinorder(T_b)
% 28.12/28.39 => ( V_x_2 != V_y_2
% 28.12/28.39 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 28.12/28.39 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_not__less__iff__gr__or__eq,axiom,
% 28.12/28.39 ! [V_y_2,V_x_2,T_b] :
% 28.12/28.39 ( class_Orderings_Olinorder(T_b)
% 28.12/28.39 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 28.12/28.39 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
% 28.12/28.39 | V_x_2 = V_y_2 ) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_linorder__less__linear,axiom,
% 28.12/28.39 ! [V_y,V_x,T_a] :
% 28.12/28.39 ( class_Orderings_Olinorder(T_a)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 28.12/28.39 | V_x = V_y
% 28.12/28.39 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_linorder__antisym__conv3,axiom,
% 28.12/28.39 ! [V_x_2,V_y_2,T_b] :
% 28.12/28.39 ( class_Orderings_Olinorder(T_b)
% 28.12/28.39 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
% 28.12/28.39 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 28.12/28.39 <=> V_x_2 = V_y_2 ) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_linorder__neqE,axiom,
% 28.12/28.39 ! [V_y,V_x,T_a] :
% 28.12/28.39 ( class_Orderings_Olinorder(T_a)
% 28.12/28.39 => ( V_x != V_y
% 28.12/28.39 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 28.12/28.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_less__imp__neq,axiom,
% 28.12/28.39 ! [V_y,V_x,T_a] :
% 28.12/28.39 ( class_Orderings_Oorder(T_a)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 28.12/28.39 => V_x != V_y ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_order__less__not__sym,axiom,
% 28.12/28.39 ! [V_y,V_x,T_a] :
% 28.12/28.39 ( class_Orderings_Opreorder(T_a)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 28.12/28.39 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_order__less__imp__not__less,axiom,
% 28.12/28.39 ! [V_y,V_x,T_a] :
% 28.12/28.39 ( class_Orderings_Opreorder(T_a)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 28.12/28.39 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_order__less__imp__not__eq,axiom,
% 28.12/28.39 ! [V_y,V_x,T_a] :
% 28.12/28.39 ( class_Orderings_Oorder(T_a)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 28.12/28.39 => V_x != V_y ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_order__less__imp__not__eq2,axiom,
% 28.12/28.39 ! [V_y,V_x,T_a] :
% 28.12/28.39 ( class_Orderings_Oorder(T_a)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 28.12/28.39 => V_y != V_x ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_order__less__asym_H,axiom,
% 28.12/28.39 ! [V_b,V_a,T_a] :
% 28.12/28.39 ( class_Orderings_Opreorder(T_a)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 28.12/28.39 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_xt1_I9_J,axiom,
% 28.12/28.39 ! [V_a,V_b,T_a] :
% 28.12/28.39 ( class_Orderings_Oorder(T_a)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 28.12/28.39 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_ord__eq__less__trans,axiom,
% 28.12/28.39 ! [V_c,V_b,V_a,T_a] :
% 28.12/28.39 ( class_Orderings_Oord(T_a)
% 28.12/28.39 => ( V_a = V_b
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 28.12/28.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_xt1_I1_J,axiom,
% 28.12/28.39 ! [V_c,V_b,V_a,T_a] :
% 28.12/28.39 ( class_Orderings_Oorder(T_a)
% 28.12/28.39 => ( V_a = V_b
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b))
% 28.12/28.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_ord__less__eq__trans,axiom,
% 28.12/28.39 ! [V_c,V_b,V_a,T_a] :
% 28.12/28.39 ( class_Orderings_Oord(T_a)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 28.12/28.39 => ( V_b = V_c
% 28.12/28.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_xt1_I2_J,axiom,
% 28.12/28.39 ! [V_c,V_a,V_b,T_a] :
% 28.12/28.39 ( class_Orderings_Oorder(T_a)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 28.12/28.39 => ( V_b = V_c
% 28.12/28.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_order__less__trans,axiom,
% 28.12/28.39 ! [V_z,V_y,V_x,T_a] :
% 28.12/28.39 ( class_Orderings_Opreorder(T_a)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 28.12/28.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_xt1_I10_J,axiom,
% 28.12/28.39 ! [V_z,V_x,V_y,T_a] :
% 28.12/28.39 ( class_Orderings_Oorder(T_a)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 28.12/28.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_order__less__asym,axiom,
% 28.12/28.39 ! [V_y,V_x,T_a] :
% 28.12/28.39 ( class_Orderings_Opreorder(T_a)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 28.12/28.39 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_linorder__cases,axiom,
% 28.12/28.39 ! [V_y,V_x,T_a] :
% 28.12/28.39 ( class_Orderings_Olinorder(T_a)
% 28.12/28.39 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 28.12/28.39 => ( V_x != V_y
% 28.12/28.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_fun__upd__idem__iff,axiom,
% 28.12/28.39 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 28.12/28.39 ( c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2) = V_f_2
% 28.12/28.39 <=> hAPP(V_f_2,V_x_2) = V_y_2 ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_fun__upd__upd,axiom,
% 28.12/28.39 ! [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) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_fun__upd__same,axiom,
% 28.12/28.39 ! [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 ).
% 28.12/28.39
% 28.12/28.39 fof(fact_fun__upd__apply,axiom,
% 28.12/28.39 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
% 28.12/28.39 ( ( V_z_2 = V_x_2
% 28.12/28.39 => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_z_2) = V_y_2 )
% 28.12/28.39 & ( V_z_2 != V_x_2
% 28.12/28.39 => 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) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_fun__upd__twist,axiom,
% 28.12/28.39 ! [V_d_2,V_b_2,V_m_2,T_c,T_b,V_c_2,V_a_2] :
% 28.12/28.39 ( V_a_2 != V_c_2
% 28.12/28.39 => 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) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_fun__upd__other,axiom,
% 28.12/28.39 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
% 28.12/28.39 ( V_z_2 != V_x_2
% 28.12/28.39 => 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) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_fun__upd__idem,axiom,
% 28.12/28.39 ! [T_b,T_c,V_y_2,V_x_2,V_f_2] :
% 28.12/28.39 ( hAPP(V_f_2,V_x_2) = V_y_2
% 28.12/28.39 => c_Fun_Ofun__upd(T_c,T_b,V_f_2,V_x_2,V_y_2) = V_f_2 ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_lessThan__strict__subset__iff,axiom,
% 28.12/28.39 ! [V_n_2,V_m_2,T_b] :
% 28.12/28.39 ( class_Orderings_Olinorder(T_b)
% 28.12/28.39 => ( 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)))
% 28.12/28.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_n_2)) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_fun__upd__def,axiom,
% 28.12/28.39 ! [V_b_2,V_f_2,T_c,T_b,V_a_2,V_x_2] :
% 28.12/28.39 ( ( V_x_2 = V_a_2
% 28.12/28.39 => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_a_2,V_b_2),V_x_2) = V_b_2 )
% 28.12/28.39 & ( V_x_2 != V_a_2
% 28.12/28.39 => 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) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_atLeastatMost__psubset__iff,axiom,
% 28.12/28.39 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 28.12/28.39 ( class_Orderings_Oorder(T_b)
% 28.12/28.39 => ( 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)))
% 28.12/28.39 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 28.12/28.39 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2))
% 28.12/28.39 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
% 28.12/28.39 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_a_2))
% 28.12/28.39 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_d_2)) ) ) )
% 28.12/28.39 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2)) ) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_less__fun__def,axiom,
% 28.12/28.39 ! [V_g_2,V_f_2,T_b,T_c] :
% 28.12/28.39 ( class_Orderings_Oord(T_c)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 28.12/28.39 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 28.12/28.39 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_g_2),V_f_2)) ) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_linorder__not__less,axiom,
% 28.12/28.39 ! [V_y_2,V_x_2,T_b] :
% 28.12/28.39 ( class_Orderings_Olinorder(T_b)
% 28.12/28.39 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 28.12/28.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_linorder__not__le,axiom,
% 28.12/28.39 ! [V_y_2,V_x_2,T_b] :
% 28.12/28.39 ( class_Orderings_Olinorder(T_b)
% 28.12/28.39 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 28.12/28.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_linorder__le__less__linear,axiom,
% 28.12/28.39 ! [V_y,V_x,T_a] :
% 28.12/28.39 ( class_Orderings_Olinorder(T_a)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 28.12/28.39 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_order__less__le,axiom,
% 28.12/28.39 ! [V_y_2,V_x_2,T_b] :
% 28.12/28.39 ( class_Orderings_Oorder(T_b)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 28.12/28.39 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 28.12/28.39 & V_x_2 != V_y_2 ) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_less__le__not__le,axiom,
% 28.12/28.39 ! [V_y_2,V_x_2,T_b] :
% 28.12/28.39 ( class_Orderings_Opreorder(T_b)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 28.12/28.39 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 28.12/28.39 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_order__le__less,axiom,
% 28.12/28.39 ! [V_y_2,V_x_2,T_b] :
% 28.12/28.39 ( class_Orderings_Oorder(T_b)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 28.12/28.39 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 28.12/28.39 | V_x_2 = V_y_2 ) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_leI,axiom,
% 28.12/28.39 ! [V_y,V_x,T_a] :
% 28.12/28.39 ( class_Orderings_Olinorder(T_a)
% 28.12/28.39 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 28.12/28.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_not__leE,axiom,
% 28.12/28.39 ! [V_x,V_y,T_a] :
% 28.12/28.39 ( class_Orderings_Olinorder(T_a)
% 28.12/28.39 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 28.12/28.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_linorder__antisym__conv1,axiom,
% 28.12/28.39 ! [V_y_2,V_x_2,T_b] :
% 28.12/28.39 ( class_Orderings_Olinorder(T_b)
% 28.12/28.39 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 28.12/28.39 <=> V_x_2 = V_y_2 ) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_order__neq__le__trans,axiom,
% 28.12/28.39 ! [V_b,V_a,T_a] :
% 28.12/28.39 ( class_Orderings_Oorder(T_a)
% 28.12/28.39 => ( V_a != V_b
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 28.12/28.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_xt1_I12_J,axiom,
% 28.12/28.39 ! [V_b,V_a,T_a] :
% 28.12/28.39 ( class_Orderings_Oorder(T_a)
% 28.12/28.39 => ( V_a != V_b
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 28.12/28.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_leD,axiom,
% 28.12/28.39 ! [V_x,V_y,T_a] :
% 28.12/28.39 ( class_Orderings_Olinorder(T_a)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 28.12/28.39 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_order__less__imp__le,axiom,
% 28.12/28.39 ! [V_y,V_x,T_a] :
% 28.12/28.39 ( class_Orderings_Opreorder(T_a)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 28.12/28.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_linorder__antisym__conv2,axiom,
% 28.12/28.39 ! [V_y_2,V_x_2,T_b] :
% 28.12/28.39 ( class_Orderings_Olinorder(T_b)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 28.12/28.39 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 28.12/28.39 <=> V_x_2 = V_y_2 ) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_order__le__imp__less__or__eq,axiom,
% 28.12/28.39 ! [V_y,V_x,T_a] :
% 28.12/28.39 ( class_Orderings_Oorder(T_a)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 28.12/28.39 | V_x = V_y ) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_order__le__neq__trans,axiom,
% 28.12/28.39 ! [V_b,V_a,T_a] :
% 28.12/28.39 ( class_Orderings_Oorder(T_a)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 28.12/28.39 => ( V_a != V_b
% 28.12/28.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_xt1_I11_J,axiom,
% 28.12/28.39 ! [V_a,V_b,T_a] :
% 28.12/28.39 ( class_Orderings_Oorder(T_a)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 28.12/28.39 => ( V_a != V_b
% 28.12/28.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_order__less__le__trans,axiom,
% 28.12/28.39 ! [V_z,V_y,V_x,T_a] :
% 28.12/28.39 ( class_Orderings_Opreorder(T_a)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 28.12/28.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_xt1_I7_J,axiom,
% 28.12/28.39 ! [V_z,V_x,V_y,T_a] :
% 28.12/28.39 ( class_Orderings_Oorder(T_a)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 28.12/28.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_order__le__less__trans,axiom,
% 28.12/28.39 ! [V_z,V_y,V_x,T_a] :
% 28.12/28.39 ( class_Orderings_Opreorder(T_a)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 28.12/28.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_xt1_I8_J,axiom,
% 28.12/28.39 ! [V_z,V_x,V_y,T_a] :
% 28.12/28.39 ( class_Orderings_Oorder(T_a)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 28.12/28.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_psubsetD,axiom,
% 28.12/28.39 ! [V_c_2,V_B_2,V_A_2,T_b] :
% 28.12/28.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 28.12/28.39 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_not__psubset__empty,axiom,
% 28.12/28.39 ! [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)))) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_diff__eq__diff__less,axiom,
% 28.12/28.39 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 28.12/28.39 ( class_Groups_Oordered__ab__group__add(T_b)
% 28.12/28.39 => ( 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)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 28.12/28.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2)) ) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_less__supI1,axiom,
% 28.12/28.39 ! [V_b,V_a,V_x,T_a] :
% 28.12/28.39 ( class_Lattices_Osemilattice__sup(T_a)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 28.12/28.39 => 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))) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_less__supI2,axiom,
% 28.12/28.39 ! [V_a,V_b,V_x,T_a] :
% 28.12/28.39 ( class_Lattices_Osemilattice__sup(T_a)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 28.12/28.39 => 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))) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_less__infI1,axiom,
% 28.12/28.39 ! [V_b,V_x,V_a,T_a] :
% 28.12/28.39 ( class_Lattices_Osemilattice__inf(T_a)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 28.12/28.39 => 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)) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_less__infI2,axiom,
% 28.12/28.39 ! [V_a,V_x,V_b,T_a] :
% 28.12/28.39 ( class_Lattices_Osemilattice__inf(T_a)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 28.12/28.39 => 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)) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_neg__less__iff__less,axiom,
% 28.12/28.39 ! [V_a_2,V_b_2,T_b] :
% 28.12/28.39 ( class_Groups_Oordered__ab__group__add(T_b)
% 28.12/28.39 => ( 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)))
% 28.12/28.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 28.12/28.39
% 28.12/28.39 fof(fact_minus__less__iff,axiom,
% 28.12/28.39 ! [V_b_2,V_a_2,T_b] :
% 28.12/28.39 ( class_Groups_Oordered__ab__group__add(T_b)
% 28.12/28.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
% 28.12/28.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_less__minus__iff,axiom,
% 28.12/28.40 ! [V_b_2,V_a_2,T_b] :
% 28.12/28.40 ( class_Groups_Oordered__ab__group__add(T_b)
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)))
% 28.12/28.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_psubset__eq,axiom,
% 28.12/28.40 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.40 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.40 & V_A_2 != V_B_2 ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_subset__iff__psubset__eq,axiom,
% 28.12/28.40 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.40 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.40 | V_A_2 = V_B_2 ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_psubset__imp__subset,axiom,
% 28.12/28.40 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_psubset__subset__trans,axiom,
% 28.12/28.40 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 28.12/28.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 28.12/28.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_subset__psubset__trans,axiom,
% 28.12/28.40 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 28.12/28.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 28.12/28.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_atLeastLessThan__eq__iff,axiom,
% 28.12/28.40 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 28.12/28.40 ( class_Orderings_Olinorder(T_b)
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
% 28.12/28.40 => ( 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)
% 28.12/28.40 <=> ( V_a_2 = V_c_2
% 28.12/28.40 & V_b_2 = V_d_2 ) ) ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_atLeastLessThan__inj_I1_J,axiom,
% 28.12/28.40 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 28.12/28.40 ( class_Orderings_Olinorder(T_b)
% 28.12/28.40 => ( 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)
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
% 28.12/28.40 => V_a_2 = V_c_2 ) ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_atLeastLessThan__inj_I2_J,axiom,
% 28.12/28.40 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 28.12/28.40 ( class_Orderings_Olinorder(T_b)
% 28.12/28.40 => ( 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)
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
% 28.12/28.40 => V_b_2 = V_d_2 ) ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_less__Sup__iff,axiom,
% 28.12/28.40 ! [V_S_2,V_a_2,T_b] :
% 28.12/28.40 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.12/28.40 & class_Orderings_Olinorder(T_b) )
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_S_2)))
% 28.12/28.40 <=> ? [B_x] :
% 28.12/28.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 28.12/28.40 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),B_x)) ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_Inf__less__iff,axiom,
% 28.12/28.40 ! [V_a_2,V_S_2,T_b] :
% 28.12/28.40 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.12/28.40 & class_Orderings_Olinorder(T_b) )
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_S_2)),V_a_2))
% 28.12/28.40 <=> ? [B_x] :
% 28.12/28.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 28.12/28.40 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_a_2)) ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_less__SUP__iff,axiom,
% 28.12/28.40 ! [V_f_2,V_A_2,T_c,V_a_2,T_b] :
% 28.12/28.40 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.12/28.40 & class_Orderings_Olinorder(T_b) )
% 28.12/28.40 => ( 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)))
% 28.12/28.40 <=> ? [B_x] :
% 28.12/28.40 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 28.12/28.40 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(V_f_2,B_x))) ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_INF__less__iff,axiom,
% 28.12/28.40 ! [V_a_2,V_f_2,V_A_2,T_c,T_b] :
% 28.12/28.40 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.12/28.40 & class_Orderings_Olinorder(T_b) )
% 28.12/28.40 => ( 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))
% 28.12/28.40 <=> ? [B_x] :
% 28.12/28.40 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 28.12/28.40 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),V_a_2)) ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_gfp__upperbound,axiom,
% 28.12/28.40 ! [V_f_2,V_X_2,T_b] :
% 28.12/28.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),hAPP(V_f_2,V_X_2)))
% 28.12/28.40 => 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))) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_strict__mono__less,axiom,
% 28.12/28.40 ! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
% 28.12/28.40 ( ( class_Orderings_Oorder(T_c)
% 28.12/28.40 & class_Orderings_Olinorder(T_b) )
% 28.12/28.40 => ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
% 28.12/28.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_strict__monoD,axiom,
% 28.12/28.40 ! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
% 28.12/28.40 ( ( class_Orderings_Oorder(T_c)
% 28.12/28.40 & class_Orderings_Oorder(T_b) )
% 28.12/28.40 => ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 28.12/28.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_not__less__Least,axiom,
% 28.12/28.40 ! [V_P_2,V_k_2,T_b] :
% 28.12/28.40 ( class_Orderings_Owellorder(T_b)
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),c_Orderings_Oord__class_OLeast(T_b,V_P_2)))
% 28.12/28.40 => ~ hBOOL(hAPP(V_P_2,V_k_2)) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_def__gfp__unfold,axiom,
% 28.12/28.40 ! [V_f_2,V_A_2,T_b] :
% 28.12/28.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.12/28.40 => ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)
% 28.12/28.40 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 28.12/28.40 => V_A_2 = hAPP(V_f_2,V_A_2) ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_gfp__unfold,axiom,
% 28.12/28.40 ! [V_f_2,T_b] :
% 28.12/28.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.12/28.40 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 28.12/28.40 => 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)) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_atLeastatMost__empty,axiom,
% 28.12/28.40 ! [V_a_2,V_b_2,T_b] :
% 28.12/28.40 ( class_Orderings_Oorder(T_b)
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
% 28.12/28.40 => 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)) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_atLeastLessThan__empty__iff2,axiom,
% 28.12/28.40 ! [V_b_2,V_a_2,T_b] :
% 28.12/28.40 ( class_Orderings_Oorder(T_b)
% 28.12/28.40 => ( 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)
% 28.12/28.40 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_atLeastLessThan__empty__iff,axiom,
% 28.12/28.40 ! [V_b_2,V_a_2,T_b] :
% 28.12/28.40 ( class_Orderings_Oorder(T_b)
% 28.12/28.40 => ( 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))
% 28.12/28.40 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_lessThan__iff,axiom,
% 28.12/28.40 ! [V_k_2,V_i_2,T_b] :
% 28.12/28.40 ( class_Orderings_Oord(T_b)
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)))
% 28.12/28.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_i_2),V_k_2)) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_greaterThanAtMost__empty__iff2,axiom,
% 28.12/28.40 ! [V_l_2,V_k_2,T_b] :
% 28.12/28.40 ( class_Orderings_Oorder(T_b)
% 28.12/28.40 => ( 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)
% 28.12/28.40 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_greaterThanAtMost__empty__iff,axiom,
% 28.12/28.40 ! [V_l_2,V_k_2,T_b] :
% 28.12/28.40 ( class_Orderings_Oorder(T_b)
% 28.12/28.40 => ( 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))
% 28.12/28.40 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_greaterThan__iff,axiom,
% 28.12/28.40 ! [V_k_2,V_i_2,T_b] :
% 28.12/28.40 ( class_Orderings_Oord(T_b)
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)))
% 28.12/28.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_i_2)) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_weak__coinduct,axiom,
% 28.12/28.40 ! [V_f_2,V_X_2,V_a_2,T_b] :
% 28.12/28.40 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
% 28.12/28.40 => ( 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)))
% 28.12/28.40 => 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))) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_gfp__lemma3,axiom,
% 28.12/28.40 ! [V_f_2,T_b] :
% 28.12/28.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.12/28.40 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 28.12/28.40 => 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))) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_gfp__lemma2,axiom,
% 28.12/28.40 ! [V_f_2,T_b] :
% 28.12/28.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.12/28.40 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 28.12/28.40 => 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)))) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_weak__coinduct__image,axiom,
% 28.12/28.40 ! [V_f_2,V_g_2,T_c,V_X_2,V_a_2,T_b] :
% 28.12/28.40 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
% 28.12/28.40 => ( 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))))
% 28.12/28.40 => 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))) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_gfp__fun__UnI2,axiom,
% 28.12/28.40 ! [V_X_2,V_a_2,V_f_2,T_b] :
% 28.12/28.40 ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 28.12/28.40 => ( 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)))
% 28.12/28.40 => 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))))) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_ivl__disj__un_I15_J,axiom,
% 28.12/28.40 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 28.12/28.40 ( class_Orderings_Olinorder(T_b)
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 28.12/28.40 => 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) ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_ivl__disj__un_I16_J,axiom,
% 28.12/28.40 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 28.12/28.40 ( class_Orderings_Olinorder(T_b)
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
% 28.12/28.40 => 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) ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_def__coinduct,axiom,
% 28.12/28.40 ! [V_X_2,V_f_2,V_A_2,T_b] :
% 28.12/28.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.12/28.40 => ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)
% 28.12/28.40 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 28.12/28.40 => ( 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))))
% 28.12/28.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),V_A_2)) ) ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_coinduct__lemma,axiom,
% 28.12/28.40 ! [V_f_2,V_X_2,T_b] :
% 28.12/28.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.12/28.40 => ( 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)))))
% 28.12/28.40 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 28.12/28.40 => 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))))) ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_coinduct,axiom,
% 28.12/28.40 ! [V_X_2,V_f_2,T_b] :
% 28.12/28.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.12/28.40 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 28.12/28.40 => ( 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)))))
% 28.12/28.40 => 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))) ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_ivl__disj__un_I7_J,axiom,
% 28.12/28.40 ! [V_u_2,V_l_2,T_b] :
% 28.12/28.40 ( class_Orderings_Olinorder(T_b)
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 28.12/28.40 => 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) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_ivl__disj__un_I12_J,axiom,
% 28.12/28.40 ! [V_u_2,V_l_2,T_b] :
% 28.12/28.40 ( class_Orderings_Olinorder(T_b)
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 28.12/28.40 => 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) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_psubset__insert__iff,axiom,
% 28.12/28.40 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 28.12/28.40 ( 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)))
% 28.12/28.40 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 28.12/28.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
% 28.12/28.40 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 28.12/28.40 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.40 => 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)) )
% 28.12/28.40 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_coinduct3,axiom,
% 28.12/28.40 ! [V_X_2,V_a_2,V_f_2,T_b] :
% 28.12/28.40 ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
% 28.12/28.40 => ( 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))))))
% 28.12/28.40 => 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))) ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_def__coinduct3,axiom,
% 28.12/28.40 ! [V_X_2,V_a_2,V_f_2,T_b,V_A_2] :
% 28.12/28.40 ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 28.12/28.40 => ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
% 28.12/28.40 => ( 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)))))
% 28.12/28.40 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_coinduct3__lemma,axiom,
% 28.12/28.40 ! [V_f_2,V_X_2,T_b] :
% 28.12/28.40 ( 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))))))
% 28.12/28.40 => ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 28.12/28.40 => 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)))))) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_the__elem__def,axiom,
% 28.12/28.40 ! [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))))) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_fold__graph_H_Ointros_I2_J,axiom,
% 28.12/28.40 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 28.12/28.40 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.40 => ( 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)
% 28.12/28.40 => 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)) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_insert__partition,axiom,
% 28.12/28.40 ! [V_F_2,V_x_2,T_b] :
% 28.12/28.40 ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2))
% 28.12/28.40 => ( ! [B_x] :
% 28.12/28.40 ( 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)))
% 28.12/28.40 => ! [B_xa] :
% 28.12/28.40 ( 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)))
% 28.12/28.40 => ( B_x != B_xa
% 28.12/28.40 => 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)) ) ) )
% 28.12/28.40 => 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)) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_def__lfp__induct,axiom,
% 28.12/28.40 ! [V_P_2,V_f_2,V_A_2,T_b] :
% 28.12/28.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.12/28.40 => ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)
% 28.12/28.40 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 28.12/28.40 => ( 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))
% 28.12/28.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_A_2),V_P_2)) ) ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_lfp__induct,axiom,
% 28.12/28.40 ! [V_P_2,V_f_2,T_b] :
% 28.12/28.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.12/28.40 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 28.12/28.40 => ( 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))
% 28.12/28.40 => 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)) ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_inj__on__Un,axiom,
% 28.12/28.40 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( 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))
% 28.12/28.40 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 28.12/28.40 & c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 28.12/28.40 & 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)) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_inj__on__empty,axiom,
% 28.12/28.40 ! [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))) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_inj__uminus,axiom,
% 28.12/28.40 ! [V_A_2,T_b] :
% 28.12/28.40 ( class_Groups_Oordered__ab__group__add(T_b)
% 28.12/28.40 => c_Fun_Oinj__on(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b),V_A_2) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_psubset__trans,axiom,
% 28.12/28.40 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 28.12/28.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 28.12/28.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_inj__fun,axiom,
% 28.12/28.40 ! [T_d,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 28.12/28.40 => 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))) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_inj__on__def,axiom,
% 28.12/28.40 ! [V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 28.12/28.40 <=> ! [B_x] :
% 28.12/28.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.12/28.40 => ! [B_xa] :
% 28.12/28.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 28.12/28.40 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa)
% 28.12/28.40 => B_x = B_xa ) ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_inj__on__id2,axiom,
% 28.12/28.40 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_COMBI(T_b),V_A_2) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_lfp__const,axiom,
% 28.12/28.40 ! [V_t_2,T_b] :
% 28.12/28.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.12/28.40 => c_Inductive_Ocomplete__lattice__class_Olfp(T_b,hAPP(c_COMBK(T_b,T_b),V_t_2)) = V_t_2 ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_inj__on__contraD,axiom,
% 28.12/28.40 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 28.12/28.40 => ( V_x_2 != V_y_2
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 28.12/28.40 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_inj__on__iff,axiom,
% 28.12/28.40 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 28.12/28.40 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 28.12/28.40 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_inj__onD,axiom,
% 28.12/28.40 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 28.12/28.40 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 28.12/28.40 => V_x_2 = V_y_2 ) ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_subset__inj__on,axiom,
% 28.12/28.40 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.40 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_injD,axiom,
% 28.12/28.40 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 28.12/28.40 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 28.12/28.40 => V_x_2 = V_y_2 ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_inj__eq,axiom,
% 28.12/28.40 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 28.12/28.40 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 28.12/28.40 <=> V_x_2 = V_y_2 ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_inj__on__strict__subset,axiom,
% 28.12/28.40 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.40 => 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))) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_inj__on__Int,axiom,
% 28.12/28.40 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 28.12/28.40 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 28.12/28.40 => 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)) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_inj__on__diff,axiom,
% 28.12/28.40 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 28.12/28.40 => 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)) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_fold__graph_H_Oequations_I1_J,axiom,
% 28.12/28.40 ! [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) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_fold__graph_H_Ointros_I1_J,axiom,
% 28.12/28.40 ! [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) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_strict__mono__imp__inj__on,axiom,
% 28.12/28.40 ! [V_A_2,V_f_2,T_b,T_c] :
% 28.12/28.40 ( ( class_Orderings_Oorder(T_c)
% 28.12/28.40 & class_Orderings_Olinorder(T_b) )
% 28.12/28.40 => ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
% 28.12/28.40 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_lfp__lowerbound,axiom,
% 28.12/28.40 ! [V_A_2,V_f_2,T_b] :
% 28.12/28.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_A_2)),V_A_2))
% 28.12/28.40 => 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)) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_inj__image__eq__iff,axiom,
% 28.12/28.40 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 28.12/28.40 => ( 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)
% 28.12/28.40 <=> V_A_2 = V_B_2 ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_inj__on__Un__image__eq__iff,axiom,
% 28.12/28.40 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( 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))
% 28.12/28.40 => ( 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)
% 28.12/28.40 <=> V_A_2 = V_B_2 ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_lfp__unfold,axiom,
% 28.12/28.40 ! [V_f_2,T_b] :
% 28.12/28.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.12/28.40 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 28.12/28.40 => 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)) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_def__lfp__unfold,axiom,
% 28.12/28.40 ! [V_f_2,V_h_2,T_b] :
% 28.12/28.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.12/28.40 => ( V_h_2 = c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)
% 28.12/28.40 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 28.12/28.40 => V_h_2 = hAPP(V_f_2,V_h_2) ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_range__ex1__eq,axiom,
% 28.12/28.40 ! [V_b_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 28.12/28.40 => ( 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)))))
% 28.12/28.40 <=> ? [B_x] :
% 28.12/28.40 ( V_b_2 = hAPP(V_f_2,B_x)
% 28.12/28.40 & ! [B_y] :
% 28.12/28.40 ( V_b_2 = hAPP(V_f_2,B_y)
% 28.12/28.40 => B_y = B_x ) ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_inj__image__mem__iff,axiom,
% 28.12/28.40 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 28.12/28.40 => ( 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)))
% 28.12/28.40 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_inj__image__subset__iff,axiom,
% 28.12/28.40 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 28.12/28.40 => ( 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)))
% 28.12/28.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_inj__on__image__Int,axiom,
% 28.12/28.40 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 28.12/28.40 => 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)) ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_image__Int,axiom,
% 28.12/28.40 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 28.12/28.40 => 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)) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_inj__on__image__set__diff,axiom,
% 28.12/28.40 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 28.12/28.40 => 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)) ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_image__set__diff,axiom,
% 28.12/28.40 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 28.12/28.40 => 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)) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_inj__on__fun__updI,axiom,
% 28.12/28.40 ! [V_x_2,V_y_2,V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 28.12/28.40 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 28.12/28.40 => 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) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_inj__singleton,axiom,
% 28.12/28.40 ! [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))) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_lfp__lemma3,axiom,
% 28.12/28.40 ! [V_f_2,T_b] :
% 28.12/28.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.12/28.40 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 28.12/28.40 => 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)))) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_lfp__lemma2,axiom,
% 28.12/28.40 ! [V_f_2,T_b] :
% 28.12/28.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.12/28.40 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 28.12/28.40 => 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))) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_inj__image__Compl__subset,axiom,
% 28.12/28.40 ! [V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 28.12/28.40 => 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)))) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_inj__on__insert,axiom,
% 28.12/28.40 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))
% 28.12/28.40 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 28.12/28.40 & ~ 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))))))) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_inj__on__iff__surj,axiom,
% 28.12/28.40 ! [V_A_H_2,T_c,T_b,V_A_2] :
% 28.12/28.40 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.40 => ( ? [B_f] :
% 28.12/28.40 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2)
% 28.12/28.40 & 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)) )
% 28.12/28.40 <=> ? [B_g] : hAPP(c_Set_Oimage(T_c,T_b,B_g),V_A_H_2) = V_A_2 ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_enum__the__def,axiom,
% 28.12/28.40 ! [V_P_2,T_b] : c_Enum_Oenum__the(T_b,V_P_2) = c_HOL_OThe(T_b,V_P_2) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_flat__lub__def,axiom,
% 28.12/28.40 ! [V_b_2,V_A_2,T_b] :
% 28.12/28.40 ( ( 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)))))
% 28.12/28.40 => c_Partial__Function_Oflat__lub(T_b,V_b_2,V_A_2) = V_b_2 )
% 28.12/28.40 & ( ~ 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)))))
% 28.12/28.40 => 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)))))) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_fold__graph_H_Oequations_I2_J,axiom,
% 28.12/28.40 ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_c,T_b] :
% 28.12/28.40 ( 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))
% 28.12/28.40 <=> ( ( V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.40 & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 )
% 28.12/28.40 | ? [B_x,B_y] :
% 28.12/28.40 ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y)
% 28.12/28.40 & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a2_2))
% 28.12/28.40 & 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) ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_image__INT,axiom,
% 28.12/28.40 ! [V_j_2,V_B_2,V_A_2,T_d,V_C_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 28.12/28.40 => ( ! [B_x] :
% 28.12/28.40 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2))
% 28.12/28.40 => 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)) )
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_member(T_d),V_j_2),V_A_2))
% 28.12/28.40 => 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)) ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_the__inv__into__into,axiom,
% 28.12/28.40 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.40 => 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)) ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_inj__vimage__singleton,axiom,
% 28.12/28.40 ! [V_a_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 28.12/28.40 => 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))))) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_inj__on__Inter,axiom,
% 28.12/28.40 ! [V_f_2,T_c,T_b,V_S_2] :
% 28.12/28.40 ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
% 28.12/28.40 => ( ! [B_A] :
% 28.12/28.40 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_A),V_S_2))
% 28.12/28.40 => c_Fun_Oinj__on(T_b,T_c,V_f_2,B_A) )
% 28.12/28.40 => 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)) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_vimageI,axiom,
% 28.12/28.40 ! [T_c,V_B_2,T_b,V_b_2,V_a_2,V_f_2] :
% 28.12/28.40 ( hAPP(V_f_2,V_a_2) = V_b_2
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_B_2))
% 28.12/28.40 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2))) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_vimage__ident,axiom,
% 28.12/28.40 ! [V_Y_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ).
% 28.12/28.40
% 28.12/28.40 fof(fact_vimage__code,axiom,
% 28.12/28.40 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2),V_x_2))
% 28.12/28.40 <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_vimage__eq,axiom,
% 28.12/28.40 ! [V_B_2,V_f_2,T_c,V_a_2,T_b] :
% 28.12/28.40 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)))
% 28.12/28.40 <=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_B_2)) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_vimageD,axiom,
% 28.12/28.40 ! [V_A_2,V_f_2,T_c,V_a_2,T_b] :
% 28.12/28.40 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)))
% 28.12/28.40 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_A_2)) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_vimageI2,axiom,
% 28.12/28.40 ! [T_c,V_A_2,V_a_2,V_f_2,T_b] :
% 28.12/28.40 ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2))
% 28.12/28.40 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_vimage__empty,axiom,
% 28.12/28.40 ! [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)) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_vimage__mono,axiom,
% 28.12/28.40 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
% 28.12/28.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.40 => 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))) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_vimage__UNIV,axiom,
% 28.12/28.40 ! [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)) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_vimage__Un,axiom,
% 28.12/28.40 ! [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)) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_vimage__Int,axiom,
% 28.12/28.40 ! [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)) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_vimage__Diff,axiom,
% 28.12/28.40 ! [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)) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_vimage__Compl,axiom,
% 28.12/28.40 ! [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)) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_vimage__UN,axiom,
% 28.12/28.40 ! [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)) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_vimage__INT,axiom,
% 28.12/28.40 ! [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)) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_image__vimage__subset,axiom,
% 28.12/28.40 ! [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)) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_surj__image__vimage__eq,axiom,
% 28.12/28.40 ! [V_A_2,V_f_2,T_b,T_c] :
% 28.12/28.40 ( 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))
% 28.12/28.40 => 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 ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_vimage__Union,axiom,
% 28.12/28.40 ! [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)) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_vimage__singleton__eq,axiom,
% 28.12/28.40 ! [V_b_2,V_f_2,T_c,V_a_2,T_b] :
% 28.12/28.40 ( 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))))))
% 28.12/28.40 <=> hAPP(V_f_2,V_a_2) = V_b_2 ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_vimage__insert,axiom,
% 28.12/28.40 ! [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)) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_vimage__subsetD,axiom,
% 28.12/28.40 ! [V_A_2,V_B_2,V_f_2,T_b,T_c] :
% 28.12/28.40 ( 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))
% 28.12/28.40 => ( 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))
% 28.12/28.40 => 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))) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_image__vimage__eq,axiom,
% 28.12/28.40 ! [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)))) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_inj__vimage__image__eq,axiom,
% 28.12/28.40 ! [V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 28.12/28.40 => 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 ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_vimage__const,axiom,
% 28.12/28.40 ! [T_c,V_A_2,V_c_2,T_b] :
% 28.12/28.40 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 28.12/28.40 => 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)) )
% 28.12/28.40 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 28.12/28.40 => 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)) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_vimage__eq__UN,axiom,
% 28.12/28.40 ! [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))))) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_the__inv__into__f__f,axiom,
% 28.12/28.40 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.40 => 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 ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_the__inv__into__f__eq,axiom,
% 28.12/28.40 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 28.12/28.40 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.40 => hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_the__inv__f__f,axiom,
% 28.12/28.40 ! [V_x_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 28.12/28.40 => 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 ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_the__inv__into__onto,axiom,
% 28.12/28.40 ! [V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 28.12/28.40 => 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 ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_inj__on__the__inv__into,axiom,
% 28.12/28.40 ! [V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 28.12/28.40 => 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)) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_vimage__subsetI,axiom,
% 28.12/28.40 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 28.12/28.40 => ( 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)))
% 28.12/28.40 => 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)) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_the__inv__into__def,axiom,
% 28.12/28.40 ! [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))) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_vimage__if,axiom,
% 28.12/28.40 ! [V_B_2,T_c,V_d_2,V_A_2,V_c_2,T_b] :
% 28.12/28.40 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 28.12/28.40 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 28.12/28.40 => 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)) )
% 28.12/28.40 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 28.12/28.40 => 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 ) ) )
% 28.12/28.40 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 28.12/28.40 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 28.12/28.40 => 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) )
% 28.12/28.40 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 28.12/28.40 => 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)) ) ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_f__the__inv__into__f,axiom,
% 28.12/28.40 ! [V_y_2,V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 28.12/28.40 => 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 ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_order__fun_I2_J,axiom,
% 28.12/28.40 ! [V_g_2,V_f_2,T_b,T_c] :
% 28.12/28.40 ( ( class_Orderings_Oorder(T_c)
% 28.12/28.40 & class_Enum_Oenum(T_b) )
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 28.12/28.40 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 28.12/28.40 & 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)))) ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_inj__on__INTER,axiom,
% 28.12/28.40 ! [V_A_2,V_f_2,T_d,T_c,T_b,V_I_2] :
% 28.12/28.40 ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.40 => ( ! [B_i] :
% 28.12/28.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_I_2))
% 28.12/28.40 => c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(V_A_2,B_i)) )
% 28.12/28.40 => 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)) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_fun__left__comm__idem__remove,axiom,
% 28.12/28.40 ! [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))))) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_the__eq__trivial,axiom,
% 28.12/28.40 ! [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 ).
% 28.12/28.40
% 28.12/28.40 fof(fact_the__sym__eq__trivial,axiom,
% 28.12/28.40 ! [V_x_2,T_b] : c_HOL_OThe(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 28.12/28.40
% 28.12/28.40 fof(fact_Diff1__fold__graph,axiom,
% 28.12/28.40 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( 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))
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.40 => 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))) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_rangeE,axiom,
% 28.12/28.40 ! [V_f_2,T_c,V_b_2,T_b] :
% 28.12/28.40 ( 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)))))
% 28.12/28.40 => ~ ! [B_x] : V_b_2 != hAPP(V_f_2,B_x) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_mk__less__def,axiom,
% 28.12/28.40 ! [V_y_2,V_x_2,V_R_2,T_b] :
% 28.12/28.40 ( c_Partial__Function_Omk__less(T_b,V_R_2,V_x_2,V_y_2)
% 28.12/28.40 <=> ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 28.12/28.40 & ~ hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_exists__code,axiom,
% 28.12/28.40 ! [V_P_2,T_b] :
% 28.12/28.40 ( class_Enum_Oenum(T_b)
% 28.12/28.40 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 28.12/28.40 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_P_2)) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_enum__ex,axiom,
% 28.12/28.40 ! [V_P_2,T_b] :
% 28.12/28.40 ( class_Enum_Oenum(T_b)
% 28.12/28.40 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_P_2))
% 28.12/28.40 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom,
% 28.12/28.40 ! [V_z_2,V_x_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 28.12/28.40 => 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) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom,
% 28.12/28.40 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 28.12/28.40 => 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)) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_fold__graph_Oequations_I1_J,axiom,
% 28.12/28.40 ! [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)) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_fold__graph_OemptyI,axiom,
% 28.12/28.40 ! [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)) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_empty__fold__graphE,axiom,
% 28.12/28.40 ! [V_x_2,V_z_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( 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))
% 28.12/28.40 => V_x_2 = V_z_2 ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_fun__left__comm__idem__insert,axiom,
% 28.12/28.40 ! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_fun__left__comm__idem__sup,axiom,
% 28.12/28.40 ! [T_b] :
% 28.12/28.40 ( class_Lattices_Osemilattice__sup(T_b)
% 28.12/28.40 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_fun__left__comm__idem__inf,axiom,
% 28.12/28.40 ! [T_b] :
% 28.12/28.40 ( class_Lattices_Osemilattice__inf(T_b)
% 28.12/28.40 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_fold__graph_OinsertI,axiom,
% 28.12/28.40 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 28.12/28.40 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.40 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 28.12/28.40 => 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))) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_fold1Set_Ointros,axiom,
% 28.12/28.40 ! [V_x_2,V_A_2,V_a_2,V_f_2,T_b] :
% 28.12/28.40 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,V_a_2,V_A_2),V_x_2))
% 28.12/28.40 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.12/28.40 => 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)) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_fold__graph__permute__diff,axiom,
% 28.12/28.40 ! [V_a_2,V_x_2,V_A_2,V_b_2,T_b] :
% 28.12/28.40 ( class_Groups_Oab__semigroup__mult(T_b)
% 28.12/28.40 => ( 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))
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.12/28.40 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 28.12/28.40 => 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)) ) ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_vimage__subset__eq,axiom,
% 28.12/28.40 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( 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)))
% 28.12/28.40 => ( 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))
% 28.12/28.40 <=> 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))) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_psubset__imp__ex__mem,axiom,
% 28.12/28.40 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.40 => ? [B_b] : 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))) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_the__inv__into__comp,axiom,
% 28.12/28.40 ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] :
% 28.12/28.40 ( 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))
% 28.12/28.40 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2)
% 28.12/28.40 => ( 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))))
% 28.12/28.40 => 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) ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_override__on__def,axiom,
% 28.12/28.40 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
% 28.12/28.40 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.12/28.40 => 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) )
% 28.12/28.40 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.12/28.40 => 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) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_vimage__inter__cong,axiom,
% 28.12/28.40 ! [V_y_2,T_c,V_g_2,V_f_2,V_S_2,T_b] :
% 28.12/28.40 ( ! [B_w] :
% 28.12/28.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_w),V_S_2))
% 28.12/28.40 => hAPP(V_f_2,B_w) = hAPP(V_g_2,B_w) )
% 28.12/28.40 => 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_y_2)),V_S_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_g_2),V_y_2)),V_S_2) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_folding__one_Osingleton,axiom,
% 28.12/28.40 ! [V_x_2,V_F_2,V_f_2,T_b] :
% 28.12/28.40 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 28.12/28.40 => 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 ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_K__record__comp,axiom,
% 28.12/28.40 ! [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 ).
% 28.12/28.40
% 28.12/28.40 fof(fact_o__eq__dest__lhs,axiom,
% 28.12/28.40 ! [V_v_2,V_c_2,V_b_2,V_a_2,T_b,T_c,T_d] :
% 28.12/28.40 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = V_c_2
% 28.12/28.40 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_times_Oidem,axiom,
% 28.12/28.40 ! [V_a,T_a] :
% 28.12/28.40 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 28.12/28.40 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_mult__idem,axiom,
% 28.12/28.40 ! [V_x,T_a] :
% 28.12/28.40 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 28.12/28.40 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_mult__left__idem,axiom,
% 28.12/28.40 ! [V_b,V_a,T_a] :
% 28.12/28.40 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 28.12/28.40 => 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) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 28.12/28.40 ! [V_c,V_b,V_a,T_a] :
% 28.12/28.40 ( class_Groups_Oab__semigroup__mult(T_a)
% 28.12/28.40 => 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)) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_o__def,axiom,
% 28.12/28.40 ! [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)) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_o__assoc,axiom,
% 28.12/28.40 ! [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) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_o__apply,axiom,
% 28.12/28.40 ! [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)) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_o__eq__dest,axiom,
% 28.12/28.40 ! [V_v_2,V_d_2,V_c_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
% 28.12/28.40 ( 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)
% 28.12/28.40 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,hAPP(V_d_2,V_v_2)) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_o__eq__elim,axiom,
% 28.12/28.40 ! [V_d_2,V_c_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
% 28.12/28.40 ( 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)
% 28.12/28.40 => ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_c_2,hAPP(V_d_2,B_v)) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_bij__betw__comp__iff,axiom,
% 28.12/28.40 ! [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] :
% 28.12/28.40 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 28.12/28.40 => ( c_Fun_Obij__betw(T_c,T_d,V_f_H_2,V_A_H_2,V_A_H_H_2)
% 28.12/28.40 <=> 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) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_bij__betw__trans,axiom,
% 28.12/28.40 ! [V_C_2,V_g_2,T_d,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 28.12/28.40 => ( c_Fun_Obij__betw(T_c,T_d,V_g_2,V_B_2,V_C_2)
% 28.12/28.40 => 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) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_bij__comp,axiom,
% 28.12/28.40 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 28.12/28.40 ( 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)))
% 28.12/28.40 => ( 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)))
% 28.12/28.40 => 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))) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_bij__betw__comp__iff2,axiom,
% 28.12/28.40 ! [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] :
% 28.12/28.40 ( c_Fun_Obij__betw(T_b,T_c,V_f_H_2,V_A_H_2,V_A_H_H_2)
% 28.12/28.40 => ( 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))
% 28.12/28.40 => ( c_Fun_Obij__betw(T_d,T_b,V_f_2,V_A_2,V_A_H_2)
% 28.12/28.40 <=> 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) ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_image__compose,axiom,
% 28.12/28.40 ! [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)) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_inj__on__imageI2,axiom,
% 28.12/28.40 ! [V_A_2,V_f_2,V_f_H_2,T_d,T_c,T_b] :
% 28.12/28.40 ( 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)
% 28.12/28.40 => c_Fun_Oinj__on(T_b,T_d,V_f_2,V_A_2) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_bij__betw__empty2,axiom,
% 28.12/28.40 ! [V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( 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)))
% 28.12/28.40 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_bij__betw__empty1,axiom,
% 28.12/28.40 ! [V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( 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)
% 28.12/28.40 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_fun__upd__comp,axiom,
% 28.12/28.40 ! [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)) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_vimage__compose,axiom,
% 28.12/28.40 ! [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)) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_bij__betw__imp__inj__on,axiom,
% 28.12/28.40 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 28.12/28.40 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom,
% 28.12/28.40 ! [V_x_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 28.12/28.40 => 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) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_bij__betw__the__inv__into,axiom,
% 28.12/28.40 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 28.12/28.40 => 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) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_fun__left__comm__idem,axiom,
% 28.12/28.40 ! [T_b] :
% 28.12/28.40 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 28.12/28.40 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_comp__surj,axiom,
% 28.12/28.40 ! [V_g_2,T_d,V_f_2,T_b,T_c] :
% 28.12/28.40 ( 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))
% 28.12/28.40 => ( 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))
% 28.12/28.40 => 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)) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_UN__o,axiom,
% 28.12/28.40 ! [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) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_inj__comp,axiom,
% 28.12/28.40 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 28.12/28.40 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))
% 28.12/28.40 => 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))) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_inj__on__imageI,axiom,
% 28.12/28.40 ! [V_A_2,V_f_2,V_g_2,T_d,T_c,T_b] :
% 28.12/28.40 ( 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)
% 28.12/28.40 => 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)) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_comp__inj__on,axiom,
% 28.12/28.40 ! [V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 28.12/28.40 => ( 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))
% 28.12/28.40 => 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) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_comp__inj__on__iff,axiom,
% 28.12/28.40 ! [V_f_H_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 28.12/28.40 => ( 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))
% 28.12/28.40 <=> 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) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_bij__betw__subset,axiom,
% 28.12/28.40 ! [V_B_H_2,V_B_2,V_A_H_2,V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 28.12/28.40 => ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2) = V_B_H_2
% 28.12/28.40 => c_Fun_Obij__betw(T_b,T_c,V_f_2,V_B_2,V_B_H_2) ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_bij__betw__imp__surj,axiom,
% 28.12/28.40 ! [V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( 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)))
% 28.12/28.40 => 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)) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_bij__is__surj,axiom,
% 28.12/28.40 ! [V_f_2,T_c,T_b] :
% 28.12/28.40 ( 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)))
% 28.12/28.40 => 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)) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_bij__is__inj,axiom,
% 28.12/28.40 ! [V_f_2,T_c,T_b] :
% 28.12/28.40 ( 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)))
% 28.12/28.40 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_inj__on__imp__bij__betw,axiom,
% 28.12/28.40 ! [V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 28.12/28.40 => 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)) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_bij__betw__def,axiom,
% 28.12/28.40 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 28.12/28.40 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 28.12/28.40 & hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = V_B_2 ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_fold1Set__nonempty,axiom,
% 28.12/28.40 ! [V_x_2,V_A_2,V_f_2,T_b] :
% 28.12/28.40 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2),V_x_2))
% 28.12/28.40 => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_empty__fold1SetE,axiom,
% 28.12/28.40 ! [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)) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_bij__betw__combine,axiom,
% 28.12/28.40 ! [V_D_2,V_C_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 28.12/28.40 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_C_2,V_D_2)
% 28.12/28.40 => ( 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))
% 28.12/28.40 => 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)) ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_bij__betw__Disj__Un,axiom,
% 28.12/28.40 ! [V_f_2,V_B_H_2,V_A_H_2,T_c,V_B_2,V_A_2,T_b] :
% 28.12/28.40 ( 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))
% 28.12/28.40 => ( 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))
% 28.12/28.40 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 28.12/28.40 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_B_2,V_B_H_2)
% 28.12/28.40 => 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)) ) ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_bij__def,axiom,
% 28.12/28.40 ! [V_f_2,T_c,T_b] :
% 28.12/28.40 ( 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)))
% 28.12/28.40 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 28.12/28.40 & 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)) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_bijI,axiom,
% 28.12/28.40 ! [V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 28.12/28.40 => ( 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))
% 28.12/28.40 => 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))) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_override__on__apply__in,axiom,
% 28.12/28.40 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
% 28.12/28.40 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.12/28.40 => 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) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_override__on__apply__notin,axiom,
% 28.12/28.40 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
% 28.12/28.40 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.12/28.40 => 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) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_bij__image__Compl__eq,axiom,
% 28.12/28.40 ! [V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( 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)))
% 28.12/28.40 => 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)) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_override__on__emptyset,axiom,
% 28.12/28.40 ! [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 ).
% 28.12/28.40
% 28.12/28.40 fof(fact_fold__graph__insert__swap,axiom,
% 28.12/28.40 ! [V_z_2,V_y_2,V_A_2,V_b_2,T_b] :
% 28.12/28.40 ( class_Groups_Oab__semigroup__mult(T_b)
% 28.12/28.40 => ( 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))
% 28.12/28.40 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 28.12/28.40 => 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))) ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_bij__image__INT,axiom,
% 28.12/28.40 ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] :
% 28.12/28.40 ( 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)))
% 28.12/28.40 => 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)) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_fold1Set__sing,axiom,
% 28.12/28.40 ! [V_b_2,V_a_2,V_f_2,T_b] :
% 28.12/28.40 ( 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))
% 28.12/28.40 <=> V_a_2 = V_b_2 ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_minus__mult__right,axiom,
% 28.12/28.40 ! [V_b,V_a,T_a] :
% 28.12/28.40 ( class_Rings_Oring(T_a)
% 28.12/28.40 => 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)) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_minus__mult__left,axiom,
% 28.12/28.40 ! [V_b,V_a,T_a] :
% 28.12/28.40 ( class_Rings_Oring(T_a)
% 28.12/28.40 => 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) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_minus__mult__commute,axiom,
% 28.12/28.40 ! [V_b,V_a,T_a] :
% 28.12/28.40 ( class_Rings_Oring(T_a)
% 28.12/28.40 => 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)) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_minus__mult__minus,axiom,
% 28.12/28.40 ! [V_b,V_a,T_a] :
% 28.12/28.40 ( class_Rings_Oring(T_a)
% 28.12/28.40 => 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) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_square__eq__iff,axiom,
% 28.12/28.40 ! [V_b_2,V_a_2,T_b] :
% 28.12/28.40 ( class_Rings_Oidom(T_b)
% 28.12/28.40 => ( 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)
% 28.12/28.40 <=> ( V_a_2 = V_b_2
% 28.12/28.40 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_folding__one_Oremove,axiom,
% 28.12/28.40 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 28.12/28.40 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 28.12/28.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.40 => ( ( 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))
% 28.12/28.40 => hAPP(V_F_2,V_A_2) = V_x_2 )
% 28.12/28.40 & ( 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))
% 28.12/28.40 => 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)))))) ) ) ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_fold1Set_Oequations,axiom,
% 28.12/28.40 ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_b] :
% 28.12/28.40 ( 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))
% 28.12/28.40 <=> ? [B_a,B_A] :
% 28.12/28.40 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A)
% 28.12/28.40 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_a3_2))
% 28.12/28.40 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_insert__fold1SetE,axiom,
% 28.12/28.40 ! [V_x_2,V_X_2,V_a_2,V_f_2,T_b] :
% 28.12/28.40 ( 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))
% 28.12/28.40 => ~ ! [B_a,B_A] :
% 28.12/28.40 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A)
% 28.12/28.40 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_x_2))
% 28.12/28.40 => hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_finite_OemptyI,axiom,
% 28.12/28.40 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_finite_OinsertI,axiom,
% 28.12/28.40 ! [V_a_2,V_A_2,T_b] :
% 28.12/28.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.40 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_finite__imageI,axiom,
% 28.12/28.40 ! [V_h_2,T_c,V_F_2,T_b] :
% 28.12/28.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 28.12/28.40 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2))) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_finite__Int,axiom,
% 28.12/28.40 ! [V_G_2,V_F_2,T_b] :
% 28.12/28.40 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 28.12/28.40 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_G_2)) )
% 28.12/28.40 => 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))) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_finite__Diff,axiom,
% 28.12/28.40 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.40 => 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))) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_finite__Inter,axiom,
% 28.12/28.40 ! [V_M_2,T_b] :
% 28.12/28.40 ( ? [B_x] :
% 28.12/28.40 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_M_2))
% 28.12/28.40 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)) )
% 28.12/28.40 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_M_2))) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_finite__INT,axiom,
% 28.12/28.40 ! [V_A_2,T_c,V_I_2,T_b] :
% 28.12/28.40 ( ? [B_x] :
% 28.12/28.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 28.12/28.40 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x))) )
% 28.12/28.40 => 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))) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_finite__Pow__iff,axiom,
% 28.12/28.40 ! [V_A_2,T_b] :
% 28.12/28.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)))
% 28.12/28.40 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_finite__code,axiom,
% 28.12/28.40 ! [V_A_2,T_b] :
% 28.12/28.40 ( class_Finite__Set_Ofinite(T_b)
% 28.12/28.40 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_finite,axiom,
% 28.12/28.40 ! [V_A_2,T_b] :
% 28.12/28.40 ( class_Finite__Set_Ofinite(T_b)
% 28.12/28.40 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_finite__UnionD,axiom,
% 28.12/28.40 ! [V_A_2,T_b] :
% 28.12/28.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))
% 28.12/28.40 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_finite__Prod__UNIV,axiom,
% 28.12/28.40 ! [T_c,T_b] :
% 28.12/28.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 28.12/28.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
% 28.12/28.40 => 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)))) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_finite__Plus__UNIV__iff,axiom,
% 28.12/28.40 ! [T_c,T_b] :
% 28.12/28.40 ( 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))))
% 28.12/28.40 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 28.12/28.40 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_finite__option__UNIV,axiom,
% 28.12/28.40 ! [T_b] :
% 28.12/28.40 ( 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))))
% 28.12/28.40 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_finite_Oequations_I1_J,axiom,
% 28.12/28.40 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_finite__insert,axiom,
% 28.12/28.40 ! [V_A_2,V_a_2,T_b] :
% 28.12/28.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)))
% 28.12/28.40 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_finite__fun__UNIVD2,axiom,
% 28.12/28.40 ! [T_c,T_b] :
% 28.12/28.40 ( 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))))
% 28.12/28.40 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_finite__subset,axiom,
% 28.12/28.40 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.40 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_rev__finite__subset,axiom,
% 28.12/28.40 ! [V_A_2,V_B_2,T_b] :
% 28.12/28.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.40 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_finite__UNIV,axiom,
% 28.12/28.40 ! [T_b] :
% 28.12/28.40 ( class_Finite__Set_Ofinite(T_b)
% 28.12/28.40 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_finite__Un,axiom,
% 28.12/28.40 ! [V_G_2,V_F_2,T_b] :
% 28.12/28.40 ( 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)))
% 28.12/28.40 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 28.12/28.40 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_G_2)) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_finite__UnI,axiom,
% 28.12/28.40 ! [V_G_2,V_F_2,T_b] :
% 28.12/28.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 28.12/28.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_G_2))
% 28.12/28.40 => 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))) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_finite__Diff2,axiom,
% 28.12/28.40 ! [V_A_2,V_B_2,T_b] :
% 28.12/28.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.40 => ( 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)))
% 28.12/28.40 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_finite__UN,axiom,
% 28.12/28.40 ! [V_B_2,T_c,V_A_2,T_b] :
% 28.12/28.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.40 => ( 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)))
% 28.12/28.40 <=> ! [B_x] :
% 28.12/28.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.12/28.40 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_bij__betw__finite,axiom,
% 28.12/28.40 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 28.12/28.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.40 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_fold__graph__imp__finite,axiom,
% 28.12/28.40 ! [V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
% 28.12/28.40 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_finite__surj,axiom,
% 28.12/28.40 ! [V_f_2,V_B_2,T_c,V_A_2,T_b] :
% 28.12/28.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.40 => ( 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)))
% 28.12/28.40 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_finite__Diff__insert,axiom,
% 28.12/28.40 ! [V_B_2,V_a_2,V_A_2,T_b] :
% 28.12/28.40 ( 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))))
% 28.12/28.40 <=> 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))) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_finite__imageD,axiom,
% 28.12/28.40 ! [V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 28.12/28.40 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2)
% 28.12/28.40 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_finite__compl,axiom,
% 28.12/28.40 ! [V_A_2,T_b] :
% 28.12/28.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 28.12/28.40 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_finite__range__imageI,axiom,
% 28.12/28.40 ! [V_f_2,T_d,V_g_2,T_c,T_b] :
% 28.12/28.40 ( 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)))))
% 28.12/28.40 => 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))))) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_linorder__neqE__linordered__idom,axiom,
% 28.12/28.40 ! [V_y,V_x,T_a] :
% 28.12/28.40 ( class_Rings_Olinordered__idom(T_a)
% 28.12/28.40 => ( V_x != V_y
% 28.12/28.40 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 28.12/28.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_finite__surj__inj,axiom,
% 28.12/28.40 ! [V_f_2,V_A_2,T_b] :
% 28.12/28.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.40 => ( 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)))
% 28.12/28.40 => c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_endo__inj__surj,axiom,
% 28.12/28.40 ! [V_f_2,V_A_2,T_b] :
% 28.12/28.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.40 => ( 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))
% 28.12/28.40 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2)
% 28.12/28.40 => hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2) = V_A_2 ) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_finite__UNIV__surj__inj,axiom,
% 28.12/28.40 ! [V_f_2,T_b] :
% 28.12/28.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 28.12/28.40 => ( 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))
% 28.12/28.40 => c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 28.12/28.40
% 28.12/28.40 fof(fact_finite__UNIV__inj__surj,axiom,
% 28.12/28.40 ! [V_f_2,T_b] :
% 28.12/28.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 28.12/28.41 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 28.12/28.41 => 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)) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_finite__vimageD,axiom,
% 28.12/28.41 ! [V_F_2,V_h_2,T_c,T_b] :
% 28.12/28.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2)))
% 28.12/28.41 => ( 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))
% 28.12/28.41 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_finite__vimageI,axiom,
% 28.12/28.41 ! [V_h_2,T_c,V_F_2,T_b] :
% 28.12/28.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 28.12/28.41 => ( c_Fun_Oinj__on(T_c,T_b,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 28.12/28.41 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Ovimage(T_c,T_b,V_h_2),V_F_2))) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_finite__vimage__iff,axiom,
% 28.12/28.41 ! [V_F_2,V_h_2,T_c,T_b] :
% 28.12/28.41 ( 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)))
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2)))
% 28.12/28.41 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_folding__one_Oinsert,axiom,
% 28.12/28.41 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 28.12/28.41 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.41 => 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)) ) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_folding__one_Oinsert__remove,axiom,
% 28.12/28.41 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 28.12/28.41 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( ( 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))
% 28.12/28.41 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 28.12/28.41 & ( 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))
% 28.12/28.41 => 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)))))) ) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_folding__one_Ounion__inter,axiom,
% 28.12/28.41 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 28.12/28.41 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.41 => ( 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))
% 28.12/28.41 => 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)) ) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_folding__one_Ounion__disjoint,axiom,
% 28.12/28.41 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 28.12/28.41 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.41 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.41 => ( 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))
% 28.12/28.41 => 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)) ) ) ) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_folding_Oremove,axiom,
% 28.12/28.41 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 28.12/28.41 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.41 => 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)) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_folding__image__simple_Oremove,axiom,
% 28.12/28.41 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 28.12/28.41 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 28.12/28.41 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 28.12/28.41 => 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)))))) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_folding__image_Oreindex,axiom,
% 28.12/28.41 ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 28.12/28.41 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 28.12/28.41 => ( c_Fun_Oinj__on(T_c,T_c,V_h_2,V_A_2)
% 28.12/28.41 => 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) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_folding_Ounion,axiom,
% 28.12/28.41 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 28.12/28.41 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.41 => ( 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))
% 28.12/28.41 => 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)) ) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_folding_Oinsert__remove,axiom,
% 28.12/28.41 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 28.12/28.41 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => 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)) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_folding__image__simple_Ounion__disjoint,axiom,
% 28.12/28.41 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 28.12/28.41 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 28.12/28.41 => ( 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))
% 28.12/28.41 => 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)) ) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_folding__image__simple_Oinsert__remove,axiom,
% 28.12/28.41 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 28.12/28.41 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 28.12/28.41 => 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)))))) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_Inf__fin_Oremove,axiom,
% 28.12/28.41 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.41 ( class_Lattices_Olattice(T_b)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.41 => ( ( 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))
% 28.12/28.41 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = V_x_2 )
% 28.12/28.41 & ( 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))
% 28.12/28.41 => 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)))))) ) ) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_folding_Ocommute__comps_I1_J,axiom,
% 28.12/28.41 ! [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] :
% 28.12/28.41 ( c_Finite__Set_Ofolding(T_b,T_c,V_fa_2,V_F_2)
% 28.12/28.41 => 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) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_folding_Ocommute__comp,axiom,
% 28.12/28.41 ! [V_x_2,V_y_2,V_F_2,V_f_2,T_c,T_b] :
% 28.12/28.41 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 28.12/28.41 => 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)) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_folding_Ocommute__left__comp,axiom,
% 28.12/28.41 ! [V_g_2,V_x_2,V_y_2,T_d,V_F_2,V_f_2,T_c,T_b] :
% 28.12/28.41 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 28.12/28.41 => 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)) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_folding__image__simple_Oempty,axiom,
% 28.12/28.41 ! [V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 28.12/28.41 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 28.12/28.41 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_Inf__fin_Osingleton,axiom,
% 28.12/28.41 ! [V_x_2,T_b] :
% 28.12/28.41 ( class_Lattices_Olattice(T_b)
% 28.12/28.41 => 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 ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_folding__image_Odistrib,axiom,
% 28.12/28.41 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 28.12/28.41 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 28.12/28.41 => 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)) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_folding_Ocommute__left__comp_H_H,axiom,
% 28.12/28.41 ! [V_g_2,T_d,V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 28.12/28.41 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.41 => 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)) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_folding_Ocommute__comp_H_H,axiom,
% 28.12/28.41 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 28.12/28.41 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.41 => 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)) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_folding_Ocommute__left__comp_H,axiom,
% 28.12/28.41 ! [V_g_2,V_x_2,T_d,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 28.12/28.41 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => 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)) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_folding_Ocommute__comp_H,axiom,
% 28.12/28.41 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 28.12/28.41 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => 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)) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_sup__Inf__absorb,axiom,
% 28.12/28.41 ! [V_a_2,V_A_2,T_b] :
% 28.12/28.41 ( class_Lattices_Olattice(T_b)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.12/28.41 => 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 ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_Inf__fin_Oin__idem,axiom,
% 28.12/28.41 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.41 ( class_Lattices_Olattice(T_b)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.41 => 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) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_Inf__fin__Inf,axiom,
% 28.12/28.41 ! [V_A_2,T_b] :
% 28.12/28.41 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.41 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_Inf__fin_Oinsert__idem,axiom,
% 28.12/28.41 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.41 ( class_Lattices_Olattice(T_b)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.41 => 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)) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_Inf__fin_Osubset__idem,axiom,
% 28.12/28.41 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.41 ( class_Lattices_Olattice(T_b)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 28.12/28.41 => 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) ) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_Inf__fin_Ounion__idem,axiom,
% 28.12/28.41 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.41 ( class_Lattices_Olattice(T_b)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.41 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.41 => 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)) ) ) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_folding__image__simple_Oinsert,axiom,
% 28.12/28.41 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 28.12/28.41 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 28.12/28.41 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 28.12/28.41 => 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)) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_folding__image__simple_Ounion__inter,axiom,
% 28.12/28.41 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 28.12/28.41 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 28.12/28.41 => 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)) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_Inf__fin_Oinsert,axiom,
% 28.12/28.41 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.41 ( class_Lattices_Olattice(T_b)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.41 => 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)) ) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_Inf__fin_Oinsert__remove,axiom,
% 28.12/28.41 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.41 ( class_Lattices_Olattice(T_b)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( ( 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))
% 28.12/28.41 => 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 )
% 28.12/28.41 & ( 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))
% 28.12/28.41 => 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)))))) ) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_Inf__fin_Ounion__disjoint,axiom,
% 28.12/28.41 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.41 ( class_Lattices_Olattice(T_b)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.41 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.41 => ( 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))
% 28.12/28.41 => 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)) ) ) ) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_Inf__fin_Ounion__inter,axiom,
% 28.12/28.41 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.41 ( class_Lattices_Olattice(T_b)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.41 => ( 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))
% 28.12/28.41 => 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)) ) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_folding_Oinsert,axiom,
% 28.12/28.41 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 28.12/28.41 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.41 => 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)) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_folding_Ounion__inter,axiom,
% 28.12/28.41 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 28.12/28.41 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.41 => 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)) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_Inf__fin_Oclosed,axiom,
% 28.12/28.41 ! [V_A_2,T_b] :
% 28.12/28.41 ( class_Lattices_Olattice(T_b)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.41 => ( ! [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))))))
% 28.12/28.41 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_finite__Union,axiom,
% 28.12/28.41 ! [V_A_2,T_b] :
% 28.12/28.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2))
% 28.12/28.41 => ( ! [B_M] :
% 28.12/28.41 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_M),V_A_2))
% 28.12/28.41 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_M)) )
% 28.12/28.41 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_Sup__fin_Oremove,axiom,
% 28.12/28.41 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.41 ( class_Lattices_Olattice(T_b)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.41 => ( ( 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))
% 28.12/28.41 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = V_x_2 )
% 28.12/28.41 & ( 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))
% 28.12/28.41 => 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)))))) ) ) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_folding__idem_Ounion__idem,axiom,
% 28.12/28.41 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 28.12/28.41 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.41 => 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)) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_folding__idem_Osubset__comp__idem,axiom,
% 28.12/28.41 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 28.12/28.41 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 28.12/28.41 => 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) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_folding__idem_Oinsert__idem,axiom,
% 28.12/28.41 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 28.12/28.41 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => 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)) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_folding__one_Oclosed,axiom,
% 28.12/28.41 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 28.12/28.41 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.41 => ( ! [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))))))
% 28.12/28.41 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_folding__idem_Oin__comp__idem,axiom,
% 28.12/28.41 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 28.12/28.41 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.41 => 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) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_Sup__fin_Osingleton,axiom,
% 28.12/28.41 ! [V_x_2,T_b] :
% 28.12/28.41 ( class_Lattices_Olattice(T_b)
% 28.12/28.41 => 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 ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_folding__idem_Oidem__left__comp,axiom,
% 28.12/28.41 ! [V_g_2,V_x_2,T_d,V_F_2,V_f_2,T_c,T_b] :
% 28.12/28.41 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 28.12/28.41 => 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) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_folding__idem_Oidem__comp,axiom,
% 28.12/28.41 ! [V_x_2,V_F_2,V_f_2,T_c,T_b] :
% 28.12/28.41 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 28.12/28.41 => 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) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_Sup__fin_Oin__idem,axiom,
% 28.12/28.41 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.41 ( class_Lattices_Olattice(T_b)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.41 => 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) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_inf__Sup__absorb,axiom,
% 28.12/28.41 ! [V_a_2,V_A_2,T_b] :
% 28.12/28.41 ( class_Lattices_Olattice(T_b)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.12/28.41 => 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 ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_Sup__fin__Sup,axiom,
% 28.12/28.41 ! [V_A_2,T_b] :
% 28.12/28.41 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.41 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_Sup__fin_Oinsert__idem,axiom,
% 28.12/28.41 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.41 ( class_Lattices_Olattice(T_b)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.41 => 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)) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_Sup__fin_Osubset__idem,axiom,
% 28.12/28.41 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.41 ( class_Lattices_Olattice(T_b)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 28.12/28.41 => 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) ) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_Sup__fin_Ounion__idem,axiom,
% 28.12/28.41 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.41 ( class_Lattices_Olattice(T_b)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.41 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.41 => 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)) ) ) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_Inf__le__Sup,axiom,
% 28.12/28.41 ! [V_A_2,T_b] :
% 28.12/28.41 ( class_Lattices_Olattice(T_b)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.41 => 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))) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_Sup__fin_Oinsert,axiom,
% 28.12/28.41 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.41 ( class_Lattices_Olattice(T_b)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.41 => 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)) ) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_Sup__fin_Oinsert__remove,axiom,
% 28.12/28.41 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.41 ( class_Lattices_Olattice(T_b)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( ( 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))
% 28.12/28.41 => 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 )
% 28.12/28.41 & ( 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))
% 28.12/28.41 => 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)))))) ) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_Sup__fin_Ounion__inter,axiom,
% 28.12/28.41 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.41 ( class_Lattices_Olattice(T_b)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.41 => ( 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))
% 28.12/28.41 => 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)) ) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_Sup__fin_Ounion__disjoint,axiom,
% 28.12/28.41 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.41 ( class_Lattices_Olattice(T_b)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.41 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.41 => ( 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))
% 28.12/28.41 => 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)) ) ) ) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_Sup__fin_Oclosed,axiom,
% 28.12/28.41 ! [V_A_2,T_b] :
% 28.12/28.41 ( class_Lattices_Olattice(T_b)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.41 => ( ! [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))))))
% 28.12/28.41 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_Inf__fin_Ohom__commute,axiom,
% 28.12/28.41 ! [V_N_2,V_h_2,T_b] :
% 28.12/28.41 ( class_Lattices_Olattice(T_b)
% 28.12/28.41 => ( ! [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))
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 28.12/28.41 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.41 => 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)) ) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_Sup__fin_Ohom__commute,axiom,
% 28.12/28.41 ! [V_N_2,V_h_2,T_b] :
% 28.12/28.41 ( class_Lattices_Olattice(T_b)
% 28.12/28.41 => ( ! [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))
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 28.12/28.41 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.41 => 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)) ) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_finite__empty__induct,axiom,
% 28.12/28.41 ! [V_P_2,V_A_2,T_b] :
% 28.12/28.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( hBOOL(hAPP(V_P_2,V_A_2))
% 28.12/28.41 => ( ! [B_a,B_A] :
% 28.12/28.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_A))
% 28.12/28.41 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))
% 28.12/28.41 => ( hBOOL(hAPP(V_P_2,B_A))
% 28.12/28.41 => 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)))))) ) ) )
% 28.12/28.41 => hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_folding__one__idem_Ounion__idem,axiom,
% 28.12/28.41 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 28.12/28.41 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.41 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.41 => 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)) ) ) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_finite__subset__induct,axiom,
% 28.12/28.41 ! [V_P_2,V_A_2,V_F_2,T_b] :
% 28.12/28.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 28.12/28.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_A_2))
% 28.12/28.41 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 28.12/28.41 => ( ! [B_a,B_F] :
% 28.12/28.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F))
% 28.12/28.41 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 28.12/28.41 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_F))
% 28.12/28.41 => ( hBOOL(hAPP(V_P_2,B_F))
% 28.12/28.41 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_F))) ) ) ) )
% 28.12/28.41 => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_folding__one__idem_Osubset__idem,axiom,
% 28.12/28.41 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 28.12/28.41 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 28.12/28.41 => 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) ) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_folding__one__idem_Oinsert__idem,axiom,
% 28.12/28.41 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 28.12/28.41 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.41 => 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)) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_folding__one__idem_Oidem,axiom,
% 28.12/28.41 ! [V_x_2,V_F_2,V_f_2,T_b] :
% 28.12/28.41 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 28.12/28.41 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_folding__one__idem_Oin__idem,axiom,
% 28.12/28.41 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 28.12/28.41 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.41 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_image__eq__fold__image,axiom,
% 28.12/28.41 ! [V_f_2,T_c,V_A_2,T_b] :
% 28.12/28.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => 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) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_fold1__Un,axiom,
% 28.12/28.41 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.41 ( class_Groups_Oab__semigroup__mult(T_b)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.41 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.41 => ( 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))
% 28.12/28.41 => 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)) ) ) ) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_folding__one__idem_Ohom__commute,axiom,
% 28.12/28.41 ! [V_N_2,V_h_2,V_F_2,V_f_2,T_b] :
% 28.12/28.41 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 28.12/28.41 => ( ! [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))
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 28.12/28.41 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.41 => 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)) ) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_folding__image__simple_Ounion__inter__neutral,axiom,
% 28.12/28.41 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 28.12/28.41 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 28.12/28.41 => ( ! [B_x] :
% 28.12/28.41 ( 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)))
% 28.12/28.41 => hAPP(V_g_2,B_x) = V_z_2 )
% 28.12/28.41 => 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)) ) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_fold1__insert,axiom,
% 28.12/28.41 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.41 ( class_Groups_Oab__semigroup__mult(T_b)
% 28.12/28.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.41 => 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)) ) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_fold__image__reindex,axiom,
% 28.12/28.41 ! [V_z_2,V_g_2,V_h_2,T_c,V_A_2,T_b,T_d] :
% 28.12/28.41 ( class_Groups_Oab__semigroup__mult(T_d)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( c_Fun_Oinj__on(T_b,T_c,V_h_2,V_A_2)
% 28.12/28.41 => 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) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_finite__UN__I,axiom,
% 28.12/28.41 ! [V_B_2,T_c,V_A_2,T_b] :
% 28.12/28.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( ! [B_a] :
% 28.12/28.41 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 28.12/28.41 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) )
% 28.12/28.41 => 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))) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_fold__image__empty,axiom,
% 28.12/28.41 ! [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 ).
% 28.12/28.41
% 28.12/28.41 fof(fact_fold1__singleton__def,axiom,
% 28.12/28.41 ! [V_a_2,V_f_2,T_b,V_g_2] :
% 28.12/28.41 ( V_g_2 = c_Finite__Set_Ofold1(T_b,V_f_2)
% 28.12/28.41 => 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 ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_fold1__singleton,axiom,
% 28.12/28.41 ! [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 ).
% 28.12/28.41
% 28.12/28.41 fof(fact_folding__image__simple_Oeq__fold__g,axiom,
% 28.12/28.41 ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 28.12/28.41 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 28.12/28.41 => 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) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_folding__image_Oeq__fold,axiom,
% 28.12/28.41 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 28.12/28.41 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 28.12/28.41 => 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) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_folding__one_Oeq__fold,axiom,
% 28.12/28.41 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 28.12/28.41 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_fold1__def,axiom,
% 28.12/28.41 ! [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)) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_Sup__fin_OF__eq,axiom,
% 28.12/28.41 ! [V_A_2,T_b] :
% 28.12/28.41 ( class_Lattices_Olattice(T_b)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => 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) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_Inf__fin_OF__eq,axiom,
% 28.12/28.41 ! [V_A_2,T_b] :
% 28.12/28.41 ( class_Lattices_Olattice(T_b)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => 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) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_fold__image__insert,axiom,
% 28.12/28.41 ! [V_z_2,V_g_2,V_a_2,V_A_2,T_b,T_c] :
% 28.12/28.41 ( class_Groups_Oab__semigroup__mult(T_c)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.12/28.41 => 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)) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_fold1__belowI,axiom,
% 28.12/28.41 ! [V_a_2,V_A_2,T_b] :
% 28.12/28.41 ( class_Lattices_Osemilattice__inf(T_b)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.12/28.41 => 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)) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_below__fold1__iff,axiom,
% 28.12/28.41 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.41 ( class_Lattices_Osemilattice__inf(T_b)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.41 => ( 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)))
% 28.12/28.41 <=> ! [B_x] :
% 28.12/28.41 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.12/28.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_fold1__insert__idem,axiom,
% 28.12/28.41 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.41 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 28.12/28.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => 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)) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_fold1__Un2,axiom,
% 28.12/28.41 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.41 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.41 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.41 => 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)) ) ) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_semilattice__big_OF__eq,axiom,
% 28.12/28.41 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 28.12/28.41 ( c_Big__Operators_Osemilattice__big(T_b,V_f_2,V_F_2)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_comm__monoid__big_OF__eq,axiom,
% 28.12/28.41 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 28.12/28.41 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 28.12/28.41 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 28.12/28.41 => 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) )
% 28.12/28.41 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 28.12/28.41 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_fold1__in,axiom,
% 28.12/28.41 ! [V_A_2,T_b] :
% 28.12/28.41 ( class_Groups_Oab__semigroup__mult(T_b)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.41 => ( ! [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))))))
% 28.12/28.41 => 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)) ) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_hom__fold1__commute,axiom,
% 28.12/28.41 ! [V_N_2,V_h_2,T_b] :
% 28.12/28.41 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 28.12/28.41 => ( ! [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))
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 28.12/28.41 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.41 => 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)) ) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_fold__Un__disjoint,axiom,
% 28.12/28.41 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 28.12/28.41 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.41 => ( 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))
% 28.12/28.41 => 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)) ) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_setsum__diff1,axiom,
% 28.12/28.41 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 28.12/28.41 ( class_Groups_Oab__group__add(T_c)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.12/28.41 => 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)) )
% 28.12/28.41 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.12/28.41 => 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) ) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_setsum__diff1__ring,axiom,
% 28.12/28.41 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 28.12/28.41 ( class_Rings_Oring(T_c)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.12/28.41 => 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)) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_one__reorient,axiom,
% 28.12/28.41 ! [V_x_2,T_b] :
% 28.12/28.41 ( class_Groups_Oone(T_b)
% 28.12/28.41 => ( c_Groups_Oone__class_Oone(T_b) = V_x_2
% 28.12/28.41 <=> V_x_2 = c_Groups_Oone__class_Oone(T_b) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_setsum__commute,axiom,
% 28.12/28.41 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 28.12/28.41 ( class_Groups_Ocomm__monoid__add(T_b)
% 28.12/28.41 => 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) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_setsum__diff__nat__ivl,axiom,
% 28.12/28.41 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
% 28.12/28.41 ( class_Groups_Oab__group__add(T_b)
% 28.12/28.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 28.12/28.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 28.12/28.41 => 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)) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_mult__1__left,axiom,
% 28.12/28.41 ! [V_a,T_a] :
% 28.12/28.41 ( class_Groups_Omonoid__mult(T_a)
% 28.12/28.41 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_mult__1,axiom,
% 28.12/28.41 ! [V_a,T_a] :
% 28.12/28.41 ( class_Groups_Ocomm__monoid__mult(T_a)
% 28.12/28.41 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_mult__1__right,axiom,
% 28.12/28.41 ! [V_a,T_a] :
% 28.12/28.41 ( class_Groups_Omonoid__mult(T_a)
% 28.12/28.41 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_mult_Ocomm__neutral,axiom,
% 28.12/28.41 ! [V_a,T_a] :
% 28.12/28.41 ( class_Groups_Ocomm__monoid__mult(T_a)
% 28.12/28.41 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_setsum__right__distrib,axiom,
% 28.12/28.41 ! [V_A_2,V_f_2,T_c,V_r_2,T_b] :
% 28.12/28.41 ( class_Rings_Osemiring__0(T_b)
% 28.12/28.41 => 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) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_setsum__left__distrib,axiom,
% 28.12/28.41 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.41 ( class_Rings_Osemiring__0(T_b)
% 28.12/28.41 => 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) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_setsum__product,axiom,
% 28.12/28.41 ! [V_B_2,V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.41 ( class_Rings_Osemiring__0(T_b)
% 28.12/28.41 => 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) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_setsum__subtractf,axiom,
% 28.12/28.41 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 28.12/28.41 ( class_Groups_Oab__group__add(T_b)
% 28.12/28.41 => 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)) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_setsum__negf,axiom,
% 28.12/28.41 ! [V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.41 ( class_Groups_Oab__group__add(T_b)
% 28.12/28.41 => 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)) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_less__1__mult,axiom,
% 28.12/28.41 ! [V_n,V_m,T_a] :
% 28.12/28.41 ( class_Rings_Olinordered__semidom(T_a)
% 28.12/28.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m))
% 28.12/28.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n))
% 28.12/28.41 => 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))) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_square__eq__1__iff,axiom,
% 28.12/28.41 ! [V_x_2,T_b] :
% 28.12/28.41 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 28.12/28.41 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_b)
% 28.12/28.41 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_b)
% 28.12/28.41 | V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_setsum__diff__nat,axiom,
% 28.12/28.41 ! [V_f_2,V_A_2,V_B_2,T_b] :
% 28.12/28.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 28.12/28.41 => 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)) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_setsum__reindex,axiom,
% 28.12/28.41 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
% 28.12/28.41 ( class_Groups_Ocomm__monoid__add(T_d)
% 28.12/28.41 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 28.12/28.41 => 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) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_fold__image__distrib,axiom,
% 28.12/28.41 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 28.12/28.41 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => 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)) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_setsum__diff1__nat,axiom,
% 28.12/28.41 ! [V_f_2,V_A_2,V_a_2,T_b] :
% 28.12/28.41 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.12/28.41 => 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)) )
% 28.12/28.41 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.12/28.41 => 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) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_setsum__diff,axiom,
% 28.12/28.41 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 28.12/28.41 ( class_Groups_Oab__group__add(T_c)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 28.12/28.41 => 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)) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_setsum_Oreindex,axiom,
% 28.12/28.41 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
% 28.12/28.41 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
% 28.12/28.41 => 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) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_comm__monoid__big_Oinfinite,axiom,
% 28.12/28.41 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 28.12/28.41 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 28.12/28.41 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 28.12/28.41 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_fold__image__Un__Int,axiom,
% 28.12/28.41 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 28.12/28.41 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.41 => 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))) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
% 28.12/28.41 ! [V_x,T_a] :
% 28.12/28.41 ( class_Rings_Ocomm__ring__1(T_a)
% 28.12/28.41 => 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) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_fold__image__Un__one,axiom,
% 28.12/28.41 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 28.12/28.41 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 28.12/28.41 => ( ! [B_x] :
% 28.12/28.41 ( 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)))
% 28.12/28.41 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 28.12/28.41 => 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)) ) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 28.12/28.41 ! [V_a,T_a] :
% 28.12/28.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.12/28.41 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 28.12/28.41 ! [V_a,T_a] :
% 28.12/28.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.12/28.41 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_setsum__strict__mono,axiom,
% 28.12/28.41 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
% 28.12/28.41 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 28.12/28.41 & class_Groups_Oordered__cancel__ab__semigroup__add(T_c) )
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.41 => ( ! [B_x] :
% 28.12/28.41 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.12/28.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 28.12/28.41 => 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))) ) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_setsum_Oremove,axiom,
% 28.12/28.41 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 28.12/28.41 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.41 => 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)))))) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_setsum__diff1_H,axiom,
% 28.12/28.41 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 28.12/28.41 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.12/28.41 => 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)))))) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_finite__atLeastLessThan,axiom,
% 28.12/28.41 ! [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))) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_setsum__add__nat__ivl,axiom,
% 28.12/28.41 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
% 28.12/28.41 ( class_Groups_Ocomm__monoid__add(T_b)
% 28.12/28.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 28.12/28.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 28.12/28.41 => 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)) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_setsum__ub__add__nat,axiom,
% 28.12/28.41 ! [V_p_2,V_f_2,V_n_2,V_m_2,T_b] :
% 28.12/28.41 ( class_Groups_Ocomm__monoid__add(T_b)
% 28.12/28.41 => ( 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))))
% 28.12/28.41 => 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)))) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_setsum__shift__bounds__nat__ivl,axiom,
% 28.12/28.41 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] :
% 28.12/28.41 ( class_Groups_Ocomm__monoid__add(T_b)
% 28.12/28.41 => 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)) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom,
% 28.12/28.41 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] :
% 28.12/28.41 ( class_Groups_Ocomm__monoid__add(T_b)
% 28.12/28.41 => 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)) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_setsum__head,axiom,
% 28.12/28.41 ! [V_P_2,V_n_2,V_m_2,T_b] :
% 28.12/28.41 ( class_Groups_Ocomm__monoid__add(T_b)
% 28.12/28.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 28.12/28.41 => 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))) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_finite__nat__set__iff__bounded__le,axiom,
% 28.12/28.41 ! [V_N_2] :
% 28.12/28.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 28.12/28.41 <=> ? [B_m] :
% 28.12/28.41 ! [B_x] :
% 28.12/28.41 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 28.12/28.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_crossproduct__eq,axiom,
% 28.12/28.41 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_b] :
% 28.12/28.41 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 28.12/28.41 => ( 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))
% 28.12/28.41 <=> ( V_w_2 = V_x_2
% 28.12/28.41 | V_y_2 = V_z_2 ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 28.12/28.41 ! [V_b,V_m,V_a,T_a] :
% 28.12/28.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.12/28.41 => 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) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 28.12/28.41 ! [V_c,V_b,V_a,T_a] :
% 28.12/28.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.12/28.41 => 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)) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_crossproduct__noteq,axiom,
% 28.12/28.41 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 28.12/28.41 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 28.12/28.41 => ( ( V_a_2 != V_b_2
% 28.12/28.41 & V_c_2 != V_d_2 )
% 28.12/28.41 <=> 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)) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 28.12/28.41 ! [V_z,V_y,V_x,T_a] :
% 28.12/28.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.12/28.41 => 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)) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_image__add__atLeastLessThan,axiom,
% 28.12/28.41 ! [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)) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_atLeastLessThan__add__Un,axiom,
% 28.12/28.41 ! [V_k_2,V_j_2,V_i_2] :
% 28.12/28.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 28.12/28.41 => 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))) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_add__right__imp__eq,axiom,
% 28.12/28.41 ! [V_c,V_a,V_b,T_a] :
% 28.12/28.41 ( class_Groups_Ocancel__semigroup__add(T_a)
% 28.12/28.41 => ( 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)
% 28.12/28.41 => V_b = V_c ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_add__imp__eq,axiom,
% 28.12/28.41 ! [V_c,V_b,V_a,T_a] :
% 28.12/28.41 ( class_Groups_Ocancel__ab__semigroup__add(T_a)
% 28.12/28.41 => ( 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)
% 28.12/28.41 => V_b = V_c ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_add__left__imp__eq,axiom,
% 28.12/28.41 ! [V_c,V_b,V_a,T_a] :
% 28.12/28.41 ( class_Groups_Ocancel__semigroup__add(T_a)
% 28.12/28.41 => ( 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)
% 28.12/28.41 => V_b = V_c ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_add__right__cancel,axiom,
% 28.12/28.41 ! [V_c_2,V_a_2,V_b_2,T_b] :
% 28.12/28.41 ( class_Groups_Ocancel__semigroup__add(T_b)
% 28.12/28.41 => ( 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)
% 28.12/28.41 <=> V_b_2 = V_c_2 ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_add__left__cancel,axiom,
% 28.12/28.41 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 28.12/28.41 ( class_Groups_Ocancel__semigroup__add(T_b)
% 28.12/28.41 => ( 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)
% 28.12/28.41 <=> V_b_2 = V_c_2 ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 28.12/28.41 ! [V_c,V_b,V_a,T_a] :
% 28.12/28.41 ( class_Groups_Oab__semigroup__add(T_a)
% 28.12/28.41 => 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)) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 28.12/28.41 ! [V_c,V_a,T_a] :
% 28.12/28.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.12/28.41 => 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) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 28.12/28.41 ! [V_d,V_c,V_a,T_a] :
% 28.12/28.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.12/28.41 => 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)) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 28.12/28.41 ! [V_d,V_c,V_a,T_a] :
% 28.12/28.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.12/28.41 => 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) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 28.12/28.41 ! [V_c,V_b,V_a,T_a] :
% 28.12/28.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.12/28.41 => 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)) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 28.12/28.41 ! [V_c,V_b,V_a,T_a] :
% 28.12/28.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.12/28.41 => 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) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 28.12/28.41 ! [V_d,V_c,V_b,V_a,T_a] :
% 28.12/28.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.12/28.41 => 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)) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_add__le__imp__le__left,axiom,
% 28.12/28.41 ! [V_b,V_a,V_c,T_a] :
% 28.12/28.41 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 28.12/28.41 => ( 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)))
% 28.12/28.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_add__le__imp__le__right,axiom,
% 28.12/28.41 ! [V_b,V_c,V_a,T_a] :
% 28.12/28.41 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 28.12/28.41 => ( 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)))
% 28.12/28.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_add__mono,axiom,
% 28.12/28.41 ! [V_d,V_c,V_b,V_a,T_a] :
% 28.12/28.41 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 28.12/28.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 28.12/28.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 28.12/28.41 => 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))) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_add__left__mono,axiom,
% 28.12/28.41 ! [V_c,V_b,V_a,T_a] :
% 28.12/28.41 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 28.12/28.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 28.12/28.41 => 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))) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_add__right__mono,axiom,
% 28.12/28.41 ! [V_c,V_b,V_a,T_a] :
% 28.12/28.41 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 28.12/28.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 28.12/28.41 => 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))) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_add__le__cancel__left,axiom,
% 28.12/28.41 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 28.12/28.41 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 28.12/28.41 => ( 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)))
% 28.12/28.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_add__le__cancel__right,axiom,
% 28.12/28.41 ! [V_b_2,V_c_2,V_a_2,T_b] :
% 28.12/28.41 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 28.12/28.41 => ( 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)))
% 28.12/28.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_add__less__imp__less__left,axiom,
% 28.12/28.41 ! [V_b,V_a,V_c,T_a] :
% 28.12/28.41 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 28.12/28.41 => ( 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)))
% 28.12/28.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_add__less__imp__less__right,axiom,
% 28.12/28.41 ! [V_b,V_c,V_a,T_a] :
% 28.12/28.41 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 28.12/28.41 => ( 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)))
% 28.12/28.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_add__strict__mono,axiom,
% 28.12/28.41 ! [V_d,V_c,V_b,V_a,T_a] :
% 28.12/28.41 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 28.12/28.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 28.12/28.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 28.12/28.41 => 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))) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_add__strict__left__mono,axiom,
% 28.12/28.41 ! [V_c,V_b,V_a,T_a] :
% 28.12/28.41 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 28.12/28.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 28.12/28.41 => 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))) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_add__strict__right__mono,axiom,
% 28.12/28.41 ! [V_c,V_b,V_a,T_a] :
% 28.12/28.41 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 28.12/28.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 28.12/28.41 => 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))) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_add__less__cancel__left,axiom,
% 28.12/28.41 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 28.12/28.41 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 28.12/28.41 => ( 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)))
% 28.12/28.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_add__less__cancel__right,axiom,
% 28.12/28.41 ! [V_b_2,V_c_2,V_a_2,T_b] :
% 28.12/28.41 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 28.12/28.41 => ( 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)))
% 28.12/28.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_combine__common__factor,axiom,
% 28.12/28.41 ! [V_c,V_b,V_e,V_a,T_a] :
% 28.12/28.41 ( class_Rings_Osemiring(T_a)
% 28.12/28.41 => 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) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_comm__semiring__class_Odistrib,axiom,
% 28.12/28.41 ! [V_c,V_b,V_a,T_a] :
% 28.12/28.41 ( class_Rings_Ocomm__semiring(T_a)
% 28.12/28.41 => 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)) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_add__diff__cancel,axiom,
% 28.12/28.41 ! [V_b,V_a,T_a] :
% 28.12/28.41 ( class_Groups_Ogroup__add(T_a)
% 28.12/28.41 => 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 ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_diff__add__cancel,axiom,
% 28.12/28.41 ! [V_b,V_a,T_a] :
% 28.12/28.41 ( class_Groups_Ogroup__add(T_a)
% 28.12/28.41 => 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 ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_minus__add__distrib,axiom,
% 28.12/28.41 ! [V_b,V_a,T_a] :
% 28.12/28.41 ( class_Groups_Oab__group__add(T_a)
% 28.12/28.41 => 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)) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_minus__add,axiom,
% 28.12/28.41 ! [V_b,V_a,T_a] :
% 28.12/28.41 ( class_Groups_Ogroup__add(T_a)
% 28.12/28.41 => 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)) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_add__minus__cancel,axiom,
% 28.12/28.41 ! [V_b,V_a,T_a] :
% 28.12/28.41 ( class_Groups_Ogroup__add(T_a)
% 28.12/28.41 => 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 ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_minus__add__cancel,axiom,
% 28.12/28.41 ! [V_b,V_a,T_a] :
% 28.12/28.41 ( class_Groups_Ogroup__add(T_a)
% 28.12/28.41 => 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 ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 28.12/28.41 ! [V_m,V_a,T_a] :
% 28.12/28.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.12/28.41 => 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) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 28.12/28.41 ! [V_a,V_m,T_a] :
% 28.12/28.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.12/28.41 => 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) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 28.12/28.41 ! [V_m,T_a] :
% 28.12/28.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.12/28.41 => 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) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
% 28.12/28.41 ! [V_y,V_x,T_a] :
% 28.12/28.41 ( class_Rings_Ocomm__ring__1(T_a)
% 28.12/28.41 => 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)) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_setsum__addf,axiom,
% 28.12/28.41 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 28.12/28.41 ( class_Groups_Ocomm__monoid__add(T_b)
% 28.12/28.41 => 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)) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_add__le__less__mono,axiom,
% 28.12/28.41 ! [V_d,V_c,V_b,V_a,T_a] :
% 28.12/28.41 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 28.12/28.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 28.12/28.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 28.12/28.41 => 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))) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_add__less__le__mono,axiom,
% 28.12/28.41 ! [V_d,V_c,V_b,V_a,T_a] :
% 28.12/28.41 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 28.12/28.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 28.12/28.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 28.12/28.41 => 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))) ) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_less__add__one,axiom,
% 28.12/28.41 ! [V_a,T_a] :
% 28.12/28.41 ( class_Rings_Olinordered__semidom(T_a)
% 28.12/28.41 => 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)))) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_eq__add__iff2,axiom,
% 28.12/28.41 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 28.12/28.41 ( class_Rings_Oring(T_b)
% 28.12/28.41 => ( 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)
% 28.12/28.41 <=> 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) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_eq__add__iff1,axiom,
% 28.12/28.41 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 28.12/28.41 ( class_Rings_Oring(T_b)
% 28.12/28.41 => ( 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)
% 28.12/28.41 <=> 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 ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_diff__def,axiom,
% 28.12/28.41 ! [V_b,V_a,T_a] :
% 28.12/28.41 ( class_Groups_Ogroup__add(T_a)
% 28.12/28.41 => 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)) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_ab__diff__minus,axiom,
% 28.12/28.41 ! [V_b,V_a,T_a] :
% 28.12/28.41 ( class_Groups_Oab__group__add(T_a)
% 28.12/28.41 => 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)) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_diff__minus__eq__add,axiom,
% 28.12/28.41 ! [V_b,V_a,T_a] :
% 28.12/28.41 ( class_Groups_Ogroup__add(T_a)
% 28.12/28.41 => 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) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_setsum_Odistrib,axiom,
% 28.12/28.41 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 28.12/28.41 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => 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)) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_le__add__iff1,axiom,
% 28.12/28.41 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 28.12/28.41 ( class_Rings_Oordered__ring(T_b)
% 28.12/28.41 => ( 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)))
% 28.12/28.41 <=> 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)) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_le__add__iff2,axiom,
% 28.12/28.41 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 28.12/28.41 ( class_Rings_Oordered__ring(T_b)
% 28.12/28.41 => ( 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)))
% 28.12/28.41 <=> 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))) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_less__add__iff2,axiom,
% 28.12/28.41 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 28.12/28.41 ( class_Rings_Oordered__ring(T_b)
% 28.12/28.41 => ( 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)))
% 28.12/28.41 <=> 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))) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_less__add__iff1,axiom,
% 28.12/28.41 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 28.12/28.41 ( class_Rings_Oordered__ring(T_b)
% 28.12/28.41 => ( 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)))
% 28.12/28.41 <=> 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)) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_setsum__Un__nat,axiom,
% 28.12/28.41 ! [V_f_2,V_B_2,V_A_2,T_b] :
% 28.12/28.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.41 => 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))) ) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 28.12/28.41 ! [V_b,V_a,T_a] :
% 28.12/28.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.12/28.41 => 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) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 28.12/28.41 ! [V_ry,V_rx,V_lx,T_a] :
% 28.12/28.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.12/28.41 => 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)) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 28.12/28.41 ! [V_ry,V_rx,V_lx,T_a] :
% 28.12/28.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.12/28.41 => 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) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 28.12/28.41 ! [V_rx,V_ly,V_lx,T_a] :
% 28.12/28.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.12/28.41 => 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)) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 28.12/28.41 ! [V_rx,V_ly,V_lx,T_a] :
% 28.12/28.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.12/28.41 => 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) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 28.12/28.41 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 28.12/28.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.12/28.41 => 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))) ) ).
% 28.12/28.41
% 28.12/28.41 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 28.12/28.41 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 28.12/28.41 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.12/28.42 => 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)) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 28.12/28.42 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 28.12/28.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.12/28.42 => 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)) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_setsum_Oinsert,axiom,
% 28.12/28.42 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 28.12/28.42 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.12/28.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.42 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.42 => 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)) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_setsum__insert,axiom,
% 28.12/28.42 ! [V_f_2,V_a_2,V_F_2,T_b,T_c] :
% 28.12/28.42 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.12/28.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 28.12/28.42 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_F_2))
% 28.12/28.42 => 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)) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_setsum__Un__Int,axiom,
% 28.12/28.42 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 28.12/28.42 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.12/28.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.42 => 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)) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_setsum_Oinsert__remove,axiom,
% 28.12/28.42 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
% 28.12/28.42 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.12/28.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.42 => 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)))))) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_setsum__Un__disjoint,axiom,
% 28.12/28.42 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 28.12/28.42 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.12/28.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.42 => ( 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))
% 28.12/28.42 => 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)) ) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_setsum__Un,axiom,
% 28.12/28.42 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 28.12/28.42 ( class_Groups_Oab__group__add(T_c)
% 28.12/28.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.42 => 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))) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_nat__less__add__iff2,axiom,
% 28.12/28.42 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 28.12/28.42 => ( 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)))
% 28.12/28.42 <=> 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))) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_nat__less__add__iff1,axiom,
% 28.12/28.42 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 28.12/28.42 => ( 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)))
% 28.12/28.42 <=> 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)) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_nat__le__add__iff1,axiom,
% 28.12/28.42 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 28.12/28.42 => ( 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)))
% 28.12/28.42 <=> 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)) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_nat__diff__add__eq1,axiom,
% 28.12/28.42 ! [V_n,V_m,V_u,V_i,V_j] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 28.12/28.42 => 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) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_nat__eq__add__iff1,axiom,
% 28.12/28.42 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 28.12/28.42 => ( 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)
% 28.12/28.42 <=> 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 ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_nat__le__add__iff2,axiom,
% 28.12/28.42 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 28.12/28.42 => ( 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)))
% 28.12/28.42 <=> 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))) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_nat__diff__add__eq2,axiom,
% 28.12/28.42 ! [V_n,V_m,V_u,V_j,V_i] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 28.12/28.42 => 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)) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_finite__greaterThanLessThan,axiom,
% 28.12/28.42 ! [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))) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_finite__atMost,axiom,
% 28.12/28.42 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_finite__lessThan,axiom,
% 28.12/28.42 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_finite__atLeastAtMost,axiom,
% 28.12/28.42 ! [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))) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_finite__greaterThanAtMost,axiom,
% 28.12/28.42 ! [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))) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_left__add__mult__distrib,axiom,
% 28.12/28.42 ! [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) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_UN__le__add__shift,axiom,
% 28.12/28.42 ! [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) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_image__add__atLeastAtMost,axiom,
% 28.12/28.42 ! [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)) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_finite__nat__set__iff__bounded,axiom,
% 28.12/28.42 ! [V_N_2] :
% 28.12/28.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 28.12/28.42 <=> ? [B_m] :
% 28.12/28.42 ! [B_x] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 28.12/28.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_infinite__UNIV__nat,axiom,
% 28.12/28.42 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_nat__eq__add__iff2,axiom,
% 28.12/28.42 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 28.12/28.42 => ( 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)
% 28.12/28.42 <=> 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) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_diff__add__assoc2,axiom,
% 28.12/28.42 ! [V_i,V_j,V_k] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 28.12/28.42 => 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) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_add__diff__assoc2,axiom,
% 28.12/28.42 ! [V_i,V_j,V_k] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 28.12/28.42 => 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) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_diff__add__assoc,axiom,
% 28.12/28.42 ! [V_i,V_j,V_k] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 28.12/28.42 => 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)) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_le__imp__diff__is__add,axiom,
% 28.12/28.42 ! [V_k_2,V_j_2,V_i_2] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 28.12/28.42 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2
% 28.12/28.42 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_le__add__diff__inverse2,axiom,
% 28.12/28.42 ! [V_m,V_n] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 28.12/28.42 => 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 ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_le__diff__conv2,axiom,
% 28.12/28.42 ! [V_i_2,V_j_2,V_k_2] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2))
% 28.12/28.42 => ( 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)))
% 28.12/28.42 <=> 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)) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_add__diff__assoc,axiom,
% 28.12/28.42 ! [V_i,V_j,V_k] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 28.12/28.42 => 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) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_INT__greaterThan__UNIV,axiom,
% 28.12/28.42 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)) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_UN__lessThan__UNIV,axiom,
% 28.12/28.42 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)) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_UN__atLeast__UNIV,axiom,
% 28.12/28.42 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)) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_UN__atMost__UNIV,axiom,
% 28.12/28.42 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)) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_less__not__refl,axiom,
% 28.12/28.42 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_nat__neq__iff,axiom,
% 28.12/28.42 ! [V_n_2,V_m_2] :
% 28.12/28.42 ( V_m_2 != V_n_2
% 28.12/28.42 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 28.12/28.42 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_linorder__neqE__nat,axiom,
% 28.12/28.42 ! [V_y,V_x] :
% 28.12/28.42 ( V_x != V_y
% 28.12/28.42 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 28.12/28.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_less__irrefl__nat,axiom,
% 28.12/28.42 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_less__not__refl2,axiom,
% 28.12/28.42 ! [V_m,V_n] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 28.12/28.42 => V_m != V_n ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_less__not__refl3,axiom,
% 28.12/28.42 ! [V_t,V_s] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t))
% 28.12/28.42 => V_s != V_t ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_nat__less__cases,axiom,
% 28.12/28.42 ! [V_P_2,V_n_2,V_m_2] :
% 28.12/28.42 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 28.12/28.42 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 28.12/28.42 => ( ( V_m_2 = V_n_2
% 28.12/28.42 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 28.12/28.42 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 28.12/28.42 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 28.12/28.42 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_nat__add__right__cancel,axiom,
% 28.12/28.42 ! [V_n_2,V_k_2,V_m_2] :
% 28.12/28.42 ( 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)
% 28.12/28.42 <=> V_m_2 = V_n_2 ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_nat__add__left__cancel,axiom,
% 28.12/28.42 ! [V_n_2,V_m_2,V_k_2] :
% 28.12/28.42 ( 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)
% 28.12/28.42 <=> V_m_2 = V_n_2 ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_nat__add__assoc,axiom,
% 28.12/28.42 ! [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)) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_nat__add__left__commute,axiom,
% 28.12/28.42 ! [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)) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_nat__add__commute,axiom,
% 28.12/28.42 ! [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) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_le__refl,axiom,
% 28.12/28.42 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_nat__le__linear,axiom,
% 28.12/28.42 ! [V_n,V_m] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 28.12/28.42 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_eq__imp__le,axiom,
% 28.12/28.42 ! [V_n,V_m] :
% 28.12/28.42 ( V_m = V_n
% 28.12/28.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_le__trans,axiom,
% 28.12/28.42 ! [V_k,V_j,V_i] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k))
% 28.12/28.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_le__antisym,axiom,
% 28.12/28.42 ! [V_n,V_m] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 28.12/28.42 => V_m = V_n ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_diff__commute,axiom,
% 28.12/28.42 ! [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) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_nat__mult__assoc,axiom,
% 28.12/28.42 ! [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)) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_nat__mult__commute,axiom,
% 28.12/28.42 ! [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) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_inj__on__add__nat,axiom,
% 28.12/28.42 ! [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) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_add__lessD1,axiom,
% 28.12/28.42 ! [V_k,V_j,V_i] :
% 28.12/28.42 ( 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))
% 28.12/28.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_less__add__eq__less,axiom,
% 28.12/28.42 ! [V_n,V_m,V_l,V_k] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 28.12/28.42 => ( 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)
% 28.12/28.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_add__less__mono,axiom,
% 28.12/28.42 ! [V_l,V_k,V_j,V_i] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 28.12/28.42 => 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))) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_add__less__mono1,axiom,
% 28.12/28.42 ! [V_k,V_j,V_i] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 28.12/28.42 => 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))) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_trans__less__add2,axiom,
% 28.12/28.42 ! [V_m,V_j,V_i] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 28.12/28.42 => 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))) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_trans__less__add1,axiom,
% 28.12/28.42 ! [V_m,V_j,V_i] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 28.12/28.42 => 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))) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_nat__add__left__cancel__less,axiom,
% 28.12/28.42 ! [V_n_2,V_m_2,V_k_2] :
% 28.12/28.42 ( 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)))
% 28.12/28.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_not__add__less2,axiom,
% 28.12/28.42 ! [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)) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_not__add__less1,axiom,
% 28.12/28.42 ! [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)) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_nat__less__le,axiom,
% 28.12/28.42 ! [V_n_2,V_m_2] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 28.12/28.42 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 28.12/28.42 & V_m_2 != V_n_2 ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_le__eq__less__or__eq,axiom,
% 28.12/28.42 ! [V_n_2,V_m_2] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 28.12/28.42 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 28.12/28.42 | V_m_2 = V_n_2 ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_less__imp__le__nat,axiom,
% 28.12/28.42 ! [V_n,V_m] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 28.12/28.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_le__neq__implies__less,axiom,
% 28.12/28.42 ! [V_n,V_m] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 28.12/28.42 => ( V_m != V_n
% 28.12/28.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_less__or__eq__imp__le,axiom,
% 28.12/28.42 ! [V_n,V_m] :
% 28.12/28.42 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 28.12/28.42 | V_m = V_n )
% 28.12/28.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_le__add2,axiom,
% 28.12/28.42 ! [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))) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_le__add1,axiom,
% 28.12/28.42 ! [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))) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_le__iff__add,axiom,
% 28.12/28.42 ! [V_n_2,V_m_2] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 28.12/28.42 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_nat__add__left__cancel__le,axiom,
% 28.12/28.42 ! [V_n_2,V_m_2,V_k_2] :
% 28.12/28.42 ( 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)))
% 28.12/28.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_trans__le__add1,axiom,
% 28.12/28.42 ! [V_m,V_j,V_i] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 28.12/28.42 => 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))) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_trans__le__add2,axiom,
% 28.12/28.42 ! [V_m,V_j,V_i] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 28.12/28.42 => 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))) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_add__le__mono1,axiom,
% 28.12/28.42 ! [V_k,V_j,V_i] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 28.12/28.42 => 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))) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_add__le__mono,axiom,
% 28.12/28.42 ! [V_l,V_k,V_j,V_i] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 28.12/28.42 => 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))) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_add__leD2,axiom,
% 28.12/28.42 ! [V_n,V_k,V_m] :
% 28.12/28.42 ( 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))
% 28.12/28.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_add__leD1,axiom,
% 28.12/28.42 ! [V_n,V_k,V_m] :
% 28.12/28.42 ( 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))
% 28.12/28.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_add__leE,axiom,
% 28.12/28.42 ! [V_n,V_k,V_m] :
% 28.12/28.42 ( 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))
% 28.12/28.42 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 28.12/28.42 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_diff__less__mono2,axiom,
% 28.12/28.42 ! [V_l,V_n,V_m] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l))
% 28.12/28.42 => 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))) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_less__imp__diff__less,axiom,
% 28.12/28.42 ! [V_n,V_k,V_j] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 28.12/28.42 => 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)) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_diff__add__inverse2,axiom,
% 28.12/28.42 ! [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 ).
% 28.12/28.42
% 28.12/28.42 fof(fact_diff__add__inverse,axiom,
% 28.12/28.42 ! [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 ).
% 28.12/28.42
% 28.12/28.42 fof(fact_diff__diff__left,axiom,
% 28.12/28.42 ! [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)) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_diff__cancel,axiom,
% 28.12/28.42 ! [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) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_diff__cancel2,axiom,
% 28.12/28.42 ! [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) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_add__mult__distrib2,axiom,
% 28.12/28.42 ! [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)) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_add__mult__distrib,axiom,
% 28.12/28.42 ! [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)) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_diff__le__self,axiom,
% 28.12/28.42 ! [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)) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_diff__le__mono2,axiom,
% 28.12/28.42 ! [V_l,V_n,V_m] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 28.12/28.42 => 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))) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_diff__le__mono,axiom,
% 28.12/28.42 ! [V_l,V_n,V_m] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 28.12/28.42 => 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))) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_diff__diff__cancel,axiom,
% 28.12/28.42 ! [V_n,V_i] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n))
% 28.12/28.42 => 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 ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_eq__diff__iff,axiom,
% 28.12/28.42 ! [V_n_2,V_m_2,V_k_2] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 28.12/28.42 => ( 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)
% 28.12/28.42 <=> V_m_2 = V_n_2 ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_Nat_Odiff__diff__eq,axiom,
% 28.12/28.42 ! [V_n,V_m,V_k] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 28.12/28.42 => 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) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_le__diff__iff,axiom,
% 28.12/28.42 ! [V_n_2,V_m_2,V_k_2] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 28.12/28.42 => ( 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)))
% 28.12/28.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_mult__le__mono,axiom,
% 28.12/28.42 ! [V_l,V_k,V_j,V_i] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 28.12/28.42 => 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))) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_mult__le__mono2,axiom,
% 28.12/28.42 ! [V_k,V_j,V_i] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 28.12/28.42 => 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))) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_mult__le__mono1,axiom,
% 28.12/28.42 ! [V_k,V_j,V_i] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 28.12/28.42 => 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))) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_le__cube,axiom,
% 28.12/28.42 ! [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)))) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_le__square,axiom,
% 28.12/28.42 ! [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))) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_diff__mult__distrib,axiom,
% 28.12/28.42 ! [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)) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_diff__mult__distrib2,axiom,
% 28.12/28.42 ! [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)) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_nat__mult__1,axiom,
% 28.12/28.42 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ).
% 28.12/28.42
% 28.12/28.42 fof(fact_nat__1__eq__mult__iff,axiom,
% 28.12/28.42 ! [V_n_2,V_m_2] :
% 28.12/28.42 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)
% 28.12/28.42 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 28.12/28.42 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_nat__mult__1__right,axiom,
% 28.12/28.42 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 28.12/28.42
% 28.12/28.42 fof(fact_nat__mult__eq__1__iff,axiom,
% 28.12/28.42 ! [V_n_2,V_m_2] :
% 28.12/28.42 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 28.12/28.42 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 28.12/28.42 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_add__diff__inverse,axiom,
% 28.12/28.42 ! [V_n,V_m] :
% 28.12/28.42 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 28.12/28.42 => 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 ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_less__diff__conv,axiom,
% 28.12/28.42 ! [V_k_2,V_j_2,V_i_2] :
% 28.12/28.42 ( 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)))
% 28.12/28.42 <=> 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)) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_less__diff__iff,axiom,
% 28.12/28.42 ! [V_n_2,V_m_2,V_k_2] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 28.12/28.42 => ( 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)))
% 28.12/28.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_diff__less__mono,axiom,
% 28.12/28.42 ! [V_c,V_b,V_a] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a))
% 28.12/28.42 => 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))) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_diff__diff__right,axiom,
% 28.12/28.42 ! [V_i,V_j,V_k] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 28.12/28.42 => 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) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_le__diff__conv,axiom,
% 28.12/28.42 ! [V_i_2,V_k_2,V_j_2] :
% 28.12/28.42 ( 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))
% 28.12/28.42 <=> 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))) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_le__add__diff,axiom,
% 28.12/28.42 ! [V_m,V_n,V_k] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 28.12/28.42 => 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))) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_le__add__diff__inverse,axiom,
% 28.12/28.42 ! [V_m,V_n] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 28.12/28.42 => 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 ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_arith__series__general,axiom,
% 28.12/28.42 ! [V_n_2,V_d_2,V_a_2,T_b] :
% 28.12/28.42 ( class_Rings_Ocomm__semiring__1(T_b)
% 28.12/28.42 => 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)))) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_setsum__natinterval__difff,axiom,
% 28.12/28.42 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 28.12/28.42 ( class_Groups_Oab__group__add(T_b)
% 28.12/28.42 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 28.12/28.42 => 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)))) )
% 28.12/28.42 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 28.12/28.42 => 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) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_termination__basic__simps_I3_J,axiom,
% 28.12/28.42 ! [V_z,V_y,V_x] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y))
% 28.12/28.42 => 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))) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_termination__basic__simps_I4_J,axiom,
% 28.12/28.42 ! [V_y,V_z,V_x] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z))
% 28.12/28.42 => 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))) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_termination__basic__simps_I5_J,axiom,
% 28.12/28.42 ! [V_y,V_x] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 28.12/28.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_termination__basic__simps_I2_J,axiom,
% 28.12/28.42 ! [V_y,V_z,V_x] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z))
% 28.12/28.42 => 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))) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_termination__basic__simps_I1_J,axiom,
% 28.12/28.42 ! [V_z,V_y,V_x] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 28.12/28.42 => 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))) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_less__zeroE,axiom,
% 28.12/28.42 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_le0,axiom,
% 28.12/28.42 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_of__nat__0__less__iff,axiom,
% 28.12/28.42 ! [V_n_2,T_b] :
% 28.12/28.42 ( class_Rings_Olinordered__semidom(T_b)
% 28.12/28.42 => ( 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)))
% 28.12/28.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_of__nat__less__0__iff,axiom,
% 28.12/28.42 ! [V_m,T_a] :
% 28.12/28.42 ( class_Rings_Olinordered__semidom(T_a)
% 28.12/28.42 => ~ 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))) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_of__nat__0,axiom,
% 28.12/28.42 ! [T_a] :
% 28.12/28.42 ( class_Rings_Osemiring__1(T_a)
% 28.12/28.42 => 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) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_of__nat__eq__iff,axiom,
% 28.12/28.42 ! [V_n_2,V_m_2,T_b] :
% 28.12/28.42 ( class_Nat_Osemiring__char__0(T_b)
% 28.12/28.42 => ( 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)
% 28.12/28.42 <=> V_m_2 = V_n_2 ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_of__nat__0__le__iff,axiom,
% 28.12/28.42 ! [V_n,T_a] :
% 28.12/28.42 ( class_Rings_Olinordered__semidom(T_a)
% 28.12/28.42 => 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))) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_zero__le__imp__of__nat,axiom,
% 28.12/28.42 ! [V_m,T_a] :
% 28.12/28.42 ( class_Rings_Olinordered__semidom(T_a)
% 28.12/28.42 => 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))) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_zero__reorient,axiom,
% 28.12/28.42 ! [V_x_2,T_b] :
% 28.12/28.42 ( class_Groups_Ozero(T_b)
% 28.12/28.42 => ( c_Groups_Ozero__class_Ozero(T_b) = V_x_2
% 28.12/28.42 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_add__0__iff,axiom,
% 28.12/28.42 ! [V_a_2,V_b_2,T_b] :
% 28.12/28.42 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 28.12/28.42 => ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2)
% 28.12/28.42 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 28.12/28.42 ! [V_a,T_a] :
% 28.12/28.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.12/28.42 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 28.12/28.42 ! [V_a,T_a] :
% 28.12/28.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.12/28.42 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_add__0__left,axiom,
% 28.12/28.42 ! [V_a,T_a] :
% 28.12/28.42 ( class_Groups_Omonoid__add(T_a)
% 28.12/28.42 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_add__0,axiom,
% 28.12/28.42 ! [V_a,T_a] :
% 28.12/28.42 ( class_Groups_Ocomm__monoid__add(T_a)
% 28.12/28.42 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_double__zero__sym,axiom,
% 28.12/28.42 ! [V_a_2,T_b] :
% 28.12/28.42 ( class_Groups_Olinordered__ab__group__add(T_b)
% 28.12/28.42 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)
% 28.12/28.42 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_add__0__right,axiom,
% 28.12/28.42 ! [V_a,T_a] :
% 28.12/28.42 ( class_Groups_Omonoid__add(T_a)
% 28.12/28.42 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_add_Ocomm__neutral,axiom,
% 28.12/28.42 ! [V_a,T_a] :
% 28.12/28.42 ( class_Groups_Ocomm__monoid__add(T_a)
% 28.12/28.42 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_mult__zero__left,axiom,
% 28.12/28.42 ! [V_a,T_a] :
% 28.12/28.42 ( class_Rings_Omult__zero(T_a)
% 28.12/28.42 => 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) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_mult__zero__right,axiom,
% 28.12/28.42 ! [V_a,T_a] :
% 28.12/28.42 ( class_Rings_Omult__zero(T_a)
% 28.12/28.42 => 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) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_mult__eq__0__iff,axiom,
% 28.12/28.42 ! [V_b_2,V_a_2,T_b] :
% 28.12/28.42 ( class_Rings_Oring__no__zero__divisors(T_b)
% 28.12/28.42 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
% 28.12/28.42 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
% 28.12/28.42 | V_b_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_no__zero__divisors,axiom,
% 28.12/28.42 ! [V_b,V_a,T_a] :
% 28.12/28.42 ( class_Rings_Ono__zero__divisors(T_a)
% 28.12/28.42 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 28.12/28.42 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 28.12/28.42 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_divisors__zero,axiom,
% 28.12/28.42 ! [V_b,V_a,T_a] :
% 28.12/28.42 ( class_Rings_Ono__zero__divisors(T_a)
% 28.12/28.42 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 28.12/28.42 => ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 28.12/28.42 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 28.12/28.42 ! [V_a,T_a] :
% 28.12/28.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.12/28.42 => 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) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 28.12/28.42 ! [V_a,T_a] :
% 28.12/28.42 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.12/28.42 => 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) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_diff__0__right,axiom,
% 28.12/28.42 ! [V_a,T_a] :
% 28.12/28.42 ( class_Groups_Ogroup__add(T_a)
% 28.12/28.42 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_diff__self,axiom,
% 28.12/28.42 ! [V_a,T_a] :
% 28.12/28.42 ( class_Groups_Ogroup__add(T_a)
% 28.12/28.42 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_eq__iff__diff__eq__0,axiom,
% 28.12/28.42 ! [V_b_2,V_a_2,T_b] :
% 28.12/28.42 ( class_Groups_Oab__group__add(T_b)
% 28.12/28.42 => ( V_a_2 = V_b_2
% 28.12/28.42 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_right__minus__eq,axiom,
% 28.12/28.42 ! [V_b_2,V_a_2,T_b] :
% 28.12/28.42 ( class_Groups_Ogroup__add(T_b)
% 28.12/28.42 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
% 28.12/28.42 <=> V_a_2 = V_b_2 ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_one__neq__zero,axiom,
% 28.12/28.42 ! [T_a] :
% 28.12/28.42 ( class_Rings_Ozero__neq__one(T_a)
% 28.12/28.42 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_zero__neq__one,axiom,
% 28.12/28.42 ! [T_a] :
% 28.12/28.42 ( class_Rings_Ozero__neq__one(T_a)
% 28.12/28.42 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_neg__equal__zero,axiom,
% 28.12/28.42 ! [V_a_2,T_b] :
% 28.12/28.42 ( class_Groups_Olinordered__ab__group__add(T_b)
% 28.12/28.42 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_a_2
% 28.12/28.42 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_neg__equal__0__iff__equal,axiom,
% 28.12/28.42 ! [V_a_2,T_b] :
% 28.12/28.42 ( class_Groups_Ogroup__add(T_b)
% 28.12/28.42 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 28.12/28.42 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_equal__neg__zero,axiom,
% 28.12/28.42 ! [V_a_2,T_b] :
% 28.12/28.42 ( class_Groups_Olinordered__ab__group__add(T_b)
% 28.12/28.42 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
% 28.12/28.42 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_neg__0__equal__iff__equal,axiom,
% 28.12/28.42 ! [V_a_2,T_b] :
% 28.12/28.42 ( class_Groups_Ogroup__add(T_b)
% 28.12/28.42 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
% 28.12/28.42 <=> c_Groups_Ozero__class_Ozero(T_b) = V_a_2 ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_minus__zero,axiom,
% 28.12/28.42 ! [T_a] :
% 28.12/28.42 ( class_Groups_Ogroup__add(T_a)
% 28.12/28.42 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_not__less0,axiom,
% 28.12/28.42 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_neq0__conv,axiom,
% 28.12/28.42 ! [V_n_2] :
% 28.12/28.42 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.12/28.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_less__nat__zero__code,axiom,
% 28.12/28.42 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_gr__implies__not0,axiom,
% 28.12/28.42 ! [V_n,V_m] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 28.12/28.42 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_gr0I,axiom,
% 28.12/28.42 ! [V_n] :
% 28.12/28.42 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.12/28.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_add__eq__self__zero,axiom,
% 28.12/28.42 ! [V_n,V_m] :
% 28.12/28.42 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m
% 28.12/28.42 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_add__is__0,axiom,
% 28.12/28.42 ! [V_n_2,V_m_2] :
% 28.12/28.42 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.12/28.42 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.12/28.42 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_Nat_Oadd__0__right,axiom,
% 28.12/28.42 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 28.12/28.42
% 28.12/28.42 fof(fact_plus__nat_Oadd__0,axiom,
% 28.12/28.42 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 28.12/28.42
% 28.12/28.42 fof(fact_less__eq__nat_Osimps_I1_J,axiom,
% 28.12/28.42 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_le__0__eq,axiom,
% 28.12/28.42 ! [V_n_2] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 28.12/28.42 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_diff__0__eq__0,axiom,
% 28.12/28.42 ! [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) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_minus__nat_Odiff__0,axiom,
% 28.12/28.42 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 28.12/28.42
% 28.12/28.42 fof(fact_diff__self__eq__0,axiom,
% 28.12/28.42 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_diffs0__imp__equal,axiom,
% 28.12/28.42 ! [V_n,V_m] :
% 28.12/28.42 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.12/28.42 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.12/28.42 => V_m = V_n ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_nat__mult__eq__cancel__disj,axiom,
% 28.12/28.42 ! [V_n_2,V_m_2,V_k_2] :
% 28.12/28.42 ( 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)
% 28.12/28.42 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.12/28.42 | V_m_2 = V_n_2 ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_mult__cancel2,axiom,
% 28.12/28.42 ! [V_n_2,V_k_2,V_m_2] :
% 28.12/28.42 ( 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)
% 28.12/28.42 <=> ( V_m_2 = V_n_2
% 28.12/28.42 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_mult__cancel1,axiom,
% 28.12/28.42 ! [V_n_2,V_m_2,V_k_2] :
% 28.12/28.42 ( 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)
% 28.12/28.42 <=> ( V_m_2 = V_n_2
% 28.12/28.42 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_mult__is__0,axiom,
% 28.12/28.42 ! [V_n_2,V_m_2] :
% 28.12/28.42 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.12/28.42 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.12/28.42 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_mult__0__right,axiom,
% 28.12/28.42 ! [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) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_mult__0,axiom,
% 28.12/28.42 ! [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) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_inj__of__nat,axiom,
% 28.12/28.42 ! [T_b] :
% 28.12/28.42 ( class_Nat_Osemiring__char__0(T_b)
% 28.12/28.42 => 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))) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_atLeastLessThan0,axiom,
% 28.12/28.42 ! [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)) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_atLeast__0,axiom,
% 28.12/28.42 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)) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_lessThan__0,axiom,
% 28.12/28.42 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)) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_atMost__0,axiom,
% 28.12/28.42 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))) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_setsum__0,axiom,
% 28.12/28.42 ! [V_A_2,T_c,T_b] :
% 28.12/28.42 ( class_Groups_Ocomm__monoid__add(T_b)
% 28.12/28.42 => 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) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_of__nat__less__imp__less,axiom,
% 28.12/28.42 ! [V_n,V_m,T_a] :
% 28.12/28.42 ( class_Rings_Olinordered__semidom(T_a)
% 28.12/28.42 => ( 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)))
% 28.12/28.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_less__imp__of__nat__less,axiom,
% 28.12/28.42 ! [V_n,V_m,T_a] :
% 28.12/28.42 ( class_Rings_Olinordered__semidom(T_a)
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 28.12/28.42 => 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))) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_of__nat__less__iff,axiom,
% 28.12/28.42 ! [V_n_2,V_m_2,T_b] :
% 28.12/28.42 ( class_Rings_Olinordered__semidom(T_b)
% 28.12/28.42 => ( 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)))
% 28.12/28.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_of__nat__le__iff,axiom,
% 28.12/28.42 ! [V_n_2,V_m_2,T_b] :
% 28.12/28.42 ( class_Rings_Olinordered__semidom(T_b)
% 28.12/28.42 => ( 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)))
% 28.12/28.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_of__nat__add,axiom,
% 28.12/28.42 ! [V_n,V_m,T_a] :
% 28.12/28.42 ( class_Rings_Osemiring__1(T_a)
% 28.12/28.42 => 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)) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
% 28.12/28.42 ! [V_a_2,T_b] :
% 28.12/28.42 ( class_Groups_Olinordered__ab__group__add(T_b)
% 28.12/28.42 => ( 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)))
% 28.12/28.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
% 28.12/28.42 ! [V_a_2,T_b] :
% 28.12/28.42 ( class_Groups_Olinordered__ab__group__add(T_b)
% 28.12/28.42 => ( 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)))
% 28.12/28.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_add__nonneg__nonneg,axiom,
% 28.12/28.42 ! [V_b,V_a,T_a] :
% 28.12/28.42 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 28.12/28.42 => 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))) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_add__nonneg__eq__0__iff,axiom,
% 28.12/28.42 ! [V_y_2,V_x_2,T_b] :
% 28.12/28.42 ( class_Groups_Oordered__comm__monoid__add(T_b)
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_x_2))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_y_2))
% 28.12/28.42 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_b)
% 28.12/28.42 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 28.12/28.42 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_add__increasing,axiom,
% 28.12/28.42 ! [V_c,V_b,V_a,T_a] :
% 28.12/28.42 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 28.12/28.42 => 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))) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_add__increasing2,axiom,
% 28.12/28.42 ! [V_a,V_b,V_c,T_a] :
% 28.12/28.42 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 28.12/28.42 => 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))) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_add__nonpos__nonpos,axiom,
% 28.12/28.42 ! [V_b,V_a,T_a] :
% 28.12/28.42 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 28.12/28.42 => 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))) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_split__mult__neg__le,axiom,
% 28.12/28.42 ! [V_b,V_a,T_a] :
% 28.12/28.42 ( class_Rings_Oordered__cancel__semiring(T_a)
% 28.12/28.42 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.12/28.42 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) )
% 28.12/28.42 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 28.12/28.42 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) )
% 28.12/28.42 => 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))) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_split__mult__pos__le,axiom,
% 28.12/28.42 ! [V_b,V_a,T_a] :
% 28.12/28.42 ( class_Rings_Oordered__ring(T_a)
% 28.12/28.42 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.12/28.42 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) )
% 28.12/28.42 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 28.12/28.42 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 28.12/28.42 => 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))) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_mult__mono,axiom,
% 28.12/28.42 ! [V_d,V_c,V_b,V_a,T_a] :
% 28.12/28.42 ( class_Rings_Oordered__semiring(T_a)
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 28.12/28.42 => 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))) ) ) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_mult__mono_H,axiom,
% 28.12/28.42 ! [V_d,V_c,V_b,V_a,T_a] :
% 28.12/28.42 ( class_Rings_Oordered__semiring(T_a)
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 28.12/28.42 => 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))) ) ) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_mult__left__mono__neg,axiom,
% 28.12/28.42 ! [V_c,V_a,V_b,T_a] :
% 28.12/28.42 ( class_Rings_Oordered__ring(T_a)
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 28.12/28.42 => 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))) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_mult__right__mono__neg,axiom,
% 28.12/28.42 ! [V_c,V_a,V_b,T_a] :
% 28.12/28.42 ( class_Rings_Oordered__ring(T_a)
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 28.12/28.42 => 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))) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_comm__mult__left__mono,axiom,
% 28.12/28.42 ! [V_c,V_b,V_a,T_a] :
% 28.12/28.42 ( class_Rings_Oordered__comm__semiring(T_a)
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 28.12/28.42 => 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))) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_mult__left__mono,axiom,
% 28.12/28.42 ! [V_c,V_b,V_a,T_a] :
% 28.12/28.42 ( class_Rings_Oordered__semiring(T_a)
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 28.12/28.42 => 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))) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_mult__right__mono,axiom,
% 28.12/28.42 ! [V_c,V_b,V_a,T_a] :
% 28.12/28.42 ( class_Rings_Oordered__semiring(T_a)
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 28.12/28.42 => 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))) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_mult__nonpos__nonpos,axiom,
% 28.12/28.42 ! [V_b,V_a,T_a] :
% 28.12/28.42 ( class_Rings_Oordered__ring(T_a)
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 28.12/28.42 => 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))) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_mult__nonpos__nonneg,axiom,
% 28.12/28.42 ! [V_b,V_a,T_a] :
% 28.12/28.42 ( class_Rings_Oordered__cancel__semiring(T_a)
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 28.12/28.42 => 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))) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_mult__nonneg__nonpos2,axiom,
% 28.12/28.42 ! [V_b,V_a,T_a] :
% 28.12/28.42 ( class_Rings_Oordered__cancel__semiring(T_a)
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 28.12/28.42 => 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))) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_mult__nonneg__nonpos,axiom,
% 28.12/28.42 ! [V_b,V_a,T_a] :
% 28.12/28.42 ( class_Rings_Oordered__cancel__semiring(T_a)
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 28.12/28.42 => 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))) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_mult__nonneg__nonneg,axiom,
% 28.12/28.42 ! [V_b,V_a,T_a] :
% 28.12/28.42 ( class_Rings_Oordered__cancel__semiring(T_a)
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 28.12/28.42 => 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))) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_mult__le__0__iff,axiom,
% 28.12/28.42 ! [V_b_2,V_a_2,T_b] :
% 28.12/28.42 ( class_Rings_Olinordered__ring__strict(T_b)
% 28.12/28.42 => ( 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)))
% 28.12/28.42 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 28.12/28.42 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 28.12/28.42 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.12/28.42 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_zero__le__mult__iff,axiom,
% 28.12/28.42 ! [V_b_2,V_a_2,T_b] :
% 28.12/28.42 ( class_Rings_Olinordered__ring__strict(T_b)
% 28.12/28.42 => ( 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)))
% 28.12/28.42 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 28.12/28.42 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 28.12/28.42 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.12/28.42 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_zero__le__square,axiom,
% 28.12/28.42 ! [V_a,T_a] :
% 28.12/28.42 ( class_Rings_Olinordered__ring(T_a)
% 28.12/28.42 => 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))) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_pos__add__strict,axiom,
% 28.12/28.42 ! [V_c,V_b,V_a,T_a] :
% 28.12/28.42 ( class_Rings_Olinordered__semidom(T_a)
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 28.12/28.42 => 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))) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
% 28.12/28.42 ! [V_a_2,T_b] :
% 28.12/28.42 ( class_Groups_Olinordered__ab__group__add(T_b)
% 28.12/28.42 => ( 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)))
% 28.12/28.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
% 28.12/28.42 ! [V_a_2,T_b] :
% 28.12/28.42 ( class_Groups_Olinordered__ab__group__add(T_b)
% 28.12/28.42 => ( 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)))
% 28.12/28.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_add__pos__pos,axiom,
% 28.12/28.42 ! [V_b,V_a,T_a] :
% 28.12/28.42 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 28.12/28.42 => 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))) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_add__neg__neg,axiom,
% 28.12/28.42 ! [V_b,V_a,T_a] :
% 28.12/28.42 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 28.12/28.42 => 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))) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_mult__strict__left__mono__neg,axiom,
% 28.12/28.42 ! [V_c,V_a,V_b,T_a] :
% 28.12/28.42 ( class_Rings_Olinordered__ring__strict(T_a)
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 28.12/28.42 => 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))) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_mult__strict__right__mono__neg,axiom,
% 28.12/28.42 ! [V_c,V_a,V_b,T_a] :
% 28.12/28.42 ( class_Rings_Olinordered__ring__strict(T_a)
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 28.12/28.42 => 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))) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_comm__mult__strict__left__mono,axiom,
% 28.12/28.42 ! [V_c,V_b,V_a,T_a] :
% 28.12/28.42 ( class_Rings_Olinordered__comm__semiring__strict(T_a)
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 28.12/28.42 => 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))) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_mult__strict__left__mono,axiom,
% 28.12/28.42 ! [V_c,V_b,V_a,T_a] :
% 28.12/28.42 ( class_Rings_Olinordered__semiring__strict(T_a)
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 28.12/28.42 => 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))) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_mult__strict__right__mono,axiom,
% 28.12/28.42 ! [V_c,V_b,V_a,T_a] :
% 28.12/28.42 ( class_Rings_Olinordered__semiring__strict(T_a)
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 28.12/28.42 => 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))) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_mult__neg__neg,axiom,
% 28.12/28.42 ! [V_b,V_a,T_a] :
% 28.12/28.42 ( class_Rings_Olinordered__ring__strict(T_a)
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 28.12/28.42 => 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))) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_mult__neg__pos,axiom,
% 28.12/28.42 ! [V_b,V_a,T_a] :
% 28.12/28.42 ( class_Rings_Olinordered__semiring__strict(T_a)
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 28.12/28.42 => 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))) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_mult__less__cancel__left__neg,axiom,
% 28.12/28.42 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 28.12/28.42 ( class_Rings_Olinordered__ring__strict(T_b)
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.12/28.42 => ( 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)))
% 28.12/28.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_zero__less__mult__pos2,axiom,
% 28.12/28.42 ! [V_a,V_b,T_a] :
% 28.12/28.42 ( class_Rings_Olinordered__semiring__strict(T_a)
% 28.12/28.42 => ( 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)))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.12/28.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_zero__less__mult__pos,axiom,
% 28.12/28.42 ! [V_b,V_a,T_a] :
% 28.12/28.42 ( class_Rings_Olinordered__semiring__strict(T_a)
% 28.12/28.42 => ( 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)))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.12/28.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_mult__pos__neg2,axiom,
% 28.12/28.42 ! [V_b,V_a,T_a] :
% 28.12/28.42 ( class_Rings_Olinordered__semiring__strict(T_a)
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 28.12/28.42 => 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))) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_mult__pos__neg,axiom,
% 28.12/28.42 ! [V_b,V_a,T_a] :
% 28.12/28.42 ( class_Rings_Olinordered__semiring__strict(T_a)
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 28.12/28.42 => 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))) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_mult__pos__pos,axiom,
% 28.12/28.42 ! [V_b,V_a,T_a] :
% 28.12/28.42 ( class_Rings_Olinordered__semiring__strict(T_a)
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 28.12/28.42 => 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))) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_mult__less__cancel__left__pos,axiom,
% 28.12/28.42 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 28.12/28.42 ( class_Rings_Olinordered__ring__strict(T_b)
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.12/28.42 => ( 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)))
% 28.12/28.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_mult__less__cancel__left__disj,axiom,
% 28.12/28.42 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 28.12/28.42 ( class_Rings_Olinordered__ring__strict(T_b)
% 28.12/28.42 => ( 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)))
% 28.12/28.42 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.12/28.42 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
% 28.12/28.42 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.12/28.42 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_mult__less__cancel__right__disj,axiom,
% 28.12/28.42 ! [V_b_2,V_c_2,V_a_2,T_b] :
% 28.12/28.42 ( class_Rings_Olinordered__ring__strict(T_b)
% 28.12/28.42 => ( 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)))
% 28.12/28.42 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.12/28.42 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
% 28.12/28.42 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.12/28.42 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_not__square__less__zero,axiom,
% 28.12/28.42 ! [V_a,T_a] :
% 28.12/28.42 ( class_Rings_Olinordered__ring(T_a)
% 28.12/28.42 => ~ 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))) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_of__nat__mult,axiom,
% 28.12/28.42 ! [V_n,V_m,T_a] :
% 28.12/28.42 ( class_Rings_Osemiring__1(T_a)
% 28.12/28.42 => 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)) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_le__iff__diff__le__0,axiom,
% 28.12/28.42 ! [V_b_2,V_a_2,T_b] :
% 28.12/28.42 ( class_Groups_Oordered__ab__group__add(T_b)
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 28.12/28.42 <=> 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))) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_less__iff__diff__less__0,axiom,
% 28.12/28.42 ! [V_b_2,V_a_2,T_b] :
% 28.12/28.42 ( class_Groups_Oordered__ab__group__add(T_b)
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 28.12/28.42 <=> 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))) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_add__scale__eq__noteq,axiom,
% 28.12/28.42 ! [V_d,V_c,V_b,V_a,V_r,T_a] :
% 28.12/28.42 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 28.12/28.42 => ( V_r != c_Groups_Ozero__class_Ozero(T_a)
% 28.12/28.42 => ( ( V_a = V_b
% 28.12/28.42 & V_c != V_d )
% 28.12/28.42 => 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)) ) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_not__one__le__zero,axiom,
% 28.12/28.42 ! [T_a] :
% 28.12/28.42 ( class_Rings_Olinordered__semidom(T_a)
% 28.12/28.42 => ~ 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))) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_zero__le__one,axiom,
% 28.12/28.42 ! [T_a] :
% 28.12/28.42 ( class_Rings_Olinordered__semidom(T_a)
% 28.12/28.42 => 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))) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_not__one__less__zero,axiom,
% 28.12/28.42 ! [T_a] :
% 28.12/28.42 ( class_Rings_Olinordered__semidom(T_a)
% 28.12/28.42 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_zero__less__one,axiom,
% 28.12/28.42 ! [T_a] :
% 28.12/28.42 ( class_Rings_Olinordered__semidom(T_a)
% 28.12/28.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_minus__le__self__iff,axiom,
% 28.12/28.42 ! [V_a_2,T_b] :
% 28.12/28.42 ( class_Groups_Olinordered__ab__group__add(T_b)
% 28.12/28.42 => ( 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))
% 28.12/28.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_neg__le__0__iff__le,axiom,
% 28.12/28.42 ! [V_a_2,T_b] :
% 28.12/28.42 ( class_Groups_Oordered__ab__group__add(T_b)
% 28.12/28.42 => ( 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)))
% 28.12/28.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_le__minus__self__iff,axiom,
% 28.12/28.42 ! [V_a_2,T_b] :
% 28.12/28.42 ( class_Groups_Olinordered__ab__group__add(T_b)
% 28.12/28.42 => ( 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)))
% 28.12/28.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_neg__0__le__iff__le,axiom,
% 28.12/28.42 ! [V_a_2,T_b] :
% 28.12/28.42 ( class_Groups_Oordered__ab__group__add(T_b)
% 28.12/28.42 => ( 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)))
% 28.12/28.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_neg__less__nonneg,axiom,
% 28.12/28.42 ! [V_a_2,T_b] :
% 28.12/28.42 ( class_Groups_Olinordered__ab__group__add(T_b)
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2))
% 28.12/28.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_neg__less__0__iff__less,axiom,
% 28.12/28.42 ! [V_a_2,T_b] :
% 28.12/28.42 ( class_Groups_Oordered__ab__group__add(T_b)
% 28.12/28.42 => ( 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)))
% 28.12/28.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_neg__0__less__iff__less,axiom,
% 28.12/28.42 ! [V_a_2,T_b] :
% 28.12/28.42 ( class_Groups_Oordered__ab__group__add(T_b)
% 28.12/28.42 => ( 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)))
% 28.12/28.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_less__minus__self__iff,axiom,
% 28.12/28.42 ! [V_a_2,T_b] :
% 28.12/28.42 ( class_Rings_Olinordered__idom(T_b)
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 28.12/28.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_minus__unique,axiom,
% 28.12/28.42 ! [V_b,V_a,T_a] :
% 28.12/28.42 ( class_Groups_Ogroup__add(T_a)
% 28.12/28.42 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 28.12/28.42 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_ab__left__minus,axiom,
% 28.12/28.42 ! [V_a,T_a] :
% 28.12/28.42 ( class_Groups_Oab__group__add(T_a)
% 28.12/28.42 => 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) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_left__minus,axiom,
% 28.12/28.42 ! [V_a,T_a] :
% 28.12/28.42 ( class_Groups_Ogroup__add(T_a)
% 28.12/28.42 => 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) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_eq__neg__iff__add__eq__0,axiom,
% 28.12/28.42 ! [V_b_2,V_a_2,T_b] :
% 28.12/28.42 ( class_Groups_Ogroup__add(T_b)
% 28.12/28.42 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 28.12/28.42 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_right__minus,axiom,
% 28.12/28.42 ! [V_a,T_a] :
% 28.12/28.42 ( class_Groups_Ogroup__add(T_a)
% 28.12/28.42 => 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) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_of__nat__1,axiom,
% 28.12/28.42 ! [T_a] :
% 28.12/28.42 ( class_Rings_Osemiring__1(T_a)
% 28.12/28.42 => 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) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_diff__0,axiom,
% 28.12/28.42 ! [V_a,T_a] :
% 28.12/28.42 ( class_Groups_Ogroup__add(T_a)
% 28.12/28.42 => 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) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_setsum__empty,axiom,
% 28.12/28.42 ! [V_f_2,T_c,T_b] :
% 28.12/28.42 ( class_Groups_Ocomm__monoid__add(T_b)
% 28.12/28.42 => 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) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_setsum_Oempty,axiom,
% 28.12/28.42 ! [V_g_2,T_c,T_b] :
% 28.12/28.42 ( class_Groups_Ocomm__monoid__add(T_b)
% 28.12/28.42 => 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) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_setsum__infinite,axiom,
% 28.12/28.42 ! [V_f_2,V_A_2,T_b,T_c] :
% 28.12/28.42 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.12/28.42 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.42 => 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) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_setsum_Oinfinite,axiom,
% 28.12/28.42 ! [V_g_2,V_A_2,T_b,T_c] :
% 28.12/28.42 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.12/28.42 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.42 => 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) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_add__gr__0,axiom,
% 28.12/28.42 ! [V_n_2,V_m_2] :
% 28.12/28.42 ( 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)))
% 28.12/28.42 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 28.12/28.42 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_diff__less,axiom,
% 28.12/28.42 ! [V_m,V_n] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 28.12/28.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 28.12/28.42 => 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)) ) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_zero__less__diff,axiom,
% 28.12/28.42 ! [V_m_2,V_n_2] :
% 28.12/28.42 ( 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)))
% 28.12/28.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 28.12/28.42
% 28.12/28.42 fof(fact_nat__mult__eq__cancel1,axiom,
% 28.12/28.42 ! [V_n_2,V_m_2,V_k_2] :
% 28.12/28.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 28.12/28.42 => ( 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)
% 28.12/28.43 <=> V_m_2 = V_n_2 ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_nat__mult__less__cancel1,axiom,
% 28.12/28.43 ! [V_n_2,V_m_2,V_k_2] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 28.12/28.43 => ( 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)))
% 28.12/28.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_nat__0__less__mult__iff,axiom,
% 28.12/28.43 ! [V_n_2,V_m_2] :
% 28.12/28.43 ( 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)))
% 28.12/28.43 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 28.12/28.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_mult__less__cancel1,axiom,
% 28.12/28.43 ! [V_n_2,V_m_2,V_k_2] :
% 28.12/28.43 ( 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)))
% 28.12/28.43 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 28.12/28.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_mult__less__cancel2,axiom,
% 28.12/28.43 ! [V_n_2,V_k_2,V_m_2] :
% 28.12/28.43 ( 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)))
% 28.12/28.43 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 28.12/28.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_mult__less__mono1,axiom,
% 28.12/28.43 ! [V_k,V_j,V_i] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 28.12/28.43 => 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))) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_mult__less__mono2,axiom,
% 28.12/28.43 ! [V_k,V_j,V_i] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 28.12/28.43 => 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))) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_diff__add__0,axiom,
% 28.12/28.43 ! [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) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_diff__is__0__eq_H,axiom,
% 28.12/28.43 ! [V_n,V_m] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 28.12/28.43 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_diff__is__0__eq,axiom,
% 28.12/28.43 ! [V_n_2,V_m_2] :
% 28.12/28.43 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.12/28.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_mult__eq__self__implies__10,axiom,
% 28.12/28.43 ! [V_n,V_m] :
% 28.12/28.43 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)
% 28.12/28.43 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 28.12/28.43 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_setsum__eq__0__iff,axiom,
% 28.12/28.43 ! [V_f_2,V_F_2,T_b] :
% 28.12/28.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 28.12/28.43 => ( 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)
% 28.12/28.43 <=> ! [B_x] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2))
% 28.12/28.43 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_atLeast0LessThan,axiom,
% 28.12/28.43 ! [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) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_atLeast0AtMost,axiom,
% 28.12/28.43 ! [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) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_add__pos__nonneg,axiom,
% 28.12/28.43 ! [V_b,V_a,T_a] :
% 28.12/28.43 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 28.12/28.43 => 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))) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_add__nonneg__pos,axiom,
% 28.12/28.43 ! [V_b,V_a,T_a] :
% 28.12/28.43 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 28.12/28.43 => 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))) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_add__strict__increasing,axiom,
% 28.12/28.43 ! [V_c,V_b,V_a,T_a] :
% 28.12/28.43 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 28.12/28.43 => 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))) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_add__strict__increasing2,axiom,
% 28.12/28.43 ! [V_c,V_b,V_a,T_a] :
% 28.12/28.43 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 28.12/28.43 => 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))) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_add__neg__nonpos,axiom,
% 28.12/28.43 ! [V_b,V_a,T_a] :
% 28.12/28.43 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 28.12/28.43 => 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))) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_add__nonpos__neg,axiom,
% 28.12/28.43 ! [V_b,V_a,T_a] :
% 28.12/28.43 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 28.12/28.43 => 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))) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_mult__le__cancel__left__pos,axiom,
% 28.12/28.43 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 28.12/28.43 ( class_Rings_Olinordered__ring__strict(T_b)
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.12/28.43 => ( 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)))
% 28.12/28.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_mult__le__cancel__left__neg,axiom,
% 28.12/28.43 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 28.12/28.43 ( class_Rings_Olinordered__ring__strict(T_b)
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.12/28.43 => ( 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)))
% 28.12/28.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_mult__strict__mono,axiom,
% 28.12/28.43 ! [V_d,V_c,V_b,V_a,T_a] :
% 28.12/28.43 ( class_Rings_Olinordered__semiring__strict(T_a)
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 28.12/28.43 => 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))) ) ) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_mult__strict__mono_H,axiom,
% 28.12/28.43 ! [V_d,V_c,V_b,V_a,T_a] :
% 28.12/28.43 ( class_Rings_Olinordered__semiring__strict(T_a)
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 28.12/28.43 => 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))) ) ) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_mult__less__le__imp__less,axiom,
% 28.12/28.43 ! [V_d,V_c,V_b,V_a,T_a] :
% 28.12/28.43 ( class_Rings_Olinordered__semiring__strict(T_a)
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 28.12/28.43 => 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))) ) ) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_mult__le__less__imp__less,axiom,
% 28.12/28.43 ! [V_d,V_c,V_b,V_a,T_a] :
% 28.12/28.43 ( class_Rings_Olinordered__semiring__strict(T_a)
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 28.12/28.43 => 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))) ) ) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_mult__right__less__imp__less,axiom,
% 28.12/28.43 ! [V_b,V_c,V_a,T_a] :
% 28.12/28.43 ( class_Rings_Olinordered__semiring(T_a)
% 28.12/28.43 => ( 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)))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 28.12/28.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_mult__less__imp__less__right,axiom,
% 28.12/28.43 ! [V_b,V_c,V_a,T_a] :
% 28.12/28.43 ( class_Rings_Olinordered__semiring__strict(T_a)
% 28.12/28.43 => ( 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)))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 28.12/28.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_mult__left__less__imp__less,axiom,
% 28.12/28.43 ! [V_b,V_a,V_c,T_a] :
% 28.12/28.43 ( class_Rings_Olinordered__semiring(T_a)
% 28.12/28.43 => ( 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)))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 28.12/28.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_mult__less__imp__less__left,axiom,
% 28.12/28.43 ! [V_b,V_a,V_c,T_a] :
% 28.12/28.43 ( class_Rings_Olinordered__semiring__strict(T_a)
% 28.12/28.43 => ( 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)))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 28.12/28.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_mult__right__le__imp__le,axiom,
% 28.12/28.43 ! [V_b,V_c,V_a,T_a] :
% 28.12/28.43 ( class_Rings_Olinordered__semiring__strict(T_a)
% 28.12/28.43 => ( 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)))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 28.12/28.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_mult__left__le__imp__le,axiom,
% 28.12/28.43 ! [V_b,V_a,V_c,T_a] :
% 28.12/28.43 ( class_Rings_Olinordered__semiring__strict(T_a)
% 28.12/28.43 => ( 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)))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 28.12/28.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_mult__right__le__one__le,axiom,
% 28.12/28.43 ! [V_y,V_x,T_a] :
% 28.12/28.43 ( class_Rings_Olinordered__idom(T_a)
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 28.12/28.43 => 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)) ) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_mult__left__le__one__le,axiom,
% 28.12/28.43 ! [V_y,V_x,T_a] :
% 28.12/28.43 ( class_Rings_Olinordered__idom(T_a)
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 28.12/28.43 => 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)) ) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zero__less__two,axiom,
% 28.12/28.43 ! [T_a] :
% 28.12/28.43 ( class_Rings_Olinordered__semidom(T_a)
% 28.12/28.43 => 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)))) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_of__nat__diff,axiom,
% 28.12/28.43 ! [V_m,V_n,T_a] :
% 28.12/28.43 ( class_Rings_Oring__1(T_a)
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 28.12/28.43 => 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)) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_nat__diff__split,axiom,
% 28.12/28.43 ! [V_b_2,V_a_2,V_P_2] :
% 28.12/28.43 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 28.12/28.43 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 28.12/28.43 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 28.12/28.43 & ! [B_d] :
% 28.12/28.43 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 28.12/28.43 => hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_nat__diff__split__asm,axiom,
% 28.12/28.43 ! [V_b_2,V_a_2,V_P_2] :
% 28.12/28.43 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 28.12/28.43 <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 28.12/28.43 & ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 28.12/28.43 | ? [B_d] :
% 28.12/28.43 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 28.12/28.43 & ~ hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_nat__mult__le__cancel1,axiom,
% 28.12/28.43 ! [V_n_2,V_m_2,V_k_2] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 28.12/28.43 => ( 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)))
% 28.12/28.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_mult__le__cancel2,axiom,
% 28.12/28.43 ! [V_n_2,V_k_2,V_m_2] :
% 28.12/28.43 ( 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)))
% 28.12/28.43 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 28.12/28.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_mult__le__cancel1,axiom,
% 28.12/28.43 ! [V_n_2,V_m_2,V_k_2] :
% 28.12/28.43 ( 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)))
% 28.12/28.43 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 28.12/28.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_comp__cong,axiom,
% 28.12/28.43 ! [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] :
% 28.12/28.43 ( 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))
% 28.12/28.43 => 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) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_setsum__eq__1__iff,axiom,
% 28.12/28.43 ! [V_f_2,V_A_2,T_b] :
% 28.12/28.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.43 => ( 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)
% 28.12/28.43 <=> ? [B_x] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.12/28.43 & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 28.12/28.43 & ! [B_xa] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 28.12/28.43 => ( B_x != B_xa
% 28.12/28.43 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_setsum__delta_H,axiom,
% 28.12/28.43 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 28.12/28.43 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.12/28.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 28.12/28.43 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 28.12/28.43 => 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) )
% 28.12/28.43 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 28.12/28.43 => 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) ) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_setsum__delta,axiom,
% 28.12/28.43 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 28.12/28.43 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.12/28.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 28.12/28.43 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 28.12/28.43 => 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) )
% 28.12/28.43 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 28.12/28.43 => 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) ) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_convex__bound__le,axiom,
% 28.12/28.43 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 28.12/28.43 ( class_Rings_Olinordered__semiring__1(T_a)
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 28.12/28.43 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 28.12/28.43 => 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)) ) ) ) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_UN__UN__finite__eq,axiom,
% 28.12/28.43 ! [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) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_setsum_Oeq__fold,axiom,
% 28.12/28.43 ! [V_g_2,V_A_2,T_b,T_c] :
% 28.12/28.43 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.12/28.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.43 => 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) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_setsum_OF__eq,axiom,
% 28.12/28.43 ! [V_g_2,V_A_2,T_b,T_c] :
% 28.12/28.43 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.12/28.43 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.43 => 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) )
% 28.12/28.43 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.43 => 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) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_setsum__restrict__set,axiom,
% 28.12/28.43 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
% 28.12/28.43 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.12/28.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.43 => 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) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_convex__bound__lt,axiom,
% 28.12/28.43 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 28.12/28.43 ( class_Rings_Olinordered__semiring__1__strict(T_a)
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 28.12/28.43 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 28.12/28.43 => 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)) ) ) ) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_image__minus__const__atLeastLessThan__nat,axiom,
% 28.12/28.43 ! [V_x_2,V_y_2,V_c_2] :
% 28.12/28.43 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2))
% 28.12/28.43 => 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)) )
% 28.12/28.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2))
% 28.12/28.43 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 28.12/28.43 => 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))) )
% 28.12/28.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 28.12/28.43 => 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)) ) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_UN__le__eq__Un0,axiom,
% 28.12/28.43 ! [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))) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_gauss__sum,axiom,
% 28.12/28.43 ! [V_n_2,T_b] :
% 28.12/28.43 ( class_Rings_Ocomm__semiring__1(T_b)
% 28.12/28.43 => 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))) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_mult__eq__if,axiom,
% 28.12/28.43 ! [V_n,V_m] :
% 28.12/28.43 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.12/28.43 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 28.12/28.43 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.12/28.43 => 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)) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_not__sum__squares__lt__zero,axiom,
% 28.12/28.43 ! [V_y,V_x,T_a] :
% 28.12/28.43 ( class_Rings_Olinordered__ring(T_a)
% 28.12/28.43 => ~ 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))) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_sum__squares__gt__zero__iff,axiom,
% 28.12/28.43 ! [V_y_2,V_x_2,T_b] :
% 28.12/28.43 ( class_Rings_Olinordered__ring__strict(T_b)
% 28.12/28.43 => ( 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))))
% 28.12/28.43 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b)
% 28.12/28.43 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_sum__squares__ge__zero,axiom,
% 28.12/28.43 ! [V_y,V_x,T_a] :
% 28.12/28.43 ( class_Rings_Olinordered__ring(T_a)
% 28.12/28.43 => 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)))) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_sum__squares__le__zero__iff,axiom,
% 28.12/28.43 ! [V_y_2,V_x_2,T_b] :
% 28.12/28.43 ( class_Rings_Olinordered__ring__strict(T_b)
% 28.12/28.43 => ( 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)))
% 28.12/28.43 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 28.12/28.43 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_of__nat__setsum,axiom,
% 28.12/28.43 ! [V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.43 ( class_Rings_Osemiring__1(T_b)
% 28.12/28.43 => 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) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_semiring__1__class_Oof__nat__code,axiom,
% 28.12/28.43 ! [V_n_2,T_b] :
% 28.12/28.43 ( class_Rings_Osemiring__1(T_b)
% 28.12/28.43 => 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)) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_of__nat__aux_Osimps_I1_J,axiom,
% 28.12/28.43 ! [V_i_2,V_inc_2,T_b] :
% 28.12/28.43 ( class_Rings_Osemiring__1(T_b)
% 28.12/28.43 => 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 ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_bot__nat__def,axiom,
% 28.12/28.43 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_int__zle__neg,axiom,
% 28.12/28.43 ! [V_m_2,V_n_2] :
% 28.12/28.43 ( 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))))
% 28.12/28.43 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.12/28.43 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_int__le__0__conv,axiom,
% 28.12/28.43 ! [V_n_2] :
% 28.12/28.43 ( 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)))
% 28.12/28.43 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_int__eq__0__conv,axiom,
% 28.12/28.43 ! [V_n_2] :
% 28.12/28.43 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.12/28.43 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_int__0,axiom,
% 28.12/28.43 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) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_negative__eq__positive,axiom,
% 28.12/28.43 ! [V_m_2,V_n_2] :
% 28.12/28.43 ( 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)
% 28.12/28.43 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.12/28.43 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zless__int,axiom,
% 28.12/28.43 ! [V_n_2,V_m_2] :
% 28.12/28.43 ( 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)))
% 28.12/28.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zero__less__int__conv,axiom,
% 28.12/28.43 ! [V_n_2] :
% 28.12/28.43 ( 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)))
% 28.12/28.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zmult__zless__mono2__lemma,axiom,
% 28.12/28.43 ! [V_k,V_j,V_i] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 28.12/28.43 => 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))) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zadd__int,axiom,
% 28.12/28.43 ! [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)) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zadd__int__left,axiom,
% 28.12/28.43 ! [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) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zle__int,axiom,
% 28.12/28.43 ! [V_n_2,V_m_2] :
% 28.12/28.43 ( 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)))
% 28.12/28.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_int__mult,axiom,
% 28.12/28.43 ! [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)) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zmult__int,axiom,
% 28.12/28.43 ! [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)) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_int__1,axiom,
% 28.12/28.43 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) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_inj__int,axiom,
% 28.12/28.43 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))) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_int__setsum,axiom,
% 28.12/28.43 ! [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) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_double__eq__0__iff,axiom,
% 28.12/28.43 ! [V_a_2,T_b] :
% 28.12/28.43 ( class_Groups_Olinordered__ab__group__add(T_b)
% 28.12/28.43 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 28.12/28.43 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zdiff__int,axiom,
% 28.12/28.43 ! [V_m,V_n] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 28.12/28.43 => 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)) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_even__less__0__iff,axiom,
% 28.12/28.43 ! [V_a_2,T_b] :
% 28.12/28.43 ( class_Rings_Olinordered__idom(T_b)
% 28.12/28.43 => ( 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)))
% 28.12/28.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_sum__squares__eq__zero__iff,axiom,
% 28.12/28.43 ! [V_y_2,V_x_2,T_b] :
% 28.12/28.43 ( class_Rings_Olinordered__ring__strict(T_b)
% 28.12/28.43 => ( 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)
% 28.12/28.43 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 28.12/28.43 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_ex__nat__less,axiom,
% 28.12/28.43 ! [V_P_2,V_n_2] :
% 28.12/28.43 ( ? [B_m] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 28.12/28.43 & hBOOL(hAPP(V_P_2,B_m)) )
% 28.12/28.43 <=> ? [B_x] :
% 28.12/28.43 ( 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)))
% 28.12/28.43 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_all__nat__less,axiom,
% 28.12/28.43 ! [V_P_2,V_n_2] :
% 28.12/28.43 ( ! [B_m] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 28.12/28.43 => hBOOL(hAPP(V_P_2,B_m)) )
% 28.12/28.43 <=> ! [B_x] :
% 28.12/28.43 ( 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)))
% 28.12/28.43 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_ex__nat__less__eq,axiom,
% 28.12/28.43 ! [V_P_2,V_n_2] :
% 28.12/28.43 ( ? [B_m] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 28.12/28.43 & hBOOL(hAPP(V_P_2,B_m)) )
% 28.12/28.43 <=> ? [B_x] :
% 28.12/28.43 ( 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)))
% 28.12/28.43 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_all__nat__less__eq,axiom,
% 28.12/28.43 ! [V_P_2,V_n_2] :
% 28.12/28.43 ( ! [B_m] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 28.12/28.43 => hBOOL(hAPP(V_P_2,B_m)) )
% 28.12/28.43 <=> ! [B_x] :
% 28.12/28.43 ( 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)))
% 28.12/28.43 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zdiff__int__split,axiom,
% 28.12/28.43 ! [V_y_2,V_x_2,V_P_2] :
% 28.12/28.43 ( 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))))
% 28.12/28.43 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2))
% 28.12/28.43 => 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)))) )
% 28.12/28.43 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 28.12/28.43 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_UN__finite2__subset,axiom,
% 28.12/28.43 ! [V_B_2,V_k_2,V_A_2,T_b] :
% 28.12/28.43 ( ! [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)))
% 28.12/28.43 => 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))) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_negative__zle,axiom,
% 28.12/28.43 ! [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))) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_negative__zle__0,axiom,
% 28.12/28.43 ! [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))) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zero__zle__int,axiom,
% 28.12/28.43 ! [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))) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_int__int__eq,axiom,
% 28.12/28.43 ! [V_n_2,V_m_2] :
% 28.12/28.43 ( 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)
% 28.12/28.43 <=> V_m_2 = V_n_2 ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zminus__0,axiom,
% 28.12/28.43 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) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_int__0__less__1,axiom,
% 28.12/28.43 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))) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_int__0__neq__1,axiom,
% 28.12/28.43 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_pos__zmult__eq__1__iff,axiom,
% 28.12/28.43 ! [V_n_2,V_m_2] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2))
% 28.12/28.43 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 28.12/28.43 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 28.12/28.43 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zmult__zless__mono2,axiom,
% 28.12/28.43 ! [V_k,V_j,V_i] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 28.12/28.43 => 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))) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_not__int__zless__negative,axiom,
% 28.12/28.43 ! [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)))) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_int__less__0__conv,axiom,
% 28.12/28.43 ! [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))) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_less__bin__lemma,axiom,
% 28.12/28.43 ! [V_l_2,V_k_2] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
% 28.12/28.43 <=> 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))) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zadd__0__right,axiom,
% 28.12/28.43 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zadd__0,axiom,
% 28.12/28.43 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zle__iff__zadd,axiom,
% 28.12/28.43 ! [V_z_2,V_w_2] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2))
% 28.12/28.43 <=> ? [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)) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zadd__zminus__inverse2,axiom,
% 28.12/28.43 ! [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) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_image__add__int__atLeastLessThan,axiom,
% 28.12/28.43 ! [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) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_finite__atLeastZeroLessThan__int,axiom,
% 28.12/28.43 ! [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))) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_odd__nonzero,axiom,
% 28.12/28.43 ! [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) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_int__one__le__iff__zero__less,axiom,
% 28.12/28.43 ! [V_z_2] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))
% 28.12/28.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_le__imp__0__less,axiom,
% 28.12/28.43 ! [V_z] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 28.12/28.43 => 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))) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_odd__less__0,axiom,
% 28.12/28.43 ! [V_z_2] :
% 28.12/28.43 ( 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)))
% 28.12/28.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_simp__from__to,axiom,
% 28.12/28.43 ! [V_i_2,V_j_2] :
% 28.12/28.43 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 28.12/28.43 => 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)) )
% 28.12/28.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 28.12/28.43 => 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)) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zle__diff1__eq,axiom,
% 28.12/28.43 ! [V_z_2,V_w_2] :
% 28.12/28.43 ( 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))))
% 28.12/28.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zless__add1__eq,axiom,
% 28.12/28.43 ! [V_z_2,V_w_2] :
% 28.12/28.43 ( 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))))
% 28.12/28.43 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 28.12/28.43 | V_w_2 = V_z_2 ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zless__imp__add1__zle,axiom,
% 28.12/28.43 ! [V_z,V_w] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z))
% 28.12/28.43 => 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)) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_add1__zle__eq,axiom,
% 28.12/28.43 ! [V_z_2,V_w_2] :
% 28.12/28.43 ( 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))
% 28.12/28.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zle__add1__eq__le,axiom,
% 28.12/28.43 ! [V_z_2,V_w_2] :
% 28.12/28.43 ( 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))))
% 28.12/28.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zadd__zmult__distrib,axiom,
% 28.12/28.43 ! [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)) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zadd__zmult__distrib2,axiom,
% 28.12/28.43 ! [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)) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zdiff__zmult__distrib,axiom,
% 28.12/28.43 ! [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)) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zdiff__zmult__distrib2,axiom,
% 28.12/28.43 ! [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)) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_diff__int__def,axiom,
% 28.12/28.43 ! [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)) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_diff__int__def__symmetric,axiom,
% 28.12/28.43 ! [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) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zminus__zadd__distrib,axiom,
% 28.12/28.43 ! [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)) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zadd__left__mono,axiom,
% 28.12/28.43 ! [V_k,V_j,V_i] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 28.12/28.43 => 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))) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zadd__commute,axiom,
% 28.12/28.43 ! [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) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zadd__left__commute,axiom,
% 28.12/28.43 ! [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)) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zadd__assoc,axiom,
% 28.12/28.43 ! [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)) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zless__le,axiom,
% 28.12/28.43 ! [V_w_2,V_z_2] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2))
% 28.12/28.43 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2))
% 28.12/28.43 & V_z_2 != V_w_2 ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zadd__zless__mono,axiom,
% 28.12/28.43 ! [V_z,V_z_H,V_w,V_w_H] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 28.12/28.43 => 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))) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zadd__strict__right__mono,axiom,
% 28.12/28.43 ! [V_k,V_j,V_i] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 28.12/28.43 => 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))) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zless__linear,axiom,
% 28.12/28.43 ! [V_y,V_x] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y))
% 28.12/28.43 | V_x = V_y
% 28.12/28.43 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zmult__zminus,axiom,
% 28.12/28.43 ! [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)) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zmult__commute,axiom,
% 28.12/28.43 ! [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) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zmult__assoc,axiom,
% 28.12/28.43 ! [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)) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zmult__1__right,axiom,
% 28.12/28.43 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zmult__1,axiom,
% 28.12/28.43 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zminus__zminus,axiom,
% 28.12/28.43 ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zle__antisym,axiom,
% 28.12/28.43 ! [V_w,V_z] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z))
% 28.12/28.43 => V_z = V_w ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zle__trans,axiom,
% 28.12/28.43 ! [V_k,V_j,V_i] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k))
% 28.12/28.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zle__linear,axiom,
% 28.12/28.43 ! [V_w,V_z] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 28.12/28.43 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zle__refl,axiom,
% 28.12/28.43 ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 28.12/28.43 ! [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) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 28.12/28.43 ! [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) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 28.12/28.43 ! [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) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_self__quotient__aux1,axiom,
% 28.12/28.43 ! [V_q,V_r,V_a] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 28.12/28.43 => ( 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))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a))
% 28.12/28.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_self__quotient__aux2,axiom,
% 28.12/28.43 ! [V_q,V_r,V_a] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 28.12/28.43 => ( 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))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 28.12/28.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_q__pos__lemma,axiom,
% 28.12/28.43 ! [V_r_H,V_q_H,V_b_H] :
% 28.12/28.43 ( 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)))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 28.12/28.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_q__neg__lemma,axiom,
% 28.12/28.43 ! [V_r_H,V_q_H,V_b_H] :
% 28.12/28.43 ( 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)))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 28.12/28.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_unique__quotient__lemma,axiom,
% 28.12/28.43 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 28.12/28.43 ( 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)))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 28.12/28.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zdiv__mono2__lemma,axiom,
% 28.12/28.43 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 28.12/28.43 ( 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)
% 28.12/28.43 => ( 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)))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 28.12/28.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_finite__atLeastAtMost__int,axiom,
% 28.12/28.43 ! [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))) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_finite__atLeastLessThan__int,axiom,
% 28.12/28.43 ! [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))) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_finite__greaterThanAtMost__int,axiom,
% 28.12/28.43 ! [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))) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_finite__greaterThanLessThan__int,axiom,
% 28.12/28.43 ! [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))) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_infinite__UNIV__int,axiom,
% 28.12/28.43 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zdiv__mono2__neg__lemma,axiom,
% 28.12/28.43 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 28.12/28.43 ( 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)
% 28.12/28.43 => ( 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)))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 28.12/28.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_unique__quotient__lemma__neg,axiom,
% 28.12/28.43 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 28.12/28.43 ( 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)))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H))
% 28.12/28.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom,
% 28.12/28.43 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))) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_transfer__nat__int__set__relations_I1_J,axiom,
% 28.12/28.43 ! [V_A_2] :
% 28.12/28.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2))
% 28.12/28.43 <=> 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))) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_transfer__int__nat__numerals_I2_J,axiom,
% 28.12/28.43 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)) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
% 28.12/28.43 ! [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)) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
% 28.12/28.43 ! [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)) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_transfer__int__nat__relations_I3_J,axiom,
% 28.12/28.43 ! [V_y_2,V_x_2] :
% 28.12/28.43 ( 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)))
% 28.12/28.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_transfer__nat__int__set__relations_I5_J,axiom,
% 28.12/28.43 ! [V_B_2,V_A_2] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.43 <=> 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))) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_transfer__nat__int__set__relations_I4_J,axiom,
% 28.12/28.43 ! [V_B_2,V_A_2] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.43 <=> 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))) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_transfer__nat__int__set__relations_I3_J,axiom,
% 28.12/28.43 ! [V_B_2,V_A_2] :
% 28.12/28.43 ( V_A_2 = V_B_2
% 28.12/28.43 <=> 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) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_transfer__nat__int__set__relations_I2_J,axiom,
% 28.12/28.43 ! [V_A_2,V_x_2] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2))
% 28.12/28.43 <=> 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))) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_transfer__int__nat__relations_I1_J,axiom,
% 28.12/28.43 ! [V_y_2,V_x_2] :
% 28.12/28.43 ( 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)
% 28.12/28.43 <=> V_x_2 = V_y_2 ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
% 28.12/28.43 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))) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_transfer__int__nat__numerals_I1_J,axiom,
% 28.12/28.43 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)) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
% 28.12/28.43 ! [V_y,V_x] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 28.12/28.43 => 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))) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom,
% 28.12/28.43 ! [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))) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom,
% 28.12/28.43 ! [V_P_2] :
% 28.12/28.43 ( ? [B_x] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 28.12/28.43 & hBOOL(hAPP(V_P_2,B_x)) )
% 28.12/28.43 <=> ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom,
% 28.12/28.43 ! [V_P_2] :
% 28.12/28.43 ( ! [B_x] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 28.12/28.43 => hBOOL(hAPP(V_P_2,B_x)) )
% 28.12/28.43 <=> ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
% 28.12/28.43 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))) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
% 28.12/28.43 ! [V_y,V_x] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 28.12/28.43 => 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))) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_transfer__int__nat__relations_I2_J,axiom,
% 28.12/28.43 ! [V_y_2,V_x_2] :
% 28.12/28.43 ( 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)))
% 28.12/28.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_aset_I8_J,axiom,
% 28.12/28.43 ! [V_t_2,V_A_2,V_D_2] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 28.12/28.43 => ! [B_x] :
% 28.12/28.43 ( ! [B_xa] :
% 28.12/28.43 ( 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)))
% 28.12/28.43 => ! [B_xb] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 28.12/28.43 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 28.12/28.43 => 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))) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_bset_I6_J,axiom,
% 28.12/28.43 ! [V_t_2,V_B_2,V_D_2] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 28.12/28.43 => ! [B_x] :
% 28.12/28.43 ( ! [B_xa] :
% 28.12/28.43 ( 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)))
% 28.12/28.43 => ! [B_xb] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 28.12/28.43 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 28.12/28.43 => 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)) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_aset_I6_J,axiom,
% 28.12/28.43 ! [V_A_2,V_t_2,V_D_2] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 28.12/28.43 => ( 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))
% 28.12/28.43 => ! [B_x] :
% 28.12/28.43 ( ! [B_xa] :
% 28.12/28.43 ( 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)))
% 28.12/28.43 => ! [B_xb] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 28.12/28.43 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 28.12/28.43 => 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)) ) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_bset_I8_J,axiom,
% 28.12/28.43 ! [V_B_2,V_t_2,V_D_2] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 28.12/28.43 => ( 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))
% 28.12/28.43 => ! [B_x] :
% 28.12/28.43 ( ! [B_xa] :
% 28.12/28.43 ( 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)))
% 28.12/28.43 => ! [B_xb] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 28.12/28.43 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 28.12/28.43 => 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))) ) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_setsum__mono2,axiom,
% 28.12/28.43 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 28.12/28.43 ( class_Groups_Oordered__comm__monoid__add(T_c)
% 28.12/28.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.43 => ( ! [B_b] :
% 28.12/28.43 ( 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)))
% 28.12/28.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_b))) )
% 28.12/28.43 => 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))) ) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_periodic__finite__ex,axiom,
% 28.12/28.43 ! [V_P_2,V_d_2] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 28.12/28.43 => ( ! [B_x,B_k] :
% 28.12/28.43 ( hBOOL(hAPP(V_P_2,B_x))
% 28.12/28.43 <=> 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)))) )
% 28.12/28.43 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 28.12/28.43 <=> ? [B_x] :
% 28.12/28.43 ( 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)))
% 28.12/28.43 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_aset_I4_J,axiom,
% 28.12/28.43 ! [V_A_2,V_t_2,V_D_2] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 28.12/28.43 => ! [B_x] :
% 28.12/28.43 ( ! [B_xa] :
% 28.12/28.43 ( 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)))
% 28.12/28.43 => ! [B_xb] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 28.12/28.43 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 28.12/28.43 => ( B_x != V_t_2
% 28.12/28.43 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_bset_I4_J,axiom,
% 28.12/28.43 ! [V_B_2,V_t_2,V_D_2] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 28.12/28.43 => ! [B_x] :
% 28.12/28.43 ( ! [B_xa] :
% 28.12/28.43 ( 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)))
% 28.12/28.43 => ! [B_xb] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 28.12/28.43 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 28.12/28.43 => ( B_x != V_t_2
% 28.12/28.43 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_bset_I7_J,axiom,
% 28.12/28.43 ! [V_B_2,V_t_2,V_D_2] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 28.12/28.43 => ! [B_x] :
% 28.12/28.43 ( ! [B_xa] :
% 28.12/28.43 ( 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)))
% 28.12/28.43 => ! [B_xb] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 28.12/28.43 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 28.12/28.43 => 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))) ) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_aset_I5_J,axiom,
% 28.12/28.43 ! [V_A_2,V_t_2,V_D_2] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 28.12/28.43 => ! [B_x] :
% 28.12/28.43 ( ! [B_xa] :
% 28.12/28.43 ( 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)))
% 28.12/28.43 => ! [B_xb] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 28.12/28.43 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 28.12/28.43 => 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)) ) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_aset_I3_J,axiom,
% 28.12/28.43 ! [V_A_2,V_t_2,V_D_2] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 28.12/28.43 => ( 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))
% 28.12/28.43 => ( ! [B_x] :
% 28.12/28.43 ( 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)))
% 28.12/28.43 => ! [B_xa] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2))
% 28.12/28.43 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) )
% 28.12/28.43 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_bset_I3_J,axiom,
% 28.12/28.43 ! [V_B_2,V_t_2,V_D_2] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 28.12/28.43 => ( 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))
% 28.12/28.43 => ( ! [B_x] :
% 28.12/28.43 ( 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)))
% 28.12/28.43 => ! [B_xa] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2))
% 28.12/28.43 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) )
% 28.12/28.43 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_aset_I7_J,axiom,
% 28.12/28.43 ! [V_t_2,V_A_2,V_D_2] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 28.12/28.43 => ! [B_x] :
% 28.12/28.43 ( ! [B_xa] :
% 28.12/28.43 ( 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)))
% 28.12/28.43 => ! [B_xb] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 28.12/28.43 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 28.12/28.43 => 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))) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_bset_I5_J,axiom,
% 28.12/28.43 ! [V_t_2,V_B_2,V_D_2] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 28.12/28.43 => ! [B_x] :
% 28.12/28.43 ( ! [B_xa] :
% 28.12/28.43 ( 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)))
% 28.12/28.43 => ! [B_xb] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 28.12/28.43 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 28.12/28.43 => 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)) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_setsum__Un__zero,axiom,
% 28.12/28.43 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 28.12/28.43 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.12/28.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 28.12/28.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 28.12/28.43 => ( ! [B_x] :
% 28.12/28.43 ( 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)))
% 28.12/28.43 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 28.12/28.43 => 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)) ) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_setsum_Ounion__inter__neutral,axiom,
% 28.12/28.43 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 28.12/28.43 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.12/28.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.43 => ( ! [B_x] :
% 28.12/28.43 ( 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)))
% 28.12/28.43 => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 28.12/28.43 => 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)) ) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_setsum__mono3,axiom,
% 28.12/28.43 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 28.12/28.43 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 28.12/28.43 & class_Groups_Oordered__ab__semigroup__add(T_c) )
% 28.12/28.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.43 => ( ! [B_x] :
% 28.12/28.43 ( 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)))
% 28.12/28.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 28.12/28.43 => 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))) ) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_setsum__reindex__nonzero,axiom,
% 28.12/28.43 ! [T_c,V_h_2,V_f_2,V_S_2,T_b,T_d] :
% 28.12/28.43 ( class_Groups_Ocomm__monoid__add(T_d)
% 28.12/28.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 28.12/28.43 => ( ! [B_x] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 28.12/28.43 => ! [B_y] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_S_2))
% 28.12/28.43 => ( B_x != B_y
% 28.12/28.43 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 28.12/28.43 => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_d) ) ) ) )
% 28.12/28.43 => 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) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_UN__finite2__eq,axiom,
% 28.12/28.43 ! [V_B_2,V_k_2,V_A_2,T_b] :
% 28.12/28.43 ( ! [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)
% 28.12/28.43 => 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) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_UN__finite__subset,axiom,
% 28.12/28.43 ! [V_C_2,V_A_2,T_b] :
% 28.12/28.43 ( ! [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))
% 28.12/28.43 => 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)) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_tsub__def,axiom,
% 28.12/28.43 ! [V_x,V_y] :
% 28.12/28.43 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 28.12/28.43 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) )
% 28.12/28.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 28.12/28.43 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_Ints__odd__less__0,axiom,
% 28.12/28.43 ! [V_a_2,T_b] :
% 28.12/28.43 ( class_Rings_Olinordered__idom(T_b)
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 28.12/28.43 => ( 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)))
% 28.12/28.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_arith__series__nat,axiom,
% 28.12/28.43 ! [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)))) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_card__Diff__singleton,axiom,
% 28.12/28.43 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.43 => 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)) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_lessI,axiom,
% 28.12/28.43 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_Suc__mono,axiom,
% 28.12/28.43 ! [V_n,V_m] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 28.12/28.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_zero__less__Suc,axiom,
% 28.12/28.43 ! [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))) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_negative__zless,axiom,
% 28.12/28.43 ! [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))) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_card__atMost,axiom,
% 28.12/28.43 ! [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) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_n__not__Suc__n,axiom,
% 28.12/28.43 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_Suc__n__not__n,axiom,
% 28.12/28.43 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ).
% 28.12/28.43
% 28.12/28.43 fof(fact_nat_Oinject,axiom,
% 28.12/28.43 ! [V_nat_H_2,V_nat_2] :
% 28.12/28.43 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2)
% 28.12/28.43 <=> V_nat_2 = V_nat_H_2 ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_Suc__inject,axiom,
% 28.12/28.43 ! [V_y,V_x] :
% 28.12/28.43 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y)
% 28.12/28.43 => V_x = V_y ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_mono__Suc,axiom,
% 28.12/28.43 c_Orderings_Oorder__class_Omono(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom,
% 28.12/28.43 ! [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)) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_card__atLeastAtMost,axiom,
% 28.12/28.43 ! [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) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_mono__iff__le__Suc,axiom,
% 28.12/28.43 ! [V_f_2,T_b] :
% 28.12/28.43 ( class_Orderings_Oorder(T_b)
% 28.12/28.43 => ( c_Orderings_Oorder__class_Omono(tc_Nat_Onat,T_b,V_f_2)
% 28.12/28.43 <=> ! [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)))) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_card__UNIV__unit,axiom,
% 28.12/28.43 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) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_Suc__neq__Zero,axiom,
% 28.12/28.43 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_Zero__neq__Suc,axiom,
% 28.12/28.43 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_nat_Osimps_I3_J,axiom,
% 28.12/28.43 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_Suc__not__Zero,axiom,
% 28.12/28.43 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_nat_Osimps_I2_J,axiom,
% 28.12/28.43 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_Zero__not__Suc,axiom,
% 28.12/28.43 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_not__less__eq,axiom,
% 28.12/28.43 ! [V_n_2,V_m_2] :
% 28.12/28.43 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 28.12/28.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_less__Suc__eq,axiom,
% 28.12/28.43 ! [V_n_2,V_m_2] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 28.12/28.43 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 28.12/28.43 | V_m_2 = V_n_2 ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_Suc__less__eq,axiom,
% 28.12/28.43 ! [V_n_2,V_m_2] :
% 28.12/28.43 ( 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)))
% 28.12/28.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_not__less__less__Suc__eq,axiom,
% 28.12/28.43 ! [V_m_2,V_n_2] :
% 28.12/28.43 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 28.12/28.43 <=> V_n_2 = V_m_2 ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_less__antisym,axiom,
% 28.12/28.43 ! [V_m,V_n] :
% 28.12/28.43 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m)))
% 28.12/28.43 => V_m = V_n ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_less__SucI,axiom,
% 28.12/28.43 ! [V_n,V_m] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 28.12/28.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_Suc__lessI,axiom,
% 28.12/28.43 ! [V_n,V_m] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 28.12/28.43 => ( hAPP(c_Nat_OSuc,V_m) != V_n
% 28.12/28.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_less__trans__Suc,axiom,
% 28.12/28.43 ! [V_k,V_j,V_i] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 28.12/28.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 28.12/28.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_less__SucE,axiom,
% 28.12/28.43 ! [V_n,V_m] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 28.12/28.43 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 28.12/28.43 => V_m = V_n ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_Suc__lessD,axiom,
% 28.12/28.43 ! [V_n,V_m] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 28.12/28.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_Suc__less__SucD,axiom,
% 28.12/28.43 ! [V_n,V_m] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)))
% 28.12/28.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_add__Suc__shift,axiom,
% 28.12/28.43 ! [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)) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_add__Suc,axiom,
% 28.12/28.43 ! [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)) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_add__Suc__right,axiom,
% 28.12/28.43 ! [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)) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_Suc__n__not__le__n,axiom,
% 28.12/28.43 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_not__less__eq__eq,axiom,
% 28.12/28.43 ! [V_n_2,V_m_2] :
% 28.12/28.43 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 28.12/28.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_le__Suc__eq,axiom,
% 28.12/28.43 ! [V_n_2,V_m_2] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 28.12/28.43 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 28.12/28.43 | V_m_2 = hAPP(c_Nat_OSuc,V_n_2) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_Suc__le__mono,axiom,
% 28.12/28.43 ! [V_m_2,V_n_2] :
% 28.12/28.43 ( 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)))
% 28.12/28.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_le__SucI,axiom,
% 28.12/28.43 ! [V_n,V_m] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 28.12/28.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_le__SucE,axiom,
% 28.12/28.43 ! [V_n,V_m] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 28.12/28.43 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 28.12/28.43 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_Suc__leD,axiom,
% 28.12/28.43 ! [V_n,V_m] :
% 28.12/28.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 28.12/28.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_bij__betw__same__card,axiom,
% 28.12/28.43 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.43 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 28.12/28.43 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_diff__Suc__Suc,axiom,
% 28.12/28.43 ! [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) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_Suc__diff__diff,axiom,
% 28.12/28.43 ! [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) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_Suc__mult__cancel1,axiom,
% 28.12/28.43 ! [V_n_2,V_m_2,V_k_2] :
% 28.12/28.43 ( 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)
% 28.12/28.43 <=> V_m_2 = V_n_2 ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_card__greaterThanLessThan,axiom,
% 28.12/28.43 ! [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)) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_card__lessThan,axiom,
% 28.12/28.43 ! [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 ).
% 28.12/28.43
% 28.12/28.43 fof(fact_card__insert__if,axiom,
% 28.12/28.43 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.43 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.43 => 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) )
% 28.12/28.43 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.43 => 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)) ) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_card__insert__disjoint,axiom,
% 28.12/28.43 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.43 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.43 => 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)) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_Least__Suc,axiom,
% 28.12/28.43 ! [V_n_2,V_P_2] :
% 28.12/28.43 ( hBOOL(hAPP(V_P_2,V_n_2))
% 28.12/28.43 => ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 28.12/28.43 => 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))) ) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_of__nat__aux_Osimps_I2_J,axiom,
% 28.12/28.43 ! [V_i_2,V_n_2,V_inc_2,T_b] :
% 28.12/28.43 ( class_Rings_Osemiring__1(T_b)
% 28.12/28.43 => 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)) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_card__insert,axiom,
% 28.12/28.43 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.43 => 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)))))) ) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_card_Oempty,axiom,
% 28.12/28.43 ! [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) ).
% 28.12/28.43
% 28.12/28.43 fof(fact_card__infinite,axiom,
% 28.12/28.43 ! [V_A_2,T_b] :
% 28.12/28.43 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.43 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_inj__Suc,axiom,
% 28.12/28.44 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
% 28.12/28.44 ! [V_A_2,T_b] :
% 28.12/28.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 28.12/28.44 => ( 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)))
% 28.12/28.44 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_card__image,axiom,
% 28.12/28.44 ! [V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 28.12/28.44 => 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) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_BIJ,axiom,
% 28.12/28.44 ! [V_B_2,T_c,V_A_2,T_b] :
% 28.12/28.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 28.12/28.44 => ( ? [B_f] : c_Fun_Obij__betw(T_b,T_c,B_f,V_A_2,V_B_2)
% 28.12/28.44 <=> hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_less__Suc__eq__0__disj,axiom,
% 28.12/28.44 ! [V_n_2,V_m_2] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 28.12/28.44 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.12/28.44 | ? [B_j] :
% 28.12/28.44 ( V_m_2 = hAPP(c_Nat_OSuc,B_j)
% 28.12/28.44 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2)) ) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_less__Suc0,axiom,
% 28.12/28.44 ! [V_n_2] :
% 28.12/28.44 ( 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))))
% 28.12/28.44 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_gr0__conv__Suc,axiom,
% 28.12/28.44 ! [V_n_2] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 28.12/28.44 <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_one__is__add,axiom,
% 28.12/28.44 ! [V_n_2,V_m_2] :
% 28.12/28.44 ( 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)
% 28.12/28.44 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 28.12/28.44 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 28.12/28.44 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.12/28.44 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_add__is__1,axiom,
% 28.12/28.44 ! [V_n_2,V_m_2] :
% 28.12/28.44 ( 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))
% 28.12/28.44 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 28.12/28.44 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 28.12/28.44 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.12/28.44 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_less__add__Suc1,axiom,
% 28.12/28.44 ! [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)))) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_less__add__Suc2,axiom,
% 28.12/28.44 ! [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)))) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_less__iff__Suc__add,axiom,
% 28.12/28.44 ! [V_n_2,V_m_2] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 28.12/28.44 <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_less__eq__Suc__le,axiom,
% 28.12/28.44 ! [V_m_2,V_n_2] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 28.12/28.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_less__Suc__eq__le,axiom,
% 28.12/28.44 ! [V_n_2,V_m_2] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 28.12/28.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_Suc__le__eq,axiom,
% 28.12/28.44 ! [V_n_2,V_m_2] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 28.12/28.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_le__imp__less__Suc,axiom,
% 28.12/28.44 ! [V_n,V_m] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 28.12/28.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_Suc__leI,axiom,
% 28.12/28.44 ! [V_n,V_m] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 28.12/28.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_le__less__Suc__eq,axiom,
% 28.12/28.44 ! [V_n_2,V_m_2] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 28.12/28.44 <=> V_n_2 = V_m_2 ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_Suc__le__lessD,axiom,
% 28.12/28.44 ! [V_n,V_m] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 28.12/28.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_mult__eq__1__iff,axiom,
% 28.12/28.44 ! [V_n_2,V_m_2] :
% 28.12/28.44 ( 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))
% 28.12/28.44 <=> ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 28.12/28.44 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_card__atLeastLessThan,axiom,
% 28.12/28.44 ! [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) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_diff__less__Suc,axiom,
% 28.12/28.44 ! [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))) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_Suc__mult__less__cancel1,axiom,
% 28.12/28.44 ! [V_n_2,V_m_2,V_k_2] :
% 28.12/28.44 ( 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)))
% 28.12/28.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_mult__Suc,axiom,
% 28.12/28.44 ! [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)) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_mult__Suc__right,axiom,
% 28.12/28.44 ! [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)) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_Suc__diff__le,axiom,
% 28.12/28.44 ! [V_m,V_n] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 28.12/28.44 => 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)) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_Suc__mult__le__cancel1,axiom,
% 28.12/28.44 ! [V_n_2,V_m_2,V_k_2] :
% 28.12/28.44 ( 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)))
% 28.12/28.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_One__nat__def,axiom,
% 28.12/28.44 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_Suc__eq__plus1,axiom,
% 28.12/28.44 ! [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)) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_Suc__eq__plus1__left,axiom,
% 28.12/28.44 ! [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) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_diff__Suc__1,axiom,
% 28.12/28.44 ! [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 ).
% 28.12/28.44
% 28.12/28.44 fof(fact_diff__Suc__eq__diff__pred,axiom,
% 28.12/28.44 ! [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) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_setsum__shift__lb__Suc0__0,axiom,
% 28.12/28.44 ! [V_k_2,V_f_2] :
% 28.12/28.44 ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.12/28.44 => 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)) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_card__Suc__Diff1,axiom,
% 28.12/28.44 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.44 => 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) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom,
% 28.12/28.44 ! [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) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_less__eq__Suc__le__raw,axiom,
% 28.12/28.44 ! [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)) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_card__eq__setsum,axiom,
% 28.12/28.44 ! [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) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_card__greaterThanAtMost,axiom,
% 28.12/28.44 ! [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) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_lessThan__Suc__atMost,axiom,
% 28.12/28.44 ! [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) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_lessThan__Suc,axiom,
% 28.12/28.44 ! [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)) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_image__Suc__atLeastLessThan,axiom,
% 28.12/28.44 ! [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)) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_atMost__Suc,axiom,
% 28.12/28.44 ! [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)) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_finite__fun__UNIVD1,axiom,
% 28.12/28.44 ! [T_c,T_b] :
% 28.12/28.44 ( 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))))
% 28.12/28.44 => ( 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))
% 28.12/28.44 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_setsum__shift__bounds__Suc__ivl,axiom,
% 28.12/28.44 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 28.12/28.44 ( class_Groups_Ocomm__monoid__add(T_b)
% 28.12/28.44 => 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)) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_image__Suc__atLeastAtMost,axiom,
% 28.12/28.44 ! [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)) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom,
% 28.12/28.44 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 28.12/28.44 ( class_Groups_Ocomm__monoid__add(T_b)
% 28.12/28.44 => 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)) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_card__eq__0__iff,axiom,
% 28.12/28.44 ! [V_A_2,T_b] :
% 28.12/28.44 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.12/28.44 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.44 | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom,
% 28.12/28.44 ! [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) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_card__ge__0__finite,axiom,
% 28.12/28.44 ! [V_A_2,T_b] :
% 28.12/28.44 ( 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)))
% 28.12/28.44 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_card__insert__le,axiom,
% 28.12/28.44 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.44 => 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)))) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_card__mono,axiom,
% 28.12/28.44 ! [V_A_2,V_B_2,T_b] :
% 28.12/28.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.44 => 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))) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_card__seteq,axiom,
% 28.12/28.44 ! [V_A_2,V_B_2,T_b] :
% 28.12/28.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.44 => ( 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)))
% 28.12/28.44 => V_A_2 = V_B_2 ) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_card__image__le,axiom,
% 28.12/28.44 ! [V_f_2,T_c,V_A_2,T_b] :
% 28.12/28.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.44 => 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))) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom,
% 28.12/28.44 ! [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) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_Ints__0,axiom,
% 28.12/28.44 ! [T_b] :
% 28.12/28.44 ( class_Rings_Oring__1(T_b)
% 28.12/28.44 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_eq__card__imp__inj__on,axiom,
% 28.12/28.44 ! [V_f_2,T_c,V_A_2,T_b] :
% 28.12/28.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.44 => ( 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)
% 28.12/28.44 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_inj__on__iff__eq__card,axiom,
% 28.12/28.44 ! [V_f_2,T_c,V_A_2,T_b] :
% 28.12/28.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.44 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 28.12/28.44 <=> 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) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_pigeonhole,axiom,
% 28.12/28.44 ! [V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.44 ( 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)))
% 28.12/28.44 => ~ c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_Ints__add,axiom,
% 28.12/28.44 ! [V_b_2,V_a_2,T_b] :
% 28.12/28.44 ( class_Rings_Oring__1(T_b)
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 28.12/28.44 => 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))) ) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_Ints__mult,axiom,
% 28.12/28.44 ! [V_b_2,V_a_2,T_b] :
% 28.12/28.44 ( class_Rings_Oring__1(T_b)
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 28.12/28.44 => 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))) ) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_Ints__diff,axiom,
% 28.12/28.44 ! [V_b_2,V_a_2,T_b] :
% 28.12/28.44 ( class_Rings_Oring__1(T_b)
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 28.12/28.44 => 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))) ) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_Ints__1,axiom,
% 28.12/28.44 ! [T_b] :
% 28.12/28.44 ( class_Rings_Oring__1(T_b)
% 28.12/28.44 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_Ints__minus,axiom,
% 28.12/28.44 ! [V_a_2,T_b] :
% 28.12/28.44 ( class_Rings_Oring__1(T_b)
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 28.12/28.44 => 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))) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_Ints__of__nat,axiom,
% 28.12/28.44 ! [V_n_2,T_b] :
% 28.12/28.44 ( class_Rings_Oring__1(T_b)
% 28.12/28.44 => 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))) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_psubset__card__mono,axiom,
% 28.12/28.44 ! [V_A_2,V_B_2,T_b] :
% 28.12/28.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.44 => 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))) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_of__nat__Suc,axiom,
% 28.12/28.44 ! [V_m,T_a] :
% 28.12/28.44 ( class_Rings_Osemiring__1(T_a)
% 28.12/28.44 => 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)) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_Suc__pred,axiom,
% 28.12/28.44 ! [V_n] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 28.12/28.44 => 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 ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_diff__Suc__less,axiom,
% 28.12/28.44 ! [V_i,V_n] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 28.12/28.44 => 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)) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_one__less__mult,axiom,
% 28.12/28.44 ! [V_m,V_n] :
% 28.12/28.44 ( 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))
% 28.12/28.44 => ( 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))
% 28.12/28.44 => 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))) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_n__less__n__mult__m,axiom,
% 28.12/28.44 ! [V_m,V_n] :
% 28.12/28.44 ( 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))
% 28.12/28.44 => ( 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))
% 28.12/28.44 => 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))) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_n__less__m__mult__n,axiom,
% 28.12/28.44 ! [V_m,V_n] :
% 28.12/28.44 ( 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))
% 28.12/28.44 => ( 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))
% 28.12/28.44 => 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))) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_one__le__mult__iff,axiom,
% 28.12/28.44 ! [V_n_2,V_m_2] :
% 28.12/28.44 ( 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)))
% 28.12/28.44 <=> ( 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))
% 28.12/28.44 & 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)) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_diff__Suc__diff__eq2,axiom,
% 28.12/28.44 ! [V_m,V_j,V_k] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 28.12/28.44 => 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)) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_diff__Suc__diff__eq1,axiom,
% 28.12/28.44 ! [V_m,V_j,V_k] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 28.12/28.44 => 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)) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_int__Suc0__eq__1,axiom,
% 28.12/28.44 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) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_zless__iff__Suc__zadd,axiom,
% 28.12/28.44 ! [V_z_2,V_w_2] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 28.12/28.44 <=> ? [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))) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_int__Suc,axiom,
% 28.12/28.44 ! [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)) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_setsum__eq__Suc0__iff,axiom,
% 28.12/28.44 ! [V_f_2,V_A_2,T_b] :
% 28.12/28.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.44 => ( 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))
% 28.12/28.44 <=> ? [B_x] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.12/28.44 & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 28.12/28.44 & ! [B_xa] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 28.12/28.44 => ( B_x != B_xa
% 28.12/28.44 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_setsum__constant,axiom,
% 28.12/28.44 ! [V_A_2,V_y_2,T_c,T_b] :
% 28.12/28.44 ( class_Rings_Osemiring__1(T_b)
% 28.12/28.44 => 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) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_atLeast__Suc__greaterThan,axiom,
% 28.12/28.44 ! [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) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_atLeastAtMostSuc__conv,axiom,
% 28.12/28.44 ! [V_n_2,V_m_2] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 28.12/28.44 => 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)) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_subset__card__intvl__is__intvl,axiom,
% 28.12/28.44 ! [V_k_2,V_A_2] :
% 28.12/28.44 ( 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)))))
% 28.12/28.44 => 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))) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_atLeastLessThan__singleton,axiom,
% 28.12/28.44 ! [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))) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_card__gt__0__iff,axiom,
% 28.12/28.44 ! [V_A_2,T_b] :
% 28.12/28.44 ( 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)))
% 28.12/28.44 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.44 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_finite__UNIV__card__ge__0,axiom,
% 28.12/28.44 ! [T_b] :
% 28.12/28.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 28.12/28.44 => 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))))) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_setsum__lessThan__Suc,axiom,
% 28.12/28.44 ! [V_n_2,V_f_2,T_b] :
% 28.12/28.44 ( class_Groups_Ocomm__monoid__add(T_b)
% 28.12/28.44 => 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)) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_card__Un__Int,axiom,
% 28.12/28.44 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.44 => 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))) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_card_Ounion__inter,axiom,
% 28.12/28.44 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.44 => 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)) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_card__bij__eq,axiom,
% 28.12/28.44 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 28.12/28.44 => ( 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))
% 28.12/28.44 => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2)
% 28.12/28.44 => ( 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))
% 28.12/28.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 28.12/28.44 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_setsum__atMost__Suc,axiom,
% 28.12/28.44 ! [V_n_2,V_f_2,T_b] :
% 28.12/28.44 ( class_Groups_Ocomm__monoid__add(T_b)
% 28.12/28.44 => 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))) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_card__Diff__subset,axiom,
% 28.12/28.44 ! [V_A_2,V_B_2,T_b] :
% 28.12/28.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 28.12/28.44 => 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)) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_card__Diff__subset__Int,axiom,
% 28.12/28.44 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.44 ( 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)))
% 28.12/28.44 => 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))) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_diff__card__le__card__Diff,axiom,
% 28.12/28.44 ! [V_A_2,V_B_2,T_b] :
% 28.12/28.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.44 => 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)))) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_card__psubset,axiom,
% 28.12/28.44 ! [V_A_2,V_B_2,T_b] :
% 28.12/28.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.44 => ( 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)))
% 28.12/28.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_Suc__diff__1,axiom,
% 28.12/28.44 ! [V_n] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 28.12/28.44 => 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 ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_Suc__pred_H,axiom,
% 28.12/28.44 ! [V_n] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 28.12/28.44 => 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))) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_add__eq__if,axiom,
% 28.12/28.44 ! [V_n,V_m] :
% 28.12/28.44 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.12/28.44 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n )
% 28.12/28.44 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.12/28.44 => 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)) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_atLeast__Suc,axiom,
% 28.12/28.44 ! [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)))) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_greaterThan__Suc,axiom,
% 28.12/28.44 ! [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)))) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_not__zle__0__negative,axiom,
% 28.12/28.44 ! [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))))) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_negative__zless__0,axiom,
% 28.12/28.44 ! [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))) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_card_Oeq__fold__g,axiom,
% 28.12/28.44 ! [V_A_2,T_b] :
% 28.12/28.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.44 => 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) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_card__def,axiom,
% 28.12/28.44 ! [V_A_2,T_b] :
% 28.12/28.44 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.44 => 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) )
% 28.12/28.44 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.44 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_Ints__double__eq__0__iff,axiom,
% 28.12/28.44 ! [V_a_2,T_b] :
% 28.12/28.44 ( class_Int_Oring__char__0(T_b)
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 28.12/28.44 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 28.12/28.44 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom,
% 28.12/28.44 ! [V_k_2,V_f_2,T_b] :
% 28.12/28.44 ( class_Groups_Ocomm__monoid__add(T_b)
% 28.12/28.44 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_b)
% 28.12/28.44 => 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)) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_setsum__head__upt__Suc,axiom,
% 28.12/28.44 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 28.12/28.44 ( class_Groups_Ocomm__monoid__add(T_b)
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 28.12/28.44 => 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))) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_setsum__head__Suc,axiom,
% 28.12/28.44 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 28.12/28.44 ( class_Groups_Ocomm__monoid__add(T_b)
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 28.12/28.44 => 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))) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_atLeastLessThanSuc,axiom,
% 28.12/28.44 ! [V_n_2,V_m_2] :
% 28.12/28.44 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 28.12/28.44 => 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)) )
% 28.12/28.44 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 28.12/28.44 => 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)) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_card__Un__disjoint,axiom,
% 28.12/28.44 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.44 => ( 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))
% 28.12/28.44 => 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)) ) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_card__Diff1__le,axiom,
% 28.12/28.44 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.44 => 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))) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_card_Oinsert,axiom,
% 28.12/28.44 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.44 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.44 => 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)) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_card__inj__on__le,axiom,
% 28.12/28.44 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 28.12/28.44 => ( 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))
% 28.12/28.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 28.12/28.44 => 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))) ) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_inj__on__iff__card__le,axiom,
% 28.12/28.44 ! [V_B_2,T_c,V_A_2,T_b] :
% 28.12/28.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 28.12/28.44 => ( ? [B_f] :
% 28.12/28.44 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2)
% 28.12/28.44 & 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)) )
% 28.12/28.44 <=> 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))) ) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
% 28.12/28.44 ! [V_y,V_x] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 28.12/28.44 => 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))) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_tsub__eq,axiom,
% 28.12/28.44 ! [V_x,V_y] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 28.12/28.44 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom,
% 28.12/28.44 ! [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)) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_lessThan__Suc__eq__insert__0,axiom,
% 28.12/28.44 ! [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))) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_setsum__op__ivl__Suc,axiom,
% 28.12/28.44 ! [V_f_2,V_m_2,V_n_2,T_b] :
% 28.12/28.44 ( class_Groups_Ocomm__monoid__add(T_b)
% 28.12/28.44 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 28.12/28.44 => 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) )
% 28.12/28.44 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 28.12/28.44 => 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)) ) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_setsum__cl__ivl__Suc,axiom,
% 28.12/28.44 ! [V_f_2,V_m_2,V_n_2,T_b] :
% 28.12/28.44 ( class_Groups_Ocomm__monoid__add(T_b)
% 28.12/28.44 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 28.12/28.44 => 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) )
% 28.12/28.44 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 28.12/28.44 => 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))) ) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_greaterThan__0,axiom,
% 28.12/28.44 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))) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_card__Diff1__less,axiom,
% 28.12/28.44 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.44 => 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))) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_card__Diff2__less,axiom,
% 28.12/28.44 ! [V_y_2,V_x_2,V_A_2,T_b] :
% 28.12/28.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 28.12/28.44 => 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))) ) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_Ints__odd__nonzero,axiom,
% 28.12/28.44 ! [V_a_2,T_b] :
% 28.12/28.44 ( class_Int_Oring__char__0(T_b)
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 28.12/28.44 => 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) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_card__Diff__insert,axiom,
% 28.12/28.44 ! [V_B_2,V_a_2,V_A_2,T_b] :
% 28.12/28.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.12/28.44 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 28.12/28.44 => 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)) ) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_card_Oinsert__remove,axiom,
% 28.12/28.44 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.44 => 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)))))) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_card_Oremove,axiom,
% 28.12/28.44 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.44 => 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)))))) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_card__Diff__singleton__if,axiom,
% 28.12/28.44 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.44 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.44 => 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)) )
% 28.12/28.44 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.44 => 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) ) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_card_Ounion__inter__neutral,axiom,
% 28.12/28.44 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.44 => ( ( ? [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)))
% 28.12/28.44 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 28.12/28.44 => 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)) ) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_setsum__bounded,axiom,
% 28.12/28.44 ! [V_K_2,V_f_2,V_A_2,T_b,T_c] :
% 28.12/28.44 ( ( class_Groups_Oordered__ab__semigroup__add(T_c)
% 28.12/28.44 & class_Rings_Osemiring__1(T_c) )
% 28.12/28.44 => ( ! [B_i] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_A_2))
% 28.12/28.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_i)),V_K_2)) )
% 28.12/28.44 => 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))) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_card__Suc__eq,axiom,
% 28.12/28.44 ! [V_k_2,V_A_2,T_b] :
% 28.12/28.44 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Nat_OSuc,V_k_2)
% 28.12/28.44 <=> ? [B_b,B_B] :
% 28.12/28.44 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_b),B_B)
% 28.12/28.44 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_b),B_B))
% 28.12/28.44 & hAPP(c_Finite__Set_Ocard(T_b),B_B) = V_k_2
% 28.12/28.44 & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.12/28.44 => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_card__Plus__conv__if,axiom,
% 28.12/28.44 ! [V_B_2,T_c,V_A_2,T_b] :
% 28.12/28.44 ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.44 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) )
% 28.12/28.44 => 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)) )
% 28.12/28.44 & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.44 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) )
% 28.12/28.44 => 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) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_image__atLeastZeroLessThan__int,axiom,
% 28.12/28.44 ! [V_u_2] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2))
% 28.12/28.44 => 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))) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_setsum__nonneg__0,axiom,
% 28.12/28.44 ! [V_i_2,V_f_2,V_s_2,T_b,T_c] :
% 28.12/28.44 ( class_Groups_Oordered__ab__group__add(T_c)
% 28.12/28.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 28.12/28.44 => ( ! [B_i] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
% 28.12/28.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
% 28.12/28.44 => ( 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)
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
% 28.12/28.44 => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_nat__int,axiom,
% 28.12/28.44 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n ).
% 28.12/28.44
% 28.12/28.44 fof(fact_nat__0,axiom,
% 28.12/28.44 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_transfer__nat__int__numerals_I1_J,axiom,
% 28.12/28.44 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_eq__nat__nat__iff,axiom,
% 28.12/28.44 ! [V_z_H_2,V_z_2] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2))
% 28.12/28.44 => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2)
% 28.12/28.44 <=> V_z_2 = V_z_H_2 ) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_transfer__nat__int__relations_I1_J,axiom,
% 28.12/28.44 ! [V_y_2,V_x_2] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 28.12/28.44 => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2)
% 28.12/28.44 <=> V_x_2 = V_y_2 ) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_all__nat,axiom,
% 28.12/28.44 ! [V_P_2] :
% 28.12/28.44 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 28.12/28.44 <=> ! [B_x] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 28.12/28.44 => hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_ex__nat,axiom,
% 28.12/28.44 ! [V_P_2] :
% 28.12/28.44 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 28.12/28.44 <=> ? [B_x] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 28.12/28.44 & hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_transfer__nat__int__numerals_I2_J,axiom,
% 28.12/28.44 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_transfer__int__nat__set__return__embed,axiom,
% 28.12/28.44 ! [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 ).
% 28.12/28.44
% 28.12/28.44 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom,
% 28.12/28.44 ! [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))) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_card__atLeastZeroLessThan__int,axiom,
% 28.12/28.44 ! [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) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_card__atLeastLessThan__int,axiom,
% 28.12/28.44 ! [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)) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_card__greaterThanAtMost__int,axiom,
% 28.12/28.44 ! [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)) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom,
% 28.12/28.44 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))) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_nat__0__iff,axiom,
% 28.12/28.44 ! [V_i_2] :
% 28.12/28.44 ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.12/28.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_nat__le__0,axiom,
% 28.12/28.44 ! [V_z] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.12/28.44 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_zless__nat__conj,axiom,
% 28.12/28.44 ! [V_z_2,V_w_2] :
% 28.12/28.44 ( 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)))
% 28.12/28.44 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 28.12/28.44 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_nat__mono__iff,axiom,
% 28.12/28.44 ! [V_w_2,V_z_2] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 28.12/28.44 => ( 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)))
% 28.12/28.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_transfer__nat__int__relations_I3_J,axiom,
% 28.12/28.44 ! [V_y_2,V_x_2] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 28.12/28.44 => ( 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)))
% 28.12/28.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_nat__1,axiom,
% 28.12/28.44 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_nat__0__le,axiom,
% 28.12/28.44 ! [V_z] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 28.12/28.44 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_int__eq__iff,axiom,
% 28.12/28.44 ! [V_z_2,V_m_2] :
% 28.12/28.44 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2
% 28.12/28.44 <=> ( V_m_2 = hAPP(c_Int_Onat,V_z_2)
% 28.12/28.44 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_int__nat__eq,axiom,
% 28.12/28.44 ! [V_z] :
% 28.12/28.44 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 28.12/28.44 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z )
% 28.12/28.44 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 28.12/28.44 => 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) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_zless__nat__eq__int__zless,axiom,
% 28.12/28.44 ! [V_z_2,V_m_2] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2)))
% 28.12/28.44 <=> 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)) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_nat__zminus__int,axiom,
% 28.12/28.44 ! [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) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom,
% 28.12/28.44 ! [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))) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_transfer__nat__int__sum__prod_I1_J,axiom,
% 28.12/28.44 ! [V_A_2,V_f_2,T_b] :
% 28.12/28.44 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 28.12/28.44 & class_Groups_Ocomm__monoid__mult(T_b) )
% 28.12/28.44 => 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)) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_zero__less__nat__eq,axiom,
% 28.12/28.44 ! [V_z_2] :
% 28.12/28.44 ( 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)))
% 28.12/28.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_nat__less__eq__zless,axiom,
% 28.12/28.44 ! [V_z_2,V_w_2] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 28.12/28.44 => ( 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)))
% 28.12/28.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_transfer__nat__int__relations_I2_J,axiom,
% 28.12/28.44 ! [V_y_2,V_x_2] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 28.12/28.44 => ( 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)))
% 28.12/28.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_nat__eq__iff2,axiom,
% 28.12/28.44 ! [V_w_2,V_m_2] :
% 28.12/28.44 ( V_m_2 = hAPP(c_Int_Onat,V_w_2)
% 28.12/28.44 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 28.12/28.44 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 28.12/28.44 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 28.12/28.44 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_nat__eq__iff,axiom,
% 28.12/28.44 ! [V_m_2,V_w_2] :
% 28.12/28.44 ( hAPP(c_Int_Onat,V_w_2) = V_m_2
% 28.12/28.44 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 28.12/28.44 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 28.12/28.44 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 28.12/28.44 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_nat__le__eq__zle,axiom,
% 28.12/28.44 ! [V_z_2,V_w_2] :
% 28.12/28.44 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 28.12/28.44 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
% 28.12/28.44 => ( 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)))
% 28.12/28.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_split__nat,axiom,
% 28.12/28.44 ! [V_i_2,V_P_2] :
% 28.12/28.44 ( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2)))
% 28.12/28.44 <=> ( ! [B_n] :
% 28.12/28.44 ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)
% 28.12/28.44 => hBOOL(hAPP(V_P_2,B_n)) )
% 28.12/28.44 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.12/28.44 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_nat__add__distrib,axiom,
% 28.12/28.44 ! [V_z_H,V_z] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 28.12/28.44 => 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)) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom,
% 28.12/28.44 ! [V_y,V_x] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 28.12/28.44 => 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)) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_nat__mult__distrib,axiom,
% 28.12/28.44 ! [V_z_H,V_z] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 28.12/28.44 => 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)) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom,
% 28.12/28.44 ! [V_y,V_x] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 28.12/28.44 => 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)) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom,
% 28.12/28.44 ! [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))) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_nat__diff__distrib,axiom,
% 28.12/28.44 ! [V_z,V_z_H] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 28.12/28.44 => 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)) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom,
% 28.12/28.44 ! [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)) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_card__atLeastAtMost__int,axiom,
% 28.12/28.44 ! [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))) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom,
% 28.12/28.44 ! [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))) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom,
% 28.12/28.44 ! [V_y,V_x] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 28.12/28.44 => 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)) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_finite__PlusD_I2_J,axiom,
% 28.12/28.44 ! [V_B_2,V_A_2,T_c,T_b] :
% 28.12/28.44 ( 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)))
% 28.12/28.44 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_finite__PlusD_I1_J,axiom,
% 28.12/28.44 ! [V_B_2,V_A_2,T_c,T_b] :
% 28.12/28.44 ( 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)))
% 28.12/28.44 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_finite__Plus,axiom,
% 28.12/28.44 ! [V_B_2,T_c,V_A_2,T_b] :
% 28.12/28.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 28.12/28.44 => 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))) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_finite__Plus__iff,axiom,
% 28.12/28.44 ! [V_B_2,V_A_2,T_c,T_b] :
% 28.12/28.44 ( 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)))
% 28.12/28.44 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.44 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_card__greaterThanLessThan__int,axiom,
% 28.12/28.44 ! [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)))) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_one__less__nat__eq,axiom,
% 28.12/28.44 ! [V_z_2] :
% 28.12/28.44 ( 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)))
% 28.12/28.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_nat__less__iff,axiom,
% 28.12/28.44 ! [V_m_2,V_w_2] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2))
% 28.12/28.44 <=> 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))) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_Suc__nat__eq__nat__zadd1,axiom,
% 28.12/28.44 ! [V_z] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 28.12/28.44 => 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)) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_nat__mult__distrib__neg,axiom,
% 28.12/28.44 ! [V_z_H,V_z] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.12/28.44 => 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))) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_card__Plus,axiom,
% 28.12/28.44 ! [V_B_2,T_c,V_A_2,T_b] :
% 28.12/28.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 28.12/28.44 => 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)) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_UNIV__Plus__UNIV,axiom,
% 28.12/28.44 ! [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)) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_nat__aux__def,axiom,
% 28.12/28.44 ! [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) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_transfer__morphism__nat__int,axiom,
% 28.12/28.44 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))) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_Plus__eq__empty__conv,axiom,
% 28.12/28.44 ! [V_B_2,V_A_2,T_c,T_b] :
% 28.12/28.44 ( 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))
% 28.12/28.44 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.44 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom,
% 28.12/28.44 ! [V_n_2,V_m_2] :
% 28.12/28.44 ( c_Nat__Transfer_Ois__nat(V_m_2)
% 28.12/28.44 => ( c_Nat__Transfer_Ois__nat(V_n_2)
% 28.12/28.44 => 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))) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom,
% 28.12/28.44 c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom,
% 28.12/28.44 ! [V_y,V_x] :
% 28.12/28.44 ( c_Nat__Transfer_Ois__nat(V_x)
% 28.12/28.44 => ( c_Nat__Transfer_Ois__nat(V_y)
% 28.12/28.44 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom,
% 28.12/28.44 ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom,
% 28.12/28.44 c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom,
% 28.12/28.44 ! [V_y,V_x] :
% 28.12/28.44 ( c_Nat__Transfer_Ois__nat(V_x)
% 28.12/28.44 => ( c_Nat__Transfer_Ois__nat(V_y)
% 28.12/28.44 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom,
% 28.12/28.44 ! [V_y,V_x] :
% 28.12/28.44 ( c_Nat__Transfer_Ois__nat(V_x)
% 28.12/28.44 => ( c_Nat__Transfer_Ois__nat(V_y)
% 28.12/28.44 => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_is__nat__def,axiom,
% 28.12/28.44 ! [V_x_2] :
% 28.12/28.44 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 28.12/28.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom,
% 28.12/28.44 ! [V_B_2,V_A_2] :
% 28.12/28.44 ( c_Nat__Transfer_Onat__set(V_A_2)
% 28.12/28.44 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 28.12/28.44 => 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))) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom,
% 28.12/28.44 ! [V_B_2,V_A_2] :
% 28.12/28.44 ( c_Nat__Transfer_Onat__set(V_A_2)
% 28.12/28.44 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 28.12/28.44 => 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))) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom,
% 28.12/28.44 ! [V_f_2,V_A_2,T_b] :
% 28.12/28.44 ( ! [B_x] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.12/28.44 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 28.12/28.44 => 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)) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_transfer__int__nat__sum__prod_I1_J,axiom,
% 28.12/28.44 ! [V_f_2,V_A_2,T_b] :
% 28.12/28.44 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 28.12/28.44 & class_Groups_Ocomm__monoid__mult(T_b) )
% 28.12/28.44 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 28.12/28.44 => 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)) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_transfer__int__nat__set__relations_I4_J,axiom,
% 28.12/28.44 ! [V_B_2,V_A_2] :
% 28.12/28.44 ( c_Nat__Transfer_Onat__set(V_A_2)
% 28.12/28.44 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.44 <=> 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))) ) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom,
% 28.12/28.44 c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom,
% 28.12/28.44 ! [V_B_2,V_A_2] :
% 28.12/28.44 ( c_Nat__Transfer_Onat__set(V_A_2)
% 28.12/28.44 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 28.12/28.44 => 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)) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom,
% 28.12/28.44 ! [V_B_2,V_A_2] :
% 28.12/28.44 ( c_Nat__Transfer_Onat__set(V_A_2)
% 28.12/28.44 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 28.12/28.44 => 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)) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_nat__set__def,axiom,
% 28.12/28.44 ! [V_S_2] :
% 28.12/28.44 ( c_Nat__Transfer_Onat__set(V_S_2)
% 28.12/28.44 <=> ! [B_x] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2))
% 28.12/28.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom,
% 28.12/28.44 ! [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)) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_transfer__int__nat__set__relations_I3_J,axiom,
% 28.12/28.44 ! [V_B_2,V_A_2] :
% 28.12/28.44 ( c_Nat__Transfer_Onat__set(V_A_2)
% 28.12/28.44 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 28.12/28.44 => ( V_A_2 = V_B_2
% 28.12/28.44 <=> 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) ) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom,
% 28.12/28.44 ! [V_y_2,V_x_2] :
% 28.12/28.44 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 28.12/28.44 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom,
% 28.12/28.44 ! [V_x_2,V_A_2] :
% 28.12/28.44 ( c_Nat__Transfer_Onat__set(V_A_2)
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 28.12/28.44 => c_Nat__Transfer_Ois__nat(V_x_2) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom,
% 28.12/28.44 ! [V_y_2,V_x_2] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 28.12/28.44 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom,
% 28.12/28.44 ! [V_x_2,V_A_2] :
% 28.12/28.44 ( c_Nat__Transfer_Onat__set(V_A_2)
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 28.12/28.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_transfer__nat__int__set__return__embed,axiom,
% 28.12/28.44 ! [V_A_2] :
% 28.12/28.44 ( c_Nat__Transfer_Onat__set(V_A_2)
% 28.12/28.44 => 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 ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_transfer__int__nat__set__relations_I1_J,axiom,
% 28.12/28.44 ! [V_A_2] :
% 28.12/28.44 ( c_Nat__Transfer_Onat__set(V_A_2)
% 28.12/28.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2))
% 28.12/28.44 <=> 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))) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom,
% 28.12/28.44 ! [V_A_2] :
% 28.12/28.44 ( c_Nat__Transfer_Onat__set(V_A_2)
% 28.12/28.44 => 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)) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_transfer__int__nat__set__relations_I2_J,axiom,
% 28.12/28.44 ! [V_A_2,V_x_2] :
% 28.12/28.44 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 28.12/28.44 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 28.12/28.44 <=> 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))) ) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_transfer__int__nat__set__relations_I5_J,axiom,
% 28.12/28.44 ! [V_B_2,V_A_2] :
% 28.12/28.44 ( c_Nat__Transfer_Onat__set(V_A_2)
% 28.12/28.44 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.44 <=> 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))) ) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_of__int__of__nat,axiom,
% 28.12/28.44 ! [V_k,T_a] :
% 28.12/28.44 ( class_Rings_Oring__1(T_a)
% 28.12/28.44 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.12/28.44 => 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)))) )
% 28.12/28.44 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.12/28.44 => 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)) ) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_setsum__nonneg__leq__bound,axiom,
% 28.12/28.44 ! [V_i_2,V_B_2,V_f_2,V_s_2,T_b,T_c] :
% 28.12/28.44 ( class_Groups_Oordered__ab__group__add(T_c)
% 28.12/28.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 28.12/28.44 => ( ! [B_i] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
% 28.12/28.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
% 28.12/28.44 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) = V_B_2
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
% 28.12/28.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_sum__diff__distrib,axiom,
% 28.12/28.44 ! [V_n_2,V_P_2,V_Q_2] :
% 28.12/28.44 ( ! [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)))
% 28.12/28.44 => 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)) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_decr__mult__lemma,axiom,
% 28.12/28.44 ! [V_k_2,V_P_2,V_d_2] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 28.12/28.44 => ( ! [B_x] :
% 28.12/28.44 ( hBOOL(hAPP(V_P_2,B_x))
% 28.12/28.44 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) )
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 28.12/28.44 => ! [B_x] :
% 28.12/28.44 ( hBOOL(hAPP(V_P_2,B_x))
% 28.12/28.44 => 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)))) ) ) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_negD,axiom,
% 28.12/28.44 ! [V_x] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.12/28.44 => ? [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))) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_of__int__eq__iff,axiom,
% 28.12/28.44 ! [V_z_2,V_w_2,T_b] :
% 28.12/28.44 ( class_Int_Oring__char__0(T_b)
% 28.12/28.44 => ( 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)
% 28.12/28.44 <=> V_w_2 = V_z_2 ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_of__int__int__eq,axiom,
% 28.12/28.44 ! [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) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_of__int__0,axiom,
% 28.12/28.44 ! [T_a] :
% 28.12/28.44 ( class_Rings_Oring__1(T_a)
% 28.12/28.44 => 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) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_of__int__0__eq__iff,axiom,
% 28.12/28.44 ! [V_z_2,T_b] :
% 28.12/28.44 ( class_Int_Oring__char__0(T_b)
% 28.12/28.44 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)
% 28.12/28.44 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_of__int__eq__0__iff,axiom,
% 28.12/28.44 ! [V_z_2,T_b] :
% 28.12/28.44 ( class_Int_Oring__char__0(T_b)
% 28.12/28.44 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) = c_Groups_Ozero__class_Ozero(T_b)
% 28.12/28.44 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_of__int__le__iff,axiom,
% 28.12/28.44 ! [V_z_2,V_w_2,T_b] :
% 28.12/28.44 ( class_Rings_Olinordered__idom(T_b)
% 28.12/28.44 => ( 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)))
% 28.12/28.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_of__int__less__iff,axiom,
% 28.12/28.44 ! [V_z_2,V_w_2,T_b] :
% 28.12/28.44 ( class_Rings_Olinordered__idom(T_b)
% 28.12/28.44 => ( 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)))
% 28.12/28.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_of__int__add,axiom,
% 28.12/28.44 ! [V_z,V_w,T_a] :
% 28.12/28.44 ( class_Rings_Oring__1(T_a)
% 28.12/28.44 => 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)) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_of__int__mult,axiom,
% 28.12/28.44 ! [V_z,V_w,T_a] :
% 28.12/28.44 ( class_Rings_Oring__1(T_a)
% 28.12/28.44 => 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)) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_of__int__1,axiom,
% 28.12/28.44 ! [T_a] :
% 28.12/28.44 ( class_Rings_Oring__1(T_a)
% 28.12/28.44 => 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) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_of__int__diff,axiom,
% 28.12/28.44 ! [V_z,V_w,T_a] :
% 28.12/28.44 ( class_Rings_Oring__1(T_a)
% 28.12/28.44 => 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)) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_of__int__of__nat__eq,axiom,
% 28.12/28.44 ! [V_n,T_a] :
% 28.12/28.44 ( class_Rings_Oring__1(T_a)
% 28.12/28.44 => 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) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_of__int__minus,axiom,
% 28.12/28.44 ! [V_z,T_a] :
% 28.12/28.44 ( class_Rings_Oring__1(T_a)
% 28.12/28.44 => 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)) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_Ints__of__int,axiom,
% 28.12/28.44 ! [V_z_2,T_b] :
% 28.12/28.44 ( class_Rings_Oring__1(T_b)
% 28.12/28.44 => 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))) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_of__int__setsum,axiom,
% 28.12/28.44 ! [V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.44 ( class_Rings_Oring__1(T_b)
% 28.12/28.44 => 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) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_of__int__0__le__iff,axiom,
% 28.12/28.44 ! [V_z_2,T_b] :
% 28.12/28.44 ( class_Rings_Olinordered__idom(T_b)
% 28.12/28.44 => ( 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)))
% 28.12/28.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_of__int__le__0__iff,axiom,
% 28.12/28.44 ! [V_z_2,T_b] :
% 28.12/28.44 ( class_Rings_Olinordered__idom(T_b)
% 28.12/28.44 => ( 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)))
% 28.12/28.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_of__int__0__less__iff,axiom,
% 28.12/28.44 ! [V_z_2,T_b] :
% 28.12/28.44 ( class_Rings_Olinordered__idom(T_b)
% 28.12/28.44 => ( 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)))
% 28.12/28.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_of__int__less__0__iff,axiom,
% 28.12/28.44 ! [V_z_2,T_b] :
% 28.12/28.44 ( class_Rings_Olinordered__idom(T_b)
% 28.12/28.44 => ( 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)))
% 28.12/28.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_of__nat__nat,axiom,
% 28.12/28.44 ! [V_z,T_a] :
% 28.12/28.44 ( class_Rings_Oring__1(T_a)
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 28.12/28.44 => 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) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_incr__mult__lemma,axiom,
% 28.12/28.44 ! [V_k_2,V_P_2,V_d_2] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 28.12/28.44 => ( ! [B_x] :
% 28.12/28.44 ( hBOOL(hAPP(V_P_2,B_x))
% 28.12/28.44 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) )
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 28.12/28.44 => ! [B_x] :
% 28.12/28.44 ( hBOOL(hAPP(V_P_2,B_x))
% 28.12/28.44 => 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)))) ) ) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_ex__least__nat__less,axiom,
% 28.12/28.44 ! [V_n_2,V_P_2] :
% 28.12/28.44 ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 28.12/28.44 => ( hBOOL(hAPP(V_P_2,V_n_2))
% 28.12/28.44 => ? [B_k] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2))
% 28.12/28.44 & ! [B_i] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k))
% 28.12/28.44 => ~ hBOOL(hAPP(V_P_2,B_i)) )
% 28.12/28.44 & 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)))) ) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_zero__less__imp__eq__int,axiom,
% 28.12/28.44 ! [V_k] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 28.12/28.44 => ? [B_n] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 28.12/28.44 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_setsum__mono__zero__left,axiom,
% 28.12/28.44 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 28.12/28.44 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.12/28.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 28.12/28.44 => ( ! [B_x] :
% 28.12/28.44 ( 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)))
% 28.12/28.44 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 28.12/28.44 => 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) ) ) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_setsum__mono__zero__right,axiom,
% 28.12/28.44 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 28.12/28.44 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.12/28.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 28.12/28.44 => ( ! [B_x] :
% 28.12/28.44 ( 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)))
% 28.12/28.44 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 28.12/28.44 => 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) ) ) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_sgn__if,axiom,
% 28.12/28.44 ! [V_x,T_a] :
% 28.12/28.44 ( class_Groups_Osgn__if(T_a)
% 28.12/28.44 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a)
% 28.12/28.44 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) )
% 28.12/28.44 & ( V_x != c_Groups_Ozero__class_Ozero(T_a)
% 28.12/28.44 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 28.12/28.44 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) )
% 28.12/28.44 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 28.12/28.44 => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_sgn__neg,axiom,
% 28.12/28.44 ! [V_a,T_a] :
% 28.12/28.44 ( class_Rings_Olinordered__idom(T_a)
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 28.12/28.44 => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_sgn__1__neg,axiom,
% 28.12/28.44 ! [V_a_2,T_b] :
% 28.12/28.44 ( class_Rings_Olinordered__idom(T_b)
% 28.12/28.44 => ( 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))
% 28.12/28.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_decr__lemma,axiom,
% 28.12/28.44 ! [V_z,V_x,V_d] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 28.12/28.44 => 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)) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_incr__lemma,axiom,
% 28.12/28.44 ! [V_x,V_z,V_d] :
% 28.12/28.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 28.12/28.44 => 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)))) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_setsum__abs,axiom,
% 28.12/28.44 ! [V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.44 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 28.12/28.44 => 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))) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_setsum__abs__ge__zero,axiom,
% 28.12/28.44 ! [V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.44 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 28.12/28.44 => 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))) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_abs__add__abs,axiom,
% 28.12/28.44 ! [V_b,V_a,T_a] :
% 28.12/28.44 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 28.12/28.44 => 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)) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_abs__mult__self,axiom,
% 28.12/28.44 ! [V_a,T_a] :
% 28.12/28.44 ( class_Rings_Olinordered__idom(T_a)
% 28.12/28.44 => 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) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_abs__mult,axiom,
% 28.12/28.44 ! [V_b,V_a,T_a] :
% 28.12/28.44 ( class_Rings_Olinordered__idom(T_a)
% 28.12/28.44 => 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)) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_abs__minus__commute,axiom,
% 28.12/28.44 ! [V_b,V_a,T_a] :
% 28.12/28.44 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 28.12/28.44 => 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)) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_abs__one,axiom,
% 28.12/28.44 ! [T_a] :
% 28.12/28.44 ( class_Rings_Olinordered__idom(T_a)
% 28.12/28.44 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_abs__minus__cancel,axiom,
% 28.12/28.44 ! [V_a,T_a] :
% 28.12/28.44 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 28.12/28.44 => 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) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_abs__of__nat,axiom,
% 28.12/28.44 ! [V_n,T_a] :
% 28.12/28.44 ( class_Rings_Olinordered__idom(T_a)
% 28.12/28.44 => 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) ) ).
% 28.12/28.44
% 28.12/28.44 fof(fact_abs__le__D1,axiom,
% 28.12/28.44 ! [V_b,V_a,T_a] :
% 28.12/28.44 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 28.12/28.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 28.12/28.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_abs__ge__self,axiom,
% 28.12/28.45 ! [V_a,T_a] :
% 28.12/28.45 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 28.12/28.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_sgn__sgn,axiom,
% 28.12/28.45 ! [V_a,T_a] :
% 28.12/28.45 ( class_Rings_Olinordered__idom(T_a)
% 28.12/28.45 => 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) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_abs__idempotent,axiom,
% 28.12/28.45 ! [V_a,T_a] :
% 28.12/28.45 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 28.12/28.45 => 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) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_mult__sgn__abs,axiom,
% 28.12/28.45 ! [V_x,T_a] :
% 28.12/28.45 ( class_Rings_Olinordered__idom(T_a)
% 28.12/28.45 => 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 ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_abs__sgn,axiom,
% 28.12/28.45 ! [V_k,T_a] :
% 28.12/28.45 ( class_Rings_Olinordered__idom(T_a)
% 28.12/28.45 => 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)) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_abs__eq__0,axiom,
% 28.12/28.45 ! [V_a_2,T_b] :
% 28.12/28.45 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 28.12/28.45 => ( hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 28.12/28.45 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_abs__zero,axiom,
% 28.12/28.45 ! [T_a] :
% 28.12/28.45 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 28.12/28.45 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_abs__int__eq,axiom,
% 28.12/28.45 ! [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) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_abs__setsum__abs,axiom,
% 28.12/28.45 ! [V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.45 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 28.12/28.45 => 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) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_sgn__0__0,axiom,
% 28.12/28.45 ! [V_a_2,T_b] :
% 28.12/28.45 ( class_Rings_Olinordered__idom(T_b)
% 28.12/28.45 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 28.12/28.45 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_sgn0,axiom,
% 28.12/28.45 ! [T_a] :
% 28.12/28.45 ( class_Groups_Osgn__if(T_a)
% 28.12/28.45 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_sgn__times,axiom,
% 28.12/28.45 ! [V_b,V_a,T_a] :
% 28.12/28.45 ( class_Rings_Olinordered__idom(T_a)
% 28.12/28.45 => 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)) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_abs__of__nonneg,axiom,
% 28.12/28.45 ! [V_a,T_a] :
% 28.12/28.45 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.12/28.45 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_abs__le__zero__iff,axiom,
% 28.12/28.45 ! [V_a_2,T_b] :
% 28.12/28.45 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 28.12/28.45 => ( 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)))
% 28.12/28.45 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_abs__ge__zero,axiom,
% 28.12/28.45 ! [V_a,T_a] :
% 28.12/28.45 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 28.12/28.45 => 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))) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_abs__of__pos,axiom,
% 28.12/28.45 ! [V_a,T_a] :
% 28.12/28.45 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.12/28.45 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_zero__less__abs__iff,axiom,
% 28.12/28.45 ! [V_a_2,T_b] :
% 28.12/28.45 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 28.12/28.45 => ( 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)))
% 28.12/28.45 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_abs__not__less__zero,axiom,
% 28.12/28.45 ! [V_a,T_a] :
% 28.12/28.45 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 28.12/28.45 => ~ 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))) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_abs__triangle__ineq,axiom,
% 28.12/28.45 ! [V_b,V_a,T_a] :
% 28.12/28.45 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 28.12/28.45 => 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)))) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_abs__mult__less,axiom,
% 28.12/28.45 ! [V_d,V_b,V_c,V_a,T_a] :
% 28.12/28.45 ( class_Rings_Olinordered__idom(T_a)
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c))
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d))
% 28.12/28.45 => 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))) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_abs__triangle__ineq3,axiom,
% 28.12/28.45 ! [V_b,V_a,T_a] :
% 28.12/28.45 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 28.12/28.45 => 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)))) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_abs__triangle__ineq2,axiom,
% 28.12/28.45 ! [V_b,V_a,T_a] :
% 28.12/28.45 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 28.12/28.45 => 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)))) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_abs__triangle__ineq2__sym,axiom,
% 28.12/28.45 ! [V_b,V_a,T_a] :
% 28.12/28.45 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 28.12/28.45 => 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)))) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_abs__le__D2,axiom,
% 28.12/28.45 ! [V_b,V_a,T_a] :
% 28.12/28.45 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 28.12/28.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_abs__leI,axiom,
% 28.12/28.45 ! [V_b,V_a,T_a] :
% 28.12/28.45 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b))
% 28.12/28.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_abs__le__iff,axiom,
% 28.12/28.45 ! [V_b_2,V_a_2,T_b] :
% 28.12/28.45 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 28.12/28.45 => ( 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))
% 28.12/28.45 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 28.12/28.45 & 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)) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_abs__ge__minus__self,axiom,
% 28.12/28.45 ! [V_a,T_a] :
% 28.12/28.45 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 28.12/28.45 => 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))) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_abs__less__iff,axiom,
% 28.12/28.45 ! [V_b_2,V_a_2,T_b] :
% 28.12/28.45 ( class_Rings_Olinordered__idom(T_b)
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2))
% 28.12/28.45 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 28.12/28.45 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_abs__zmult__eq__1,axiom,
% 28.12/28.45 ! [V_n,V_m] :
% 28.12/28.45 ( 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)
% 28.12/28.45 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_abs__mult__pos,axiom,
% 28.12/28.45 ! [V_y,V_x,T_a] :
% 28.12/28.45 ( class_Rings_Olinordered__idom(T_a)
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 28.12/28.45 => 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)) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_abs__eq__mult,axiom,
% 28.12/28.45 ! [V_b,V_a,T_a] :
% 28.12/28.45 ( class_Rings_Oordered__ring__abs(T_a)
% 28.12/28.45 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.12/28.45 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) )
% 28.12/28.45 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 28.12/28.45 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 28.12/28.45 => 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)) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_abs__triangle__ineq4,axiom,
% 28.12/28.45 ! [V_b,V_a,T_a] :
% 28.12/28.45 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 28.12/28.45 => 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)))) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_abs__diff__triangle__ineq,axiom,
% 28.12/28.45 ! [V_d,V_c,V_b,V_a,T_a] :
% 28.12/28.45 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 28.12/28.45 => 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))))) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_abs__of__nonpos,axiom,
% 28.12/28.45 ! [V_a,T_a] :
% 28.12/28.45 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 28.12/28.45 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_abs__minus__le__zero,axiom,
% 28.12/28.45 ! [V_a,T_a] :
% 28.12/28.45 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 28.12/28.45 => 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))) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_abs__of__neg,axiom,
% 28.12/28.45 ! [V_a,T_a] :
% 28.12/28.45 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 28.12/28.45 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_abs__if,axiom,
% 28.12/28.45 ! [V_a,T_a] :
% 28.12/28.45 ( class_Groups_Oabs__if(T_a)
% 28.12/28.45 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 28.12/28.45 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) )
% 28.12/28.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 28.12/28.45 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_zabs__less__one__iff,axiom,
% 28.12/28.45 ! [V_z_2] :
% 28.12/28.45 ( 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)))
% 28.12/28.45 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_zabs__def,axiom,
% 28.12/28.45 ! [V_i] :
% 28.12/28.45 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.12/28.45 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) )
% 28.12/28.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.12/28.45 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_nat__abs__mult__distrib,axiom,
% 28.12/28.45 ! [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))) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_sgn__less,axiom,
% 28.12/28.45 ! [V_a_2,T_b] :
% 28.12/28.45 ( class_Rings_Olinordered__idom(T_b)
% 28.12/28.45 => ( 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)))
% 28.12/28.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_sgn__greater,axiom,
% 28.12/28.45 ! [V_a_2,T_b] :
% 28.12/28.45 ( class_Rings_Olinordered__idom(T_b)
% 28.12/28.45 => ( 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)))
% 28.12/28.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_sgn__1__pos,axiom,
% 28.12/28.45 ! [V_a_2,T_b] :
% 28.12/28.45 ( class_Rings_Olinordered__idom(T_b)
% 28.12/28.45 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Oone__class_Oone(T_b)
% 28.12/28.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_sgn__pos,axiom,
% 28.12/28.45 ! [V_a,T_a] :
% 28.12/28.45 ( class_Rings_Olinordered__idom(T_a)
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.12/28.45 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_zsgn__def,axiom,
% 28.12/28.45 ! [V_i] :
% 28.12/28.45 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.12/28.45 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 28.12/28.45 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.12/28.45 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 28.12/28.45 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 28.12/28.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 28.12/28.45 => 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)) ) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_Nitpick_Oint__lcm__def,axiom,
% 28.12/28.45 ! [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)))) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom,
% 28.12/28.45 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
% 28.12/28.45 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 28.12/28.45 & class_Groups_Ocomm__monoid__mult(T_b) )
% 28.12/28.45 => ( V_A_2 = V_B_2
% 28.12/28.45 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 28.12/28.45 => ( ! [B_x] :
% 28.12/28.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 28.12/28.45 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 28.12/28.45 => 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) ) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_diff__Suc,axiom,
% 28.12/28.45 ! [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)) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_int__val__lemma,axiom,
% 28.12/28.45 ! [V_k_2,V_f_2,V_n_2] :
% 28.12/28.45 ( ! [B_i] :
% 28.12/28.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 28.12/28.45 => 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))) )
% 28.12/28.45 => ( 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))
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 28.12/28.45 => ? [B_i] :
% 28.12/28.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 28.12/28.45 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_nat0__intermed__int__val,axiom,
% 28.12/28.45 ! [V_k_2,V_f_2,V_n_2] :
% 28.12/28.45 ( ! [B_i] :
% 28.12/28.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 28.12/28.45 => 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))) )
% 28.12/28.45 => ( 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))
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 28.12/28.45 => ? [B_i] :
% 28.12/28.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 28.12/28.45 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_nat__case__0,axiom,
% 28.12/28.45 ! [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 ).
% 28.12/28.45
% 28.12/28.45 fof(fact_nat__case__Suc,axiom,
% 28.12/28.45 ! [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) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_card__less__Suc,axiom,
% 28.12/28.45 ! [V_i_2,V_M_2] :
% 28.12/28.45 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 28.12/28.45 => 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))))) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_card__less,axiom,
% 28.12/28.45 ! [V_i_2,V_M_2] :
% 28.12/28.45 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 28.12/28.45 => 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) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_card__less__Suc2,axiom,
% 28.12/28.45 ! [V_i_2,V_M_2] :
% 28.12/28.45 ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 28.12/28.45 => 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))))) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_ex__bij__betw__nat__finite__1,axiom,
% 28.12/28.45 ! [V_M_2,T_b] :
% 28.12/28.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2))
% 28.12/28.45 => ? [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) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_inj__on__diff__nat,axiom,
% 28.12/28.45 ! [V_k_2,V_N_2] :
% 28.12/28.45 ( ! [B_x] :
% 28.12/28.45 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 28.12/28.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) )
% 28.12/28.45 => 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) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_CollectI,axiom,
% 28.12/28.45 ! [T_b,V_a_2,V_P_2] :
% 28.12/28.45 ( hBOOL(hAPP(V_P_2,V_a_2))
% 28.12/28.45 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2))) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_finite__Collect__conjI,axiom,
% 28.12/28.45 ! [V_Q_2,V_P_2,T_b] :
% 28.12/28.45 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 28.12/28.45 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2))) )
% 28.12/28.45 => 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)))) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_finite__Collect__less__nat,axiom,
% 28.12/28.45 ! [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)))) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_finite__Collect__le__nat,axiom,
% 28.12/28.45 ! [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)))) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_Collect__def,axiom,
% 28.12/28.45 ! [V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),V_P_2) = V_P_2 ).
% 28.12/28.45
% 28.12/28.45 fof(fact_empty__Collect__eq,axiom,
% 28.12/28.45 ! [V_P_2,T_b] :
% 28.12/28.45 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),V_P_2)
% 28.12/28.45 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_Collect__empty__eq,axiom,
% 28.12/28.45 ! [V_P_2,T_b] :
% 28.12/28.45 ( hAPP(c_Set_OCollect(T_b),V_P_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.45 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_Collect__mem__eq,axiom,
% 28.12/28.45 ! [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 ).
% 28.12/28.45
% 28.12/28.45 fof(fact_mem__Collect__eq,axiom,
% 28.12/28.45 ! [V_P_2,V_a_2,T_b] :
% 28.12/28.45 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 28.12/28.45 <=> hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_CollectD,axiom,
% 28.12/28.45 ! [V_P_2,V_a_2,T_b] :
% 28.12/28.45 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 28.12/28.45 => hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_CollectE,axiom,
% 28.12/28.45 ! [V_P_2,V_a_2,T_b] :
% 28.12/28.45 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 28.12/28.45 => hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_empty__def,axiom,
% 28.12/28.45 ! [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)) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_finite__Collect__disjI,axiom,
% 28.12/28.45 ! [V_Q_2,V_P_2,T_b] :
% 28.12/28.45 ( 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))))
% 28.12/28.45 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 28.12/28.45 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2))) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_insert__Collect,axiom,
% 28.12/28.45 ! [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)) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_UNIV__def,axiom,
% 28.12/28.45 ! [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)) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_Collect__disj__eq,axiom,
% 28.12/28.45 ! [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)) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_Collect__conj__eq,axiom,
% 28.12/28.45 ! [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)) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_Collect__neg__eq,axiom,
% 28.12/28.45 ! [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)) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_vimage__Collect__eq,axiom,
% 28.12/28.45 ! [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)) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_insert__compr,axiom,
% 28.12/28.45 ! [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))) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_insert__compr__raw,axiom,
% 28.12/28.45 ! [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))) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_Un__def,axiom,
% 28.12/28.45 ! [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))) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_Int__def,axiom,
% 28.12/28.45 ! [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))) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_Int__Collect,axiom,
% 28.12/28.45 ! [V_P_2,V_A_2,V_x_2,T_b] :
% 28.12/28.45 ( 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))))
% 28.12/28.45 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.45 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_singleton__conv2,axiom,
% 28.12/28.45 ! [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))) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_singleton__conv,axiom,
% 28.12/28.45 ! [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))) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_Collect__conv__if2,axiom,
% 28.12/28.45 ! [T_b,V_a_2,V_P_2] :
% 28.12/28.45 ( ( hBOOL(hAPP(V_P_2,V_a_2))
% 28.12/28.45 => 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))) )
% 28.12/28.45 & ( ~ hBOOL(hAPP(V_P_2,V_a_2))
% 28.12/28.45 => 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)) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_Collect__conv__if,axiom,
% 28.12/28.45 ! [T_b,V_a_2,V_P_2] :
% 28.12/28.45 ( ( hBOOL(hAPP(V_P_2,V_a_2))
% 28.12/28.45 => 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))) )
% 28.12/28.45 & ( ~ hBOOL(hAPP(V_P_2,V_a_2))
% 28.12/28.45 => 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)) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_set__diff__eq,axiom,
% 28.12/28.45 ! [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)))) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_finite__Collect__not,axiom,
% 28.12/28.45 ! [V_P_2,T_b] :
% 28.12/28.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 28.12/28.45 => ( 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))))
% 28.12/28.45 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_insert__def,axiom,
% 28.12/28.45 ! [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) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_Compl__eq,axiom,
% 28.12/28.45 ! [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))) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_vimage__def,axiom,
% 28.12/28.45 ! [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)) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_Collect__imp__eq,axiom,
% 28.12/28.45 ! [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)) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_finite__M__bounded__by__nat,axiom,
% 28.12/28.45 ! [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))))) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_setsum__setsum__restrict,axiom,
% 28.12/28.45 ! [V_R_2,V_f_2,V_T_2,T_c,V_S_2,T_b,T_d] :
% 28.12/28.45 ( class_Groups_Ocomm__monoid__add(T_d)
% 28.12/28.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 28.12/28.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
% 28.12/28.45 => 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) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_if__image__distrib,axiom,
% 28.12/28.45 ! [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))))) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_nat__seg__image__imp__finite,axiom,
% 28.12/28.45 ! [V_n_2,V_f_2,T_b,V_A_2] :
% 28.12/28.45 ( 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)))
% 28.12/28.45 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_setsum__restrict__set_H,axiom,
% 28.12/28.45 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
% 28.12/28.45 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.12/28.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.45 => 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) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_setsum__image__gen,axiom,
% 28.12/28.45 ! [V_f_2,T_d,V_g_2,V_S_2,T_b,T_c] :
% 28.12/28.45 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.12/28.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 28.12/28.45 => 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)) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_setsum__cases,axiom,
% 28.12/28.45 ! [V_g_2,V_f_2,V_P_2,V_A_2,T_b,T_c] :
% 28.12/28.45 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.12/28.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.45 => 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))))) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_less__eq__nat_Osimps_I2_J,axiom,
% 28.12/28.45 ! [V_n_2,V_m_2] :
% 28.12/28.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 28.12/28.45 <=> 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)) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_setsum__multicount,axiom,
% 28.12/28.45 ! [V_k_2,V_R_2,V_T_2,T_c,V_S_2,T_b] :
% 28.12/28.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 28.12/28.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
% 28.12/28.45 => ( ! [B_x] :
% 28.12/28.45 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_T_2))
% 28.12/28.45 => 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 )
% 28.12/28.45 => 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)) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_ex__bij__betw__nat__finite,axiom,
% 28.12/28.45 ! [V_M_2,T_b] :
% 28.12/28.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2))
% 28.12/28.45 => ? [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) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_lfp__induct__set,axiom,
% 28.12/28.45 ! [V_P_2,V_f_2,V_a_2,T_b] :
% 28.12/28.45 ( 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)))
% 28.12/28.45 => ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 28.12/28.45 => ( ! [B_x] :
% 28.12/28.45 ( 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)))))
% 28.12/28.45 => hBOOL(hAPP(V_P_2,B_x)) )
% 28.12/28.45 => hBOOL(hAPP(V_P_2,V_a_2)) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_def__lfp__induct__set,axiom,
% 28.12/28.45 ! [V_P_2,V_a_2,V_f_2,T_b,V_A_2] :
% 28.12/28.45 ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 28.12/28.45 => ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.12/28.45 => ( ! [B_x] :
% 28.12/28.45 ( 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)))))
% 28.12/28.45 => hBOOL(hAPP(V_P_2,B_x)) )
% 28.12/28.45 => hBOOL(hAPP(V_P_2,V_a_2)) ) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_def__Collect__coinduct,axiom,
% 28.12/28.45 ! [V_X_2,V_a_2,V_P_2,T_b,V_A_2] :
% 28.12/28.45 ( 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))
% 28.12/28.45 => ( 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))
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
% 28.12/28.45 => ( ! [B_z] :
% 28.12/28.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_z),V_X_2))
% 28.12/28.45 => 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)) )
% 28.12/28.45 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_finite__Collect__subsets,axiom,
% 28.12/28.45 ! [V_A_2,T_b] :
% 28.12/28.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.45 => 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)))) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_Pow__def,axiom,
% 28.12/28.45 ! [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)) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom,
% 28.12/28.45 ! [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))) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom,
% 28.12/28.45 ! [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)))) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom,
% 28.12/28.45 ! [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)))) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_setsum__multicount__gen,axiom,
% 28.12/28.45 ! [V_k_2,V_R_2,V_t_2,T_c,V_s_2,T_b] :
% 28.12/28.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 28.12/28.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_t_2))
% 28.12/28.45 => ( ! [B_x] :
% 28.12/28.45 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_t_2))
% 28.12/28.45 => 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) )
% 28.12/28.45 => 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) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_inf__Sup2__distrib,axiom,
% 28.12/28.45 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.45 ( class_Lattices_Odistrib__lattice(T_b)
% 28.12/28.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.45 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.45 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.45 => 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))))))) ) ) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_inf__Sup1__distrib,axiom,
% 28.12/28.45 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.45 ( class_Lattices_Odistrib__lattice(T_b)
% 28.12/28.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.45 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.45 => 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))))) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_sup__Inf2__distrib,axiom,
% 28.12/28.45 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.45 ( class_Lattices_Odistrib__lattice(T_b)
% 28.12/28.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.45 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.45 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.45 => 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))))))) ) ) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_sup__Inf1__distrib,axiom,
% 28.12/28.45 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.45 ( class_Lattices_Odistrib__lattice(T_b)
% 28.12/28.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.45 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.45 => 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))))) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_finite__image__set,axiom,
% 28.12/28.45 ! [V_f_2,T_c,V_P_2,T_b] :
% 28.12/28.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 28.12/28.45 => 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))))) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_finite__Collect__bounded__ex,axiom,
% 28.12/28.45 ! [V_Q_2,T_c,V_P_2,T_b] :
% 28.12/28.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 28.12/28.45 => ( 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)))))
% 28.12/28.45 <=> ! [B_y] :
% 28.12/28.45 ( hBOOL(hAPP(V_P_2,B_y))
% 28.12/28.45 => 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)))) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_Pow__Compl,axiom,
% 28.12/28.45 ! [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))))) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_add__Min__commute,axiom,
% 28.12/28.45 ! [V_k_2,V_N_2,T_b] :
% 28.12/28.45 ( class_Groups_Olinordered__ab__semigroup__add(T_b)
% 28.12/28.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 28.12/28.45 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.45 => 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))))) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_add__Max__commute,axiom,
% 28.12/28.45 ! [V_k_2,V_N_2,T_b] :
% 28.12/28.45 ( class_Groups_Olinordered__ab__semigroup__add(T_b)
% 28.12/28.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 28.12/28.45 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.45 => 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))))) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_finite__conv__nat__seg__image,axiom,
% 28.12/28.45 ! [V_A_2,T_b] :
% 28.12/28.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.45 <=> ? [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))) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_pigeonhole__infinite,axiom,
% 28.12/28.45 ! [V_f_2,T_c,V_A_2,T_b] :
% 28.12/28.45 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 28.12/28.45 => ? [B_x] :
% 28.12/28.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.12/28.45 & ~ 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)))))) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_diff__nat__eq__if,axiom,
% 28.12/28.45 ! [V_z_2,V_z_H_2] :
% 28.12/28.45 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 28.12/28.45 => 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) )
% 28.12/28.45 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 28.12/28.45 => 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)) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_not__neg__0,axiom,
% 28.12/28.45 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_not__neg__int,axiom,
% 28.12/28.45 ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_not__neg__1,axiom,
% 28.12/28.45 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_minus__Min__eq__Max,axiom,
% 28.12/28.45 ! [V_S_2,T_b] :
% 28.12/28.45 ( class_Groups_Olinordered__ab__group__add(T_b)
% 28.12/28.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 28.12/28.45 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.45 => 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)) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_minus__Max__eq__Min,axiom,
% 28.12/28.45 ! [V_S_2,T_b] :
% 28.12/28.45 ( class_Groups_Olinordered__ab__group__add(T_b)
% 28.12/28.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 28.12/28.45 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.45 => 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)) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_Min_Osingleton,axiom,
% 28.12/28.45 ! [V_x_2,T_b] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_b)
% 28.12/28.45 => 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 ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_Max_Osingleton,axiom,
% 28.12/28.45 ! [V_x_2,T_b] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_b)
% 28.12/28.45 => 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 ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_not__neg__eq__ge__0,axiom,
% 28.12/28.45 ! [V_x_2] :
% 28.12/28.45 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2))
% 28.12/28.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_neg__def,axiom,
% 28.12/28.45 ! [V_Z_2] :
% 28.12/28.45 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2))
% 28.12/28.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_neg__nat,axiom,
% 28.12/28.45 ! [V_z] :
% 28.12/28.45 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 28.12/28.45 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_not__neg__nat,axiom,
% 28.12/28.45 ! [V_z] :
% 28.12/28.45 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 28.12/28.45 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_Max__ge,axiom,
% 28.12/28.45 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_b)
% 28.12/28.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.45 => 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))) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_Min__le,axiom,
% 28.12/28.45 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_b)
% 28.12/28.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.45 => 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)) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_Min__in,axiom,
% 28.12/28.45 ! [V_A_2,T_b] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_b)
% 28.12/28.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.45 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.45 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_Max__in,axiom,
% 28.12/28.45 ! [V_A_2,T_b] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_b)
% 28.12/28.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.45 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.45 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_neg__zminus__int,axiom,
% 28.12/28.45 ! [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))))) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_Max__mono,axiom,
% 28.12/28.45 ! [V_N_2,V_M_2,T_b] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_b)
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
% 28.12/28.45 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 28.12/28.45 => 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))) ) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_Min__antimono,axiom,
% 28.12/28.45 ! [V_N_2,V_M_2,T_b] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_b)
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
% 28.12/28.45 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 28.12/28.45 => 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))) ) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_Min_Oremove,axiom,
% 28.12/28.45 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_b)
% 28.12/28.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.45 => ( ( 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))
% 28.12/28.45 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 )
% 28.12/28.45 & ( 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))
% 28.12/28.45 => 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)))))) ) ) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_Max_Oremove,axiom,
% 28.12/28.45 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_b)
% 28.12/28.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.45 => ( ( 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))
% 28.12/28.45 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 )
% 28.12/28.45 & ( 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))
% 28.12/28.45 => 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)))))) ) ) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_setsum__SucD,axiom,
% 28.12/28.45 ! [V_n_2,V_A_2,V_f_2,T_b] :
% 28.12/28.45 ( 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)
% 28.12/28.45 => ? [B_x] :
% 28.12/28.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.12/28.45 & 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))) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_Cantor__Bernstein,axiom,
% 28.12/28.45 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.45 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 28.12/28.45 => ( 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))
% 28.12/28.45 => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2)
% 28.12/28.45 => ( 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))
% 28.12/28.45 => ? [B_h] : c_Fun_Obij__betw(T_b,T_c,B_h,V_A_2,V_B_2) ) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_setprod_Oremove,axiom,
% 28.12/28.45 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 28.12/28.45 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.12/28.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.45 => 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)))))) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_max__of__mono,axiom,
% 28.12/28.45 ! [V_n_2,V_m_2,V_f_2,T_b,T_c] :
% 28.12/28.45 ( ( class_Orderings_Olinorder(T_c)
% 28.12/28.45 & class_Orderings_Olinorder(T_b) )
% 28.12/28.45 => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
% 28.12/28.45 => 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)) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__of__mono,axiom,
% 28.12/28.45 ! [V_n_2,V_m_2,V_f_2,T_b,T_c] :
% 28.12/28.45 ( ( class_Orderings_Olinorder(T_c)
% 28.12/28.45 & class_Orderings_Olinorder(T_b) )
% 28.12/28.45 => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
% 28.12/28.45 => 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)) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_of__int__setprod,axiom,
% 28.12/28.45 ! [V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.45 ( ( class_Groups_Ocomm__monoid__mult(T_b)
% 28.12/28.45 & class_Rings_Oring__1(T_b) )
% 28.12/28.45 => 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) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom,
% 28.12/28.45 ! [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)) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_le__max__iff__disj,axiom,
% 28.12/28.45 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_b)
% 28.12/28.45 => ( 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)))
% 28.12/28.45 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_x_2))
% 28.12/28.45 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_y_2)) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Ole__supE,axiom,
% 28.12/28.45 ! [V_x,V_b,V_a,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => ( 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))
% 28.12/28.45 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 28.12/28.45 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Osup__mono,axiom,
% 28.12/28.45 ! [V_d,V_b,V_c,V_a,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 28.12/28.45 => 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))) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Osup__least,axiom,
% 28.12/28.45 ! [V_z,V_x,V_y,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 28.12/28.45 => 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)) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Ole__supI,axiom,
% 28.12/28.45 ! [V_b,V_x,V_a,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 28.12/28.45 => 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)) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Osup__absorb1,axiom,
% 28.12/28.45 ! [V_x,V_y,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 28.12/28.45 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Osup__absorb2,axiom,
% 28.12/28.45 ! [V_y,V_x,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 28.12/28.45 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Ole__supI2,axiom,
% 28.12/28.45 ! [V_a,V_b,V_x,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 28.12/28.45 => 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))) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Ole__supI1,axiom,
% 28.12/28.45 ! [V_b,V_a,V_x,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 28.12/28.45 => 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))) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Ole__sup__iff,axiom,
% 28.12/28.45 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_b)
% 28.12/28.45 => ( 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))
% 28.12/28.45 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 28.12/28.45 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Ole__iff__sup,axiom,
% 28.12/28.45 ! [V_y_2,V_x_2,T_b] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_b)
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 28.12/28.45 <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2) = V_y_2 ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_le__maxI2,axiom,
% 28.12/28.45 ! [V_x,V_y,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => 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))) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_le__maxI1,axiom,
% 28.12/28.45 ! [V_y,V_x,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => 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))) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__le__iff__disj,axiom,
% 28.12/28.45 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_b)
% 28.12/28.45 => ( 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))
% 28.12/28.45 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 28.12/28.45 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Ole__infE,axiom,
% 28.12/28.45 ! [V_b,V_a,V_x,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => ( 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)))
% 28.12/28.45 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 28.12/28.45 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Oinf__mono,axiom,
% 28.12/28.45 ! [V_d,V_b,V_c,V_a,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 28.12/28.45 => 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))) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Oinf__greatest,axiom,
% 28.12/28.45 ! [V_z,V_y,V_x,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 28.12/28.45 => 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))) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Ole__infI,axiom,
% 28.12/28.45 ! [V_b,V_a,V_x,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 28.12/28.45 => 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))) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Oinf__absorb2,axiom,
% 28.12/28.45 ! [V_x,V_y,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 28.12/28.45 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Oinf__absorb1,axiom,
% 28.12/28.45 ! [V_y,V_x,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 28.12/28.45 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Ole__infI2,axiom,
% 28.12/28.45 ! [V_a,V_x,V_b,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 28.12/28.45 => 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)) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Ole__infI1,axiom,
% 28.12/28.45 ! [V_b,V_x,V_a,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 28.12/28.45 => 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)) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Ole__inf__iff,axiom,
% 28.12/28.45 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_b)
% 28.12/28.45 => ( 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)))
% 28.12/28.45 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 28.12/28.45 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Ole__iff__inf,axiom,
% 28.12/28.45 ! [V_y_2,V_x_2,T_b] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_b)
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 28.12/28.45 <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2) = V_x_2 ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Oinf__le2,axiom,
% 28.12/28.45 ! [V_y,V_x,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => 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)) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Oinf__le1,axiom,
% 28.12/28.45 ! [V_y,V_x,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => 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)) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Oless__supI2,axiom,
% 28.12/28.45 ! [V_a,V_b,V_x,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 28.12/28.45 => 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))) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Oless__supI1,axiom,
% 28.12/28.45 ! [V_b,V_a,V_x,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 28.12/28.45 => 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))) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_max__less__iff__conj,axiom,
% 28.12/28.45 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_b)
% 28.12/28.45 => ( 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))
% 28.12/28.45 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2))
% 28.12/28.45 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_less__max__iff__disj,axiom,
% 28.12/28.45 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_b)
% 28.12/28.45 => ( 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)))
% 28.12/28.45 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2))
% 28.12/28.45 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Oless__infI2,axiom,
% 28.12/28.45 ! [V_a,V_x,V_b,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 28.12/28.45 => 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)) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Oless__infI1,axiom,
% 28.12/28.45 ! [V_b,V_x,V_a,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 28.12/28.45 => 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)) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__less__iff__disj,axiom,
% 28.12/28.45 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_b)
% 28.12/28.45 => ( 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))
% 28.12/28.45 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2))
% 28.12/28.45 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__less__iff__conj,axiom,
% 28.12/28.45 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_b)
% 28.12/28.45 => ( 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)))
% 28.12/28.45 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2))
% 28.12/28.45 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_max__add__distrib__left,axiom,
% 28.12/28.45 ! [V_z,V_y,V_x,T_a] :
% 28.12/28.45 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 28.12/28.45 => 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)) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__add__distrib__left,axiom,
% 28.12/28.45 ! [V_z,V_y,V_x,T_a] :
% 28.12/28.45 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 28.12/28.45 => 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)) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_max__diff__distrib__left,axiom,
% 28.12/28.45 ! [V_z,V_y,V_x,T_a] :
% 28.12/28.45 ( class_Groups_Oordered__ab__group__add(T_a)
% 28.12/28.45 => 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)) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__diff__distrib__left,axiom,
% 28.12/28.45 ! [V_z,V_y,V_x,T_a] :
% 28.12/28.45 ( class_Groups_Oordered__ab__group__add(T_a)
% 28.12/28.45 => 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)) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_max__0L,axiom,
% 28.12/28.45 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 28.12/28.45
% 28.12/28.45 fof(fact_max__0R,axiom,
% 28.12/28.45 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__0L,axiom,
% 28.12/28.45 ! [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) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__0R,axiom,
% 28.12/28.45 ! [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) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_max__Suc__Suc,axiom,
% 28.12/28.45 ! [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)) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__Suc__Suc,axiom,
% 28.12/28.45 ! [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)) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Odistrib__inf__le,axiom,
% 28.12/28.45 ! [V_z,V_y,V_x,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => 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)))) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Odistrib__sup__le,axiom,
% 28.12/28.45 ! [V_z,V_y,V_x,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => 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)))) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_Max_Oidem,axiom,
% 28.12/28.45 ! [V_x,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_Min_Oidem,axiom,
% 28.12/28.45 ! [V_x,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Osup_Oidem,axiom,
% 28.12/28.45 ! [V_a,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Oinf_Oidem,axiom,
% 28.12/28.45 ! [V_a,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Osup_Ocommute,axiom,
% 28.12/28.45 ! [V_b,V_a,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => 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) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Osup__commute,axiom,
% 28.12/28.45 ! [V_y,V_x,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => 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) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Oinf_Ocommute,axiom,
% 28.12/28.45 ! [V_b,V_a,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => 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) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Oinf__commute,axiom,
% 28.12/28.45 ! [V_y,V_x,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => 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) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Osup__inf__absorb,axiom,
% 28.12/28.45 ! [V_y,V_x,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => 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 ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Oinf__sup__absorb,axiom,
% 28.12/28.45 ! [V_y,V_x,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => 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 ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Osup_Oleft__idem,axiom,
% 28.12/28.45 ! [V_b,V_a,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => 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) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Osup__left__idem,axiom,
% 28.12/28.45 ! [V_y,V_x,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => 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) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Oinf_Oleft__idem,axiom,
% 28.12/28.45 ! [V_b,V_a,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => 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) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Oinf__left__idem,axiom,
% 28.12/28.45 ! [V_y,V_x,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => 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) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Osup_Oleft__commute,axiom,
% 28.12/28.45 ! [V_c,V_a,V_b,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => 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)) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Osup__left__commute,axiom,
% 28.12/28.45 ! [V_z,V_y,V_x,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => 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)) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Oinf_Oleft__commute,axiom,
% 28.12/28.45 ! [V_c,V_a,V_b,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => 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)) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Oinf__left__commute,axiom,
% 28.12/28.45 ! [V_z,V_y,V_x,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => 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)) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Osup__inf__distrib1,axiom,
% 28.12/28.45 ! [V_z,V_y,V_x,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => 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)) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Oinf__sup__distrib1,axiom,
% 28.12/28.45 ! [V_z,V_y,V_x,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => 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)) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Osup_Oassoc,axiom,
% 28.12/28.45 ! [V_c,V_b,V_a,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => 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)) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Osup__assoc,axiom,
% 28.12/28.45 ! [V_z,V_y,V_x,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => 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)) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Oinf_Oassoc,axiom,
% 28.12/28.45 ! [V_c,V_b,V_a,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => 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)) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Oinf__assoc,axiom,
% 28.12/28.45 ! [V_z,V_y,V_x,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => 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)) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Osup__inf__distrib2,axiom,
% 28.12/28.45 ! [V_x,V_z,V_y,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => 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)) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Oinf__sup__distrib2,axiom,
% 28.12/28.45 ! [V_x,V_z,V_y,T_a] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_a)
% 28.12/28.45 => 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)) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_minus__max__eq__min,axiom,
% 28.12/28.45 ! [V_y,V_x,T_a] :
% 28.12/28.45 ( class_Groups_Olinordered__ab__group__add(T_a)
% 28.12/28.45 => 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)) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_minus__min__eq__max,axiom,
% 28.12/28.45 ! [V_y,V_x,T_a] :
% 28.12/28.45 ( class_Groups_Olinordered__ab__group__add(T_a)
% 28.12/28.45 => 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)) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_of__nat__setprod,axiom,
% 28.12/28.45 ! [V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.45 ( ( class_Groups_Ocomm__monoid__mult(T_b)
% 28.12/28.45 & class_Rings_Osemiring__1(T_b) )
% 28.12/28.45 => 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) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_int__setprod,axiom,
% 28.12/28.45 ! [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) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__diff,axiom,
% 28.12/28.45 ! [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) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_Int__atLeastLessThan,axiom,
% 28.12/28.45 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_b)
% 28.12/28.45 => 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)) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_Int__atLeastAtMost,axiom,
% 28.12/28.45 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_b)
% 28.12/28.45 => 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)) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_Int__greaterThanAtMost,axiom,
% 28.12/28.45 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_b)
% 28.12/28.45 => 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)) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_inf__min,axiom,
% 28.12/28.45 ! [T_b] :
% 28.12/28.45 ( ( class_Lattices_Osemilattice__inf(T_b)
% 28.12/28.45 & class_Orderings_Olinorder(T_b) )
% 28.12/28.45 => c_Lattices_Osemilattice__inf__class_Oinf(T_b) = c_Orderings_Oord__class_Omin(T_b) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_sup__max,axiom,
% 28.12/28.45 ! [T_b] :
% 28.12/28.45 ( ( class_Lattices_Osemilattice__sup(T_b)
% 28.12/28.45 & class_Orderings_Olinorder(T_b) )
% 28.12/28.45 => c_Lattices_Osemilattice__sup__class_Osup(T_b) = c_Orderings_Oord__class_Omax(T_b) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_Int__greaterThanLessThan,axiom,
% 28.12/28.45 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_b)
% 28.12/28.45 => 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)) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_setprod__timesf,axiom,
% 28.12/28.45 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 28.12/28.45 ( class_Groups_Ocomm__monoid__mult(T_b)
% 28.12/28.45 => 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)) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_setprod__1,axiom,
% 28.12/28.45 ! [V_A_2,T_c,T_b] :
% 28.12/28.45 ( class_Groups_Ocomm__monoid__mult(T_b)
% 28.12/28.45 => 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) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_abs__setprod,axiom,
% 28.12/28.45 ! [V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.45 ( class_Fields_Olinordered__field(T_b)
% 28.12/28.45 => 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) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Ofun__left__comm__idem__sup,axiom,
% 28.12/28.45 ! [T_b] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_b)
% 28.12/28.45 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Ofun__left__comm__idem__inf,axiom,
% 28.12/28.45 ! [T_b] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_b)
% 28.12/28.45 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_transfer__nat__int__sum__prod_I2_J,axiom,
% 28.12/28.45 ! [V_A_2,V_f_2,T_b] :
% 28.12/28.45 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 28.12/28.45 & class_Groups_Ocomm__monoid__mult(T_b) )
% 28.12/28.45 => 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)) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_setprod__zero,axiom,
% 28.12/28.45 ! [V_f_2,V_A_2,T_b,T_c] :
% 28.12/28.45 ( class_Rings_Ocomm__semiring__1(T_c)
% 28.12/28.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.45 => ( ? [B_x] :
% 28.12/28.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.12/28.45 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 28.12/28.45 => 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) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_setprod__zero__iff,axiom,
% 28.12/28.45 ! [V_f_2,V_A_2,T_b,T_c] :
% 28.12/28.45 ( ( class_Rings_Ocomm__semiring__1(T_c)
% 28.12/28.45 & class_Rings_Ono__zero__divisors(T_c) )
% 28.12/28.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.45 => ( 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)
% 28.12/28.45 <=> ? [B_x] :
% 28.12/28.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.12/28.45 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_setprod__empty,axiom,
% 28.12/28.45 ! [V_f_2,T_c,T_b] :
% 28.12/28.45 ( class_Groups_Ocomm__monoid__mult(T_b)
% 28.12/28.45 => 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) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_setprod_Oempty,axiom,
% 28.12/28.45 ! [V_g_2,T_c,T_b] :
% 28.12/28.45 ( class_Groups_Ocomm__monoid__mult(T_b)
% 28.12/28.45 => 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) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_setprod__infinite,axiom,
% 28.12/28.45 ! [V_f_2,V_A_2,T_b,T_c] :
% 28.12/28.45 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.12/28.45 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.45 => 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) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_setprod_Oinfinite,axiom,
% 28.12/28.45 ! [V_g_2,V_A_2,T_b,T_c] :
% 28.12/28.45 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.12/28.45 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.45 => 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) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_setprod__eq__1__iff,axiom,
% 28.12/28.45 ! [V_f_2,V_F_2,T_b] :
% 28.12/28.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 28.12/28.45 => ( 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)
% 28.12/28.45 <=> ! [B_x] :
% 28.12/28.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2))
% 28.12/28.45 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_transfer__int__nat__sum__prod_I2_J,axiom,
% 28.12/28.45 ! [V_f_2,V_A_2,T_b] :
% 28.12/28.45 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 28.12/28.45 & class_Groups_Ocomm__monoid__mult(T_b) )
% 28.12/28.45 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 28.12/28.45 => 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)) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_nat__minus__add__max,axiom,
% 28.12/28.45 ! [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) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_setprod_Odistrib,axiom,
% 28.12/28.45 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 28.12/28.45 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.12/28.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.45 => 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)) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_setprod__pos__nat__iff,axiom,
% 28.12/28.45 ! [V_f_2,V_S_2,T_b] :
% 28.12/28.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 28.12/28.45 => ( 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)))
% 28.12/28.45 <=> ! [B_x] :
% 28.12/28.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 28.12/28.45 => 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))) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_setprod__reindex__cong,axiom,
% 28.12/28.45 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 28.12/28.45 ( class_Groups_Ocomm__monoid__mult(T_d)
% 28.12/28.45 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 28.12/28.45 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 28.12/28.45 => ( V_g_2 = hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)
% 28.12/28.45 => 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) ) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_setprod__reindex,axiom,
% 28.12/28.45 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
% 28.12/28.45 ( class_Groups_Ocomm__monoid__mult(T_d)
% 28.12/28.45 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 28.12/28.45 => 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) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_max__Suc1,axiom,
% 28.12/28.45 ! [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) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_max__Suc2,axiom,
% 28.12/28.45 ! [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) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_setprod__delta_H,axiom,
% 28.12/28.45 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 28.12/28.45 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.12/28.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 28.12/28.45 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 28.12/28.45 => 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) )
% 28.12/28.45 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 28.12/28.45 => 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) ) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_setprod__delta,axiom,
% 28.12/28.45 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 28.12/28.45 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.12/28.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 28.12/28.45 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 28.12/28.45 => 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) )
% 28.12/28.45 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 28.12/28.45 => 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) ) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_Max_Oin__idem,axiom,
% 28.12/28.45 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_b)
% 28.12/28.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.45 => 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) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_Min_Oin__idem,axiom,
% 28.12/28.45 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_b)
% 28.12/28.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.45 => 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) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Omono__sup,axiom,
% 28.12/28.45 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
% 28.12/28.45 ( ( class_Lattices_Osemilattice__sup(T_c)
% 28.12/28.45 & class_Orderings_Olinorder(T_b) )
% 28.12/28.45 => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
% 28.12/28.45 => 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)))) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Omono__inf,axiom,
% 28.12/28.45 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
% 28.12/28.45 ( ( class_Lattices_Osemilattice__inf(T_c)
% 28.12/28.45 & class_Orderings_Olinorder(T_b) )
% 28.12/28.45 => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
% 28.12/28.45 => 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)))) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_Int__atLeastAtMostR1,axiom,
% 28.12/28.45 ! [V_d_2,V_c_2,V_b_2,T_b] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_b)
% 28.12/28.45 => 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)) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_Int__atLeastAtMostL1,axiom,
% 28.12/28.45 ! [V_d_2,V_b_2,V_a_2,T_b] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_b)
% 28.12/28.45 => 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)) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_Int__atLeastAtMostR2,axiom,
% 28.12/28.45 ! [V_d_2,V_c_2,V_a_2,T_b] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_b)
% 28.12/28.45 => 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) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_Int__atLeastAtMostL2,axiom,
% 28.12/28.45 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_b)
% 28.12/28.45 => 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) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_Max_OF__eq,axiom,
% 28.12/28.45 ! [V_A_2,T_b] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_b)
% 28.12/28.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.45 => 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) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_Min_OF__eq,axiom,
% 28.12/28.45 ! [V_A_2,T_b] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_b)
% 28.12/28.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.45 => 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) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_setprod_Oinsert,axiom,
% 28.12/28.45 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 28.12/28.45 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.12/28.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.45 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.45 => 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)) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_setprod__insert,axiom,
% 28.12/28.45 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 28.12/28.45 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.12/28.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.45 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.12/28.45 => 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)) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_setprod__Un__Int,axiom,
% 28.12/28.45 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 28.12/28.45 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.12/28.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.45 => 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)) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_setprod_Ounion__inter,axiom,
% 28.12/28.45 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 28.12/28.45 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.12/28.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.45 => 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)) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_setprod_Oreindex,axiom,
% 28.12/28.45 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
% 28.12/28.45 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.12/28.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.45 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
% 28.12/28.45 => 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) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_setprod_Oeq__fold,axiom,
% 28.12/28.45 ! [V_g_2,V_A_2,T_b,T_c] :
% 28.12/28.45 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.12/28.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.45 => 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) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_setprod_OF__eq,axiom,
% 28.12/28.45 ! [V_g_2,V_A_2,T_b,T_c] :
% 28.12/28.45 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.12/28.45 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.45 => 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) )
% 28.12/28.45 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.45 => 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) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__Suc1,axiom,
% 28.12/28.45 ! [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) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__Suc2,axiom,
% 28.12/28.45 ! [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) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_min__max_Ofold1__belowI,axiom,
% 28.12/28.45 ! [V_a_2,V_A_2,T_b] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_b)
% 28.12/28.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.12/28.45 => 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)) ) ) ) ).
% 28.12/28.45
% 28.12/28.45 fof(fact_fold1__below__iff,axiom,
% 28.12/28.45 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.45 ( class_Orderings_Olinorder(T_b)
% 28.12/28.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.45 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.45 => ( 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))
% 28.12/28.46 <=> ? [B_x] :
% 28.12/28.46 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.12/28.46 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_x_2)) ) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_min__max_Obelow__fold1__iff,axiom,
% 28.12/28.46 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => ( 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)))
% 28.12/28.46 <=> ! [B_x] :
% 28.12/28.46 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.12/28.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_fold1__strict__below__iff,axiom,
% 28.12/28.46 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => ( 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))
% 28.12/28.46 <=> ? [B_x] :
% 28.12/28.46 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.12/28.46 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_x_2)) ) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_strict__below__fold1__iff,axiom,
% 28.12/28.46 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => ( 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)))
% 28.12/28.46 <=> ! [B_x] :
% 28.12/28.46 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.12/28.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_Max__insert,axiom,
% 28.12/28.46 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => 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)) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_Min__insert,axiom,
% 28.12/28.46 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => 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)) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_Max_Osubset__idem,axiom,
% 28.12/28.46 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 28.12/28.46 => 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) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_Min_Osubset__idem,axiom,
% 28.12/28.46 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 28.12/28.46 => 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) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_Max__Un,axiom,
% 28.12/28.46 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.46 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => 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)) ) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_Min__Un,axiom,
% 28.12/28.46 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.46 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => 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)) ) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_setprod_Oinsert__remove,axiom,
% 28.12/28.46 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
% 28.12/28.46 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => 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)))))) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_setprod__Un__disjoint,axiom,
% 28.12/28.46 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 28.12/28.46 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.46 => ( 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))
% 28.12/28.46 => 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)) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_setprod_Ounion__disjoint,axiom,
% 28.12/28.46 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 28.12/28.46 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.46 => ( 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))
% 28.12/28.46 => 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)) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_Max_Oinsert,axiom,
% 28.12/28.46 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => 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)) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_Min_Oinsert,axiom,
% 28.12/28.46 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => 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)) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_fold1__antimono,axiom,
% 28.12/28.46 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.46 => 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))) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_Max_Oinsert__remove,axiom,
% 28.12/28.46 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( ( 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))
% 28.12/28.46 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 28.12/28.46 & ( 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))
% 28.12/28.46 => 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)))))) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_Max_Ounion__inter,axiom,
% 28.12/28.46 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.46 => ( 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))
% 28.12/28.46 => 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)) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_Max_Ounion__disjoint,axiom,
% 28.12/28.46 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.46 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => ( 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))
% 28.12/28.46 => 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)) ) ) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_Min_Oinsert__remove,axiom,
% 28.12/28.46 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( ( 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))
% 28.12/28.46 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 28.12/28.46 & ( 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))
% 28.12/28.46 => 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)))))) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_Min_Ounion__inter,axiom,
% 28.12/28.46 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.46 => ( 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))
% 28.12/28.46 => 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)) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_Min_Ounion__disjoint,axiom,
% 28.12/28.46 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.46 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => ( 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))
% 28.12/28.46 => 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)) ) ) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_dual__min,axiom,
% 28.12/28.46 ! [T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => 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) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_dual__max,axiom,
% 28.12/28.46 ! [T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => 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) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_max__ord__max,axiom,
% 28.12/28.46 ! [T_b] :
% 28.12/28.46 ( class_Orderings_Oord(T_b)
% 28.12/28.46 => c_Orderings_Oord__class_Omax(T_b) = c_Orderings_Oord_Omax(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_min__ord__min,axiom,
% 28.12/28.46 ! [T_b] :
% 28.12/28.46 ( class_Orderings_Oord(T_b)
% 28.12/28.46 => c_Orderings_Oord__class_Omin(T_b) = c_Orderings_Oord_Omin(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_min__max_Osup__Inf1__distrib,axiom,
% 28.12/28.46 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => 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))))) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_inf__nat__def,axiom,
% 28.12/28.46 c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_sup__nat__def,axiom,
% 28.12/28.46 c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_min__max_OInf__fin_Oin__idem,axiom,
% 28.12/28.46 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.46 => 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) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_min__max_OInf__fin_Osingleton,axiom,
% 28.12/28.46 ! [V_x_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => 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 ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_min__max_OInf__fin_OF__eq,axiom,
% 28.12/28.46 ! [V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => 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) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_min__max_OInf__fin_Oinsert__idem,axiom,
% 28.12/28.46 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => 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)) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_min__max_OInf__fin_Osubset__idem,axiom,
% 28.12/28.46 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 28.12/28.46 => 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) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_min__max_Osup__Inf__absorb,axiom,
% 28.12/28.46 ! [V_a_2,V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.12/28.46 => 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 ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_min__max_OInf__fin_Ounion__idem,axiom,
% 28.12/28.46 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.46 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => 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)) ) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_min__max_OInf__fin_Oinsert,axiom,
% 28.12/28.46 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => 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)) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_min__max_OInf__fin_Oinsert__remove,axiom,
% 28.12/28.46 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( ( 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))
% 28.12/28.46 => 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 )
% 28.12/28.46 & ( 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))
% 28.12/28.46 => 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)))))) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom,
% 28.12/28.46 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.46 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => ( 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))
% 28.12/28.46 => 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)) ) ) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_min__max_OInf__fin_Ounion__inter,axiom,
% 28.12/28.46 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.46 => ( 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))
% 28.12/28.46 => 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)) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_min__max_OInf__fin_Oremove,axiom,
% 28.12/28.46 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.46 => ( ( 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))
% 28.12/28.46 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = V_x_2 )
% 28.12/28.46 & ( 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))
% 28.12/28.46 => 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)))))) ) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_min__max_Osup__Inf2__distrib,axiom,
% 28.12/28.46 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.46 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => 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))))))) ) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom,
% 28.12/28.46 ! [V_f_2,V_A_2,T_b] :
% 28.12/28.46 ( ! [B_x] :
% 28.12/28.46 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.12/28.46 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 28.12/28.46 => 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)) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_min__max_Oinf__Sup2__distrib,axiom,
% 28.12/28.46 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.46 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => 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))))))) ) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_min__max_Oinf__Sup1__distrib,axiom,
% 28.12/28.46 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => 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))))) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_min__max_OInf__fin_Oclosed,axiom,
% 28.12/28.46 ! [V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => ( ! [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))))))
% 28.12/28.46 => 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)) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_min__max_OSup__fin_Oin__idem,axiom,
% 28.12/28.46 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.46 => 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) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_min__max_OSup__fin_Osingleton,axiom,
% 28.12/28.46 ! [V_x_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => 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 ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_min__max_OSup__fin_OF__eq,axiom,
% 28.12/28.46 ! [V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => 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) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_min__max_OSup__fin_Oinsert__idem,axiom,
% 28.12/28.46 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => 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)) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_min__max_OSup__fin_Osubset__idem,axiom,
% 28.12/28.46 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 28.12/28.46 => 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) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_min__max_Oinf__Sup__absorb,axiom,
% 28.12/28.46 ! [V_a_2,V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.12/28.46 => 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 ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_min__max_OSup__fin_Ounion__idem,axiom,
% 28.12/28.46 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.46 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => 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)) ) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_min__max_OSup__fin_Oinsert,axiom,
% 28.12/28.46 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => 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)) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_min__max_OSup__fin_Oinsert__remove,axiom,
% 28.12/28.46 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( ( 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))
% 28.12/28.46 => 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 )
% 28.12/28.46 & ( 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))
% 28.12/28.46 => 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)))))) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_min__max_OSup__fin_Ounion__inter,axiom,
% 28.12/28.46 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.46 => ( 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))
% 28.12/28.46 => 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)) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom,
% 28.12/28.46 ! [V_B_2,V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.46 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => ( 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))
% 28.12/28.46 => 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)) ) ) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_min__max_OSup__fin_Oremove,axiom,
% 28.12/28.46 ! [V_x_2,V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.12/28.46 => ( ( 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))
% 28.12/28.46 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = V_x_2 )
% 28.12/28.46 & ( 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))
% 28.12/28.46 => 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)))))) ) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_min__max_OInf__le__Sup,axiom,
% 28.12/28.46 ! [V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => 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))) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_min__max_OSup__fin_Oclosed,axiom,
% 28.12/28.46 ! [V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => ( ! [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))))))
% 28.12/28.46 => 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)) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_Max_Oclosed,axiom,
% 28.12/28.46 ! [V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => ( ! [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))))))
% 28.12/28.46 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_Min_Oclosed,axiom,
% 28.12/28.46 ! [V_A_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => ( ! [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))))))
% 28.12/28.46 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_setprod_Ounion__inter__neutral,axiom,
% 28.12/28.46 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 28.12/28.46 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.46 => ( ! [B_x] :
% 28.12/28.46 ( 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)))
% 28.12/28.46 => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 28.12/28.46 => 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)) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_setprod__Un__one,axiom,
% 28.12/28.46 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 28.12/28.46 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 28.12/28.46 => ( ! [B_x] :
% 28.12/28.46 ( 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)))
% 28.12/28.46 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 28.12/28.46 => 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)) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_setprod__gen__delta,axiom,
% 28.12/28.46 ! [V_c_2,V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 28.12/28.46 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 28.12/28.46 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 28.12/28.46 => 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)))) )
% 28.12/28.46 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 28.12/28.46 => 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)) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_setprod__diff1,axiom,
% 28.12/28.46 ! [V_a_2,V_f_2,V_A_2,T_b,T_c] :
% 28.12/28.46 ( class_Fields_Ofield(T_c)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_c)
% 28.12/28.46 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.12/28.46 => 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)) )
% 28.12/28.46 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.12/28.46 => 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) ) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_min__max_OSup__fin_Ohom__commute,axiom,
% 28.12/28.46 ! [V_N_2,V_h_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( ! [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))
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 28.12/28.46 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => 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)) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom,
% 28.12/28.46 ! [V_n,V_x] :
% 28.12/28.46 ( c_Nat__Transfer_Ois__nat(V_x)
% 28.12/28.46 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_of__int__power,axiom,
% 28.12/28.46 ! [V_n,V_z,T_a] :
% 28.12/28.46 ( class_Rings_Oring__1(T_a)
% 28.12/28.46 => 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) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 28.12/28.46 ! [V_x,T_a] :
% 28.12/28.46 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.12/28.46 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_zpower__zpower,axiom,
% 28.12/28.46 ! [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)) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_divide__zero,axiom,
% 28.12/28.46 ! [V_a,T_a] :
% 28.12/28.46 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 28.12/28.46 => 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) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_divide__zero__left,axiom,
% 28.12/28.46 ! [V_a,T_a] :
% 28.12/28.46 ( class_Rings_Odivision__ring(T_a)
% 28.12/28.46 => 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) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_add__divide__distrib,axiom,
% 28.12/28.46 ! [V_c,V_b,V_a,T_a] :
% 28.12/28.46 ( class_Rings_Odivision__ring(T_a)
% 28.12/28.46 => 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)) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_times__divide__eq__right,axiom,
% 28.12/28.46 ! [V_c,V_b,V_a,T_a] :
% 28.12/28.46 ( class_Rings_Odivision__ring(T_a)
% 28.12/28.46 => 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) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_diff__divide__distrib,axiom,
% 28.12/28.46 ! [V_c,V_b,V_a,T_a] :
% 28.12/28.46 ( class_Rings_Odivision__ring(T_a)
% 28.12/28.46 => 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)) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 28.12/28.46 ! [V_q,V_y,V_x,T_a] :
% 28.12/28.46 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.12/28.46 => 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)) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_divide__1,axiom,
% 28.12/28.46 ! [V_a,T_a] :
% 28.12/28.46 ( class_Rings_Odivision__ring(T_a)
% 28.12/28.46 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_minus__divide__left,axiom,
% 28.12/28.46 ! [V_b,V_a,T_a] :
% 28.12/28.46 ( class_Rings_Odivision__ring(T_a)
% 28.12/28.46 => 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) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_int__power,axiom,
% 28.12/28.46 ! [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) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_zpower__int,axiom,
% 28.12/28.46 ! [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)) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom,
% 28.12/28.46 ! [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)) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 28.12/28.46 ! [V_q,V_p,V_x,T_a] :
% 28.12/28.46 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.12/28.46 => 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)) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom,
% 28.12/28.46 ! [V_n,V_x] :
% 28.12/28.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 28.12/28.46 => 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)) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_nat__power__eq,axiom,
% 28.12/28.46 ! [V_n,V_z] :
% 28.12/28.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 28.12/28.46 => 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) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_setsum__divide__distrib,axiom,
% 28.12/28.46 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
% 28.12/28.46 ( class_Fields_Ofield(T_b)
% 28.12/28.46 => 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) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_nonzero__eq__divide__eq,axiom,
% 28.12/28.46 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 28.12/28.46 ( class_Rings_Odivision__ring(T_b)
% 28.12/28.46 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 28.12/28.46 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
% 28.12/28.46 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2 ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_nonzero__divide__eq__eq,axiom,
% 28.12/28.46 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 28.12/28.46 ( class_Rings_Odivision__ring(T_b)
% 28.12/28.46 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 28.12/28.46 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2
% 28.12/28.46 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_divide__eq__imp,axiom,
% 28.12/28.46 ! [V_a,V_b,V_c,T_a] :
% 28.12/28.46 ( class_Rings_Odivision__ring(T_a)
% 28.12/28.46 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 28.12/28.46 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)
% 28.12/28.46 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_eq__divide__imp,axiom,
% 28.12/28.46 ! [V_b,V_a,V_c,T_a] :
% 28.12/28.46 ( class_Rings_Odivision__ring(T_a)
% 28.12/28.46 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 28.12/28.46 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b
% 28.12/28.46 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_divide__self__if,axiom,
% 28.12/28.46 ! [V_a,T_a] :
% 28.12/28.46 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 28.12/28.46 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 28.12/28.46 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) )
% 28.12/28.46 & ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 28.12/28.46 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_divide__self,axiom,
% 28.12/28.46 ! [V_a,T_a] :
% 28.12/28.46 ( class_Rings_Odivision__ring(T_a)
% 28.12/28.46 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 28.12/28.46 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_right__inverse__eq,axiom,
% 28.12/28.46 ! [V_a_2,V_b_2,T_b] :
% 28.12/28.46 ( class_Rings_Odivision__ring(T_b)
% 28.12/28.46 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_b)
% 28.12/28.46 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_b)
% 28.12/28.46 <=> V_a_2 = V_b_2 ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_nonzero__minus__divide__right,axiom,
% 28.12/28.46 ! [V_a,V_b,T_a] :
% 28.12/28.46 ( class_Rings_Odivision__ring(T_a)
% 28.12/28.46 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 28.12/28.46 => 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)) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_nonzero__minus__divide__divide,axiom,
% 28.12/28.46 ! [V_a,V_b,T_a] :
% 28.12/28.46 ( class_Rings_Odivision__ring(T_a)
% 28.12/28.46 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 28.12/28.46 => 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) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
% 28.12/28.46 ! [V_q,V_x,T_a] :
% 28.12/28.46 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.12/28.46 => 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)) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
% 28.12/28.46 ! [V_q,V_x,T_a] :
% 28.12/28.46 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.12/28.46 => 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)) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
% 28.12/28.46 ! [V_q,V_x,T_a] :
% 28.12/28.46 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.12/28.46 => 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)) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 28.12/28.46 ! [V_x,T_a] :
% 28.12/28.46 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.12/28.46 => 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) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 28.12/28.46 ! [V_q,V_p,V_x,T_a] :
% 28.12/28.46 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.12/28.46 => 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)) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
% 28.12/28.46 ! [V_n,V_x] :
% 28.12/28.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 28.12/28.46 => 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))) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_zpower__zadd__distrib,axiom,
% 28.12/28.46 ! [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)) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_Ints__power,axiom,
% 28.12/28.46 ! [V_n_2,V_a_2,T_b] :
% 28.12/28.46 ( class_Rings_Oring__1(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 28.12/28.46 => 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))) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_setprod__dividef,axiom,
% 28.12/28.46 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
% 28.12/28.46 ( class_Fields_Ofield__inverse__zero(T_c)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => 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)) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_geometric__sum,axiom,
% 28.12/28.46 ! [V_n_2,V_x_2,T_b] :
% 28.12/28.46 ( class_Fields_Ofield(T_b)
% 28.12/28.46 => ( V_x_2 != c_Groups_Oone__class_Oone(T_b)
% 28.12/28.46 => 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))) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_zero__le__zpower__abs,axiom,
% 28.12/28.46 ! [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))) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_setprod__constant,axiom,
% 28.12/28.46 ! [V_y_2,V_A_2,T_b,T_c] :
% 28.12/28.46 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => 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)) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_power__eq__if,axiom,
% 28.12/28.46 ! [V_p,V_m] :
% 28.12/28.46 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.12/28.46 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 28.12/28.46 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.12/28.46 => 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)))) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_zero__less__zpower__abs__iff,axiom,
% 28.12/28.46 ! [V_n_2,V_x_2] :
% 28.12/28.46 ( 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)))
% 28.12/28.46 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.12/28.46 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_card__Pow,axiom,
% 28.12/28.46 ! [V_A_2,T_b] :
% 28.12/28.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => 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)) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_power__strict__mono,axiom,
% 28.12/28.46 ! [V_n,V_b,V_a,T_a] :
% 28.12/28.46 ( class_Rings_Olinordered__semidom(T_a)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 28.12/28.46 => 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))) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_power__diff,axiom,
% 28.12/28.46 ! [V_m,V_n,V_a,T_a] :
% 28.12/28.46 ( class_Fields_Ofield(T_a)
% 28.12/28.46 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 28.12/28.46 => 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)) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_one__less__power,axiom,
% 28.12/28.46 ! [V_n,V_a,T_a] :
% 28.12/28.46 ( class_Rings_Olinordered__semidom(T_a)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 28.12/28.46 => 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))) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_power__increasing__iff,axiom,
% 28.12/28.46 ! [V_y_2,V_x_2,V_b_2,T_b] :
% 28.12/28.46 ( class_Rings_Olinordered__semidom(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
% 28.12/28.46 => ( 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)))
% 28.12/28.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_field__power__not__zero,axiom,
% 28.12/28.46 ! [V_n,V_a,T_a] :
% 28.12/28.46 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 28.12/28.46 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 28.12/28.46 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_power__Suc__0,axiom,
% 28.12/28.46 ! [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)) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_nat__power__eq__Suc__0__iff,axiom,
% 28.12/28.46 ! [V_m_2,V_x_2] :
% 28.12/28.46 ( 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))
% 28.12/28.46 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.12/28.46 | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_nat__power__less__imp__less,axiom,
% 28.12/28.46 ! [V_n,V_m,V_i] :
% 28.12/28.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i))
% 28.12/28.46 => ( 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)))
% 28.12/28.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_nat__zero__less__power__iff,axiom,
% 28.12/28.46 ! [V_n_2,V_x_2] :
% 28.12/28.46 ( 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)))
% 28.12/28.46 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2))
% 28.12/28.46 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_power__mult__distrib,axiom,
% 28.12/28.46 ! [V_n,V_b,V_a,T_a] :
% 28.12/28.46 ( class_Groups_Ocomm__monoid__mult(T_a)
% 28.12/28.46 => 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)) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_power__commutes,axiom,
% 28.12/28.46 ! [V_n,V_a,T_a] :
% 28.12/28.46 ( class_Groups_Omonoid__mult(T_a)
% 28.12/28.46 => 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)) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_power__one,axiom,
% 28.12/28.46 ! [V_n,T_a] :
% 28.12/28.46 ( class_Groups_Omonoid__mult(T_a)
% 28.12/28.46 => 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) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_of__nat__power,axiom,
% 28.12/28.46 ! [V_n,V_m,T_a] :
% 28.12/28.46 ( class_Rings_Osemiring__1(T_a)
% 28.12/28.46 => 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) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_power__mult,axiom,
% 28.12/28.46 ! [V_n,V_m,V_a,T_a] :
% 28.12/28.46 ( class_Groups_Omonoid__mult(T_a)
% 28.12/28.46 => 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) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_power__divide,axiom,
% 28.12/28.46 ! [V_n,V_b,V_a,T_a] :
% 28.12/28.46 ( class_Fields_Ofield__inverse__zero(T_a)
% 28.12/28.46 => 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)) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_power__abs,axiom,
% 28.12/28.46 ! [V_n,V_a,T_a] :
% 28.12/28.46 ( class_Rings_Olinordered__idom(T_a)
% 28.12/28.46 => 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) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_power__one__right,axiom,
% 28.12/28.46 ! [V_a,T_a] :
% 28.12/28.46 ( class_Groups_Omonoid__mult(T_a)
% 28.12/28.46 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_zero__le__power,axiom,
% 28.12/28.46 ! [V_n,V_a,T_a] :
% 28.12/28.46 ( class_Rings_Olinordered__semidom(T_a)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.12/28.46 => 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))) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_power__mono,axiom,
% 28.12/28.46 ! [V_n,V_b,V_a,T_a] :
% 28.12/28.46 ( class_Rings_Olinordered__semidom(T_a)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.12/28.46 => 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))) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_zero__less__power,axiom,
% 28.12/28.46 ! [V_n,V_a,T_a] :
% 28.12/28.46 ( class_Rings_Olinordered__semidom(T_a)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.12/28.46 => 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))) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_power__eq__0__iff,axiom,
% 28.12/28.46 ! [V_n_2,V_a_2,T_b] :
% 28.12/28.46 ( ( class_Power_Opower(T_b)
% 28.12/28.46 & class_Rings_Omult__zero(T_b)
% 28.12/28.46 & class_Rings_Ono__zero__divisors(T_b)
% 28.12/28.46 & class_Rings_Ozero__neq__one(T_b) )
% 28.12/28.46 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_b)
% 28.12/28.46 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
% 28.12/28.46 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_one__le__power,axiom,
% 28.12/28.46 ! [V_n,V_a,T_a] :
% 28.12/28.46 ( class_Rings_Olinordered__semidom(T_a)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 28.12/28.46 => 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))) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_power__0__Suc,axiom,
% 28.12/28.46 ! [V_n,T_a] :
% 28.12/28.46 ( ( class_Power_Opower(T_a)
% 28.12/28.46 & class_Rings_Osemiring__0(T_a) )
% 28.12/28.46 => 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) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_power__inject__exp,axiom,
% 28.12/28.46 ! [V_n_2,V_m_2,V_a_2,T_b] :
% 28.12/28.46 ( class_Rings_Olinordered__semidom(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2))
% 28.12/28.46 => ( 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)
% 28.12/28.46 <=> V_m_2 = V_n_2 ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_power__Suc,axiom,
% 28.12/28.46 ! [V_n,V_a,T_a] :
% 28.12/28.46 ( class_Power_Opower(T_a)
% 28.12/28.46 => 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)) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_power__Suc2,axiom,
% 28.12/28.46 ! [V_n,V_a,T_a] :
% 28.12/28.46 ( class_Groups_Omonoid__mult(T_a)
% 28.12/28.46 => 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) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_nat__one__le__power,axiom,
% 28.12/28.46 ! [V_n,V_i] :
% 28.12/28.46 ( 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))
% 28.12/28.46 => 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))) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_power__0,axiom,
% 28.12/28.46 ! [V_a,T_a] :
% 28.12/28.46 ( class_Power_Opower(T_a)
% 28.12/28.46 => 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) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_power__add,axiom,
% 28.12/28.46 ! [V_n,V_m,V_a,T_a] :
% 28.12/28.46 ( class_Groups_Omonoid__mult(T_a)
% 28.12/28.46 => 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)) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_nonzero__power__divide,axiom,
% 28.12/28.46 ! [V_n,V_a,V_b,T_a] :
% 28.12/28.46 ( class_Fields_Ofield(T_a)
% 28.12/28.46 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 28.12/28.46 => 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)) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_power__one__over,axiom,
% 28.12/28.46 ! [V_n,V_a,T_a] :
% 28.12/28.46 ( class_Fields_Ofield__inverse__zero(T_a)
% 28.12/28.46 => 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) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_abs__power__minus,axiom,
% 28.12/28.46 ! [V_n,V_a,T_a] :
% 28.12/28.46 ( class_Rings_Olinordered__idom(T_a)
% 28.12/28.46 => 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)) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_power__less__imp__less__base,axiom,
% 28.12/28.46 ! [V_b,V_n,V_a,T_a] :
% 28.12/28.46 ( class_Rings_Olinordered__semidom(T_a)
% 28.12/28.46 => ( 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)))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 28.12/28.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_power__inject__base,axiom,
% 28.12/28.46 ! [V_b,V_n,V_a,T_a] :
% 28.12/28.46 ( class_Rings_Olinordered__semidom(T_a)
% 28.12/28.46 => ( 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))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 28.12/28.46 => V_a = V_b ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_power__le__imp__le__base,axiom,
% 28.12/28.46 ! [V_b,V_n,V_a,T_a] :
% 28.12/28.46 ( class_Rings_Olinordered__semidom(T_a)
% 28.12/28.46 => ( 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))))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 28.12/28.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_power__less__power__Suc,axiom,
% 28.12/28.46 ! [V_n,V_a,T_a] :
% 28.12/28.46 ( class_Rings_Olinordered__semidom(T_a)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 28.12/28.46 => 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)))) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_power__gt1__lemma,axiom,
% 28.12/28.46 ! [V_n,V_a,T_a] :
% 28.12/28.46 ( class_Rings_Olinordered__semidom(T_a)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 28.12/28.46 => 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)))) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_power__0__left,axiom,
% 28.12/28.46 ! [V_n,T_a] :
% 28.12/28.46 ( ( class_Power_Opower(T_a)
% 28.12/28.46 & class_Rings_Osemiring__0(T_a) )
% 28.12/28.46 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.12/28.46 => 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) )
% 28.12/28.46 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.12/28.46 => 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) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_power__gt1,axiom,
% 28.12/28.46 ! [V_n,V_a,T_a] :
% 28.12/28.46 ( class_Rings_Olinordered__semidom(T_a)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 28.12/28.46 => 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)))) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_power__strict__increasing__iff,axiom,
% 28.12/28.46 ! [V_y_2,V_x_2,V_b_2,T_b] :
% 28.12/28.46 ( class_Rings_Olinordered__semidom(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
% 28.12/28.46 => ( 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)))
% 28.12/28.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_power__less__imp__less__exp,axiom,
% 28.12/28.46 ! [V_n,V_m,V_a,T_a] :
% 28.12/28.46 ( class_Rings_Olinordered__semidom(T_a)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 28.12/28.46 => ( 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)))
% 28.12/28.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_power__strict__increasing,axiom,
% 28.12/28.46 ! [V_a,V_N,V_n,T_a] :
% 28.12/28.46 ( class_Rings_Olinordered__semidom(T_a)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 28.12/28.46 => 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))) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_zero__le__power__abs,axiom,
% 28.12/28.46 ! [V_n,V_a,T_a] :
% 28.12/28.46 ( class_Rings_Olinordered__idom(T_a)
% 28.12/28.46 => 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))) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_power__increasing,axiom,
% 28.12/28.46 ! [V_a,V_N,V_n,T_a] :
% 28.12/28.46 ( class_Rings_Olinordered__semidom(T_a)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 28.12/28.46 => 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))) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_power__minus,axiom,
% 28.12/28.46 ! [V_n,V_a,T_a] :
% 28.12/28.46 ( class_Rings_Oring__1(T_a)
% 28.12/28.46 => 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)) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_power__Suc__less,axiom,
% 28.12/28.46 ! [V_n,V_a,T_a] :
% 28.12/28.46 ( class_Rings_Olinordered__semidom(T_a)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 28.12/28.46 => 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))) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_power__eq__imp__eq__base,axiom,
% 28.12/28.46 ! [V_b,V_n,V_a,T_a] :
% 28.12/28.46 ( class_Rings_Olinordered__semidom(T_a)
% 28.12/28.46 => ( 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)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 28.12/28.46 => V_a = V_b ) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_power__Suc__less__one,axiom,
% 28.12/28.46 ! [V_n,V_a,T_a] :
% 28.12/28.46 ( class_Rings_Olinordered__semidom(T_a)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 28.12/28.46 => 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))) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_power__strict__decreasing,axiom,
% 28.12/28.46 ! [V_a,V_N,V_n,T_a] :
% 28.12/28.46 ( class_Rings_Olinordered__semidom(T_a)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 28.12/28.46 => 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))) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_power__decreasing,axiom,
% 28.12/28.46 ! [V_a,V_N,V_n,T_a] :
% 28.12/28.46 ( class_Rings_Olinordered__semidom(T_a)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 28.12/28.46 => 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))) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_power__le__imp__le__exp,axiom,
% 28.12/28.46 ! [V_n,V_m,V_a,T_a] :
% 28.12/28.46 ( class_Rings_Olinordered__semidom(T_a)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 28.12/28.46 => ( 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)))
% 28.12/28.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_le__divide__eq,axiom,
% 28.12/28.46 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 28.12/28.46 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 28.12/28.46 => ( 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)))
% 28.12/28.46 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.12/28.46 => 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)) )
% 28.12/28.46 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.12/28.46 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.12/28.46 => 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))) )
% 28.12/28.46 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.12/28.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_divide__le__eq,axiom,
% 28.12/28.46 ! [V_a_2,V_c_2,V_b_2,T_b] :
% 28.12/28.46 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 28.12/28.46 => ( 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))
% 28.12/28.46 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.12/28.46 => 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))) )
% 28.12/28.46 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.12/28.46 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.12/28.46 => 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)) )
% 28.12/28.46 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.12/28.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_pos__le__divide__eq,axiom,
% 28.12/28.46 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 28.12/28.46 ( class_Fields_Olinordered__field(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.12/28.46 => ( 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)))
% 28.12/28.46 <=> 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)) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_pos__divide__le__eq,axiom,
% 28.12/28.46 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 28.12/28.46 ( class_Fields_Olinordered__field(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.12/28.46 => ( 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))
% 28.12/28.46 <=> 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))) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_times__divide__times__eq,axiom,
% 28.12/28.46 ! [V_w,V_z,V_y,V_x,T_a] :
% 28.12/28.46 ( class_Fields_Ofield__inverse__zero(T_a)
% 28.12/28.46 => 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)) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_minus__divide__divide,axiom,
% 28.12/28.46 ! [V_b,V_a,T_a] :
% 28.12/28.46 ( class_Fields_Ofield__inverse__zero(T_a)
% 28.12/28.46 => 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) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_minus__divide__right,axiom,
% 28.12/28.46 ! [V_b,V_a,T_a] :
% 28.12/28.46 ( class_Fields_Ofield__inverse__zero(T_a)
% 28.12/28.46 => 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)) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_abs__divide,axiom,
% 28.12/28.46 ! [V_b,V_a,T_a] :
% 28.12/28.46 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 28.12/28.46 => 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)) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_divide__right__mono__neg,axiom,
% 28.12/28.46 ! [V_c,V_b,V_a,T_a] :
% 28.12/28.46 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 28.12/28.46 => 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))) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_divide__right__mono,axiom,
% 28.12/28.46 ! [V_c,V_b,V_a,T_a] :
% 28.12/28.46 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 28.12/28.46 => 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))) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_divide__le__0__iff,axiom,
% 28.12/28.46 ! [V_b_2,V_a_2,T_b] :
% 28.12/28.46 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 28.12/28.46 => ( 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)))
% 28.12/28.46 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 28.12/28.46 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 28.12/28.46 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.12/28.46 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_zero__le__divide__iff,axiom,
% 28.12/28.46 ! [V_b_2,V_a_2,T_b] :
% 28.12/28.46 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 28.12/28.46 => ( 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)))
% 28.12/28.46 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 28.12/28.46 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 28.12/28.46 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.12/28.46 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_divide__strict__right__mono__neg,axiom,
% 28.12/28.46 ! [V_c,V_a,V_b,T_a] :
% 28.12/28.46 ( class_Fields_Olinordered__field(T_a)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 28.12/28.46 => 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))) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_divide__strict__right__mono,axiom,
% 28.12/28.46 ! [V_c,V_b,V_a,T_a] :
% 28.12/28.46 ( class_Fields_Olinordered__field(T_a)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 28.12/28.46 => 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))) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_divide__neg__neg,axiom,
% 28.12/28.46 ! [V_y,V_x,T_a] :
% 28.12/28.46 ( class_Fields_Olinordered__field(T_a)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 28.12/28.46 => 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))) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_divide__neg__pos,axiom,
% 28.12/28.46 ! [V_y,V_x,T_a] :
% 28.12/28.46 ( class_Fields_Olinordered__field(T_a)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 28.12/28.46 => 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))) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_divide__pos__neg,axiom,
% 28.12/28.46 ! [V_y,V_x,T_a] :
% 28.12/28.46 ( class_Fields_Olinordered__field(T_a)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 28.12/28.46 => 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))) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_divide__pos__pos,axiom,
% 28.12/28.46 ! [V_y,V_x,T_a] :
% 28.12/28.46 ( class_Fields_Olinordered__field(T_a)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 28.12/28.46 => 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))) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_divide__less__0__iff,axiom,
% 28.12/28.46 ! [V_b_2,V_a_2,T_b] :
% 28.12/28.46 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 28.12/28.46 => ( 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)))
% 28.12/28.46 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 28.12/28.46 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 28.12/28.46 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.12/28.46 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_zero__less__divide__iff,axiom,
% 28.12/28.46 ! [V_b_2,V_a_2,T_b] :
% 28.12/28.46 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 28.12/28.46 => ( 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)))
% 28.12/28.46 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 28.12/28.46 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 28.12/28.46 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.12/28.46 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_eq__divide__eq,axiom,
% 28.12/28.46 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 28.12/28.46 ( class_Fields_Ofield__inverse__zero(T_b)
% 28.12/28.46 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
% 28.12/28.46 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 28.12/28.46 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2 )
% 28.12/28.46 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 28.12/28.46 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_divide__eq__eq,axiom,
% 28.12/28.46 ! [V_a_2,V_c_2,V_b_2,T_b] :
% 28.12/28.46 ( class_Fields_Ofield__inverse__zero(T_b)
% 28.12/28.46 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2
% 28.12/28.46 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 28.12/28.46 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) )
% 28.12/28.46 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 28.12/28.46 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_mult__divide__mult__cancel__right,axiom,
% 28.12/28.46 ! [V_b,V_a,V_c,T_a] :
% 28.12/28.46 ( class_Fields_Ofield__inverse__zero(T_a)
% 28.12/28.46 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 28.12/28.46 => 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) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_mult__divide__mult__cancel__left,axiom,
% 28.12/28.46 ! [V_b,V_a,V_c,T_a] :
% 28.12/28.46 ( class_Fields_Ofield__inverse__zero(T_a)
% 28.12/28.46 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 28.12/28.46 => 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) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_frac__eq__eq,axiom,
% 28.12/28.46 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_b] :
% 28.12/28.46 ( class_Fields_Ofield(T_b)
% 28.12/28.46 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
% 28.12/28.46 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_b)
% 28.12/28.46 => ( 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)
% 28.12/28.46 <=> 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) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_nonzero__abs__divide,axiom,
% 28.12/28.46 ! [V_a,V_b,T_a] :
% 28.12/28.46 ( class_Fields_Olinordered__field(T_a)
% 28.12/28.46 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 28.12/28.46 => 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)) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_divide__nonneg__pos,axiom,
% 28.12/28.46 ! [V_y,V_x,T_a] :
% 28.12/28.46 ( class_Fields_Olinordered__field(T_a)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 28.12/28.46 => 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))) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_divide__nonneg__neg,axiom,
% 28.12/28.46 ! [V_y,V_x,T_a] :
% 28.12/28.46 ( class_Fields_Olinordered__field(T_a)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 28.12/28.46 => 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))) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_frac__less2,axiom,
% 28.12/28.46 ! [V_z,V_w,V_y,V_x,T_a] :
% 28.12/28.46 ( class_Fields_Olinordered__field(T_a)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z))
% 28.12/28.46 => 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))) ) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_frac__less,axiom,
% 28.12/28.46 ! [V_z,V_w,V_y,V_x,T_a] :
% 28.12/28.46 ( class_Fields_Olinordered__field(T_a)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 28.12/28.46 => 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))) ) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_frac__le,axiom,
% 28.12/28.46 ! [V_z,V_w,V_y,V_x,T_a] :
% 28.12/28.46 ( class_Fields_Olinordered__field(T_a)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 28.12/28.46 => 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))) ) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_divide__nonpos__pos,axiom,
% 28.12/28.46 ! [V_y,V_x,T_a] :
% 28.12/28.46 ( class_Fields_Olinordered__field(T_a)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 28.12/28.46 => 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))) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_divide__nonpos__neg,axiom,
% 28.12/28.46 ! [V_y,V_x,T_a] :
% 28.12/28.46 ( class_Fields_Olinordered__field(T_a)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 28.12/28.46 => 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))) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_divide__strict__left__mono__neg,axiom,
% 28.12/28.46 ! [V_c,V_b,V_a,T_a] :
% 28.12/28.46 ( class_Fields_Olinordered__field(T_a)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 28.12/28.46 => ( 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)))
% 28.12/28.46 => 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))) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_divide__strict__left__mono,axiom,
% 28.12/28.46 ! [V_c,V_a,V_b,T_a] :
% 28.12/28.46 ( class_Fields_Olinordered__field(T_a)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 28.12/28.46 => ( 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)))
% 28.12/28.46 => 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))) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_neg__divide__less__eq,axiom,
% 28.12/28.46 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 28.12/28.46 ( class_Fields_Olinordered__field(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.12/28.46 => ( 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))
% 28.12/28.46 <=> 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)) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_neg__less__divide__eq,axiom,
% 28.12/28.46 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 28.12/28.46 ( class_Fields_Olinordered__field(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.12/28.46 => ( 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)))
% 28.12/28.46 <=> 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))) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_mult__imp__less__div__pos,axiom,
% 28.12/28.46 ! [V_x,V_z,V_y,T_a] :
% 28.12/28.46 ( class_Fields_Olinordered__field(T_a)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 28.12/28.46 => ( 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))
% 28.12/28.46 => 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))) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_mult__imp__div__pos__less,axiom,
% 28.12/28.46 ! [V_z,V_x,V_y,T_a] :
% 28.12/28.46 ( class_Fields_Olinordered__field(T_a)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 28.12/28.46 => ( 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)))
% 28.12/28.46 => 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)) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_pos__divide__less__eq,axiom,
% 28.12/28.46 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 28.12/28.46 ( class_Fields_Olinordered__field(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.12/28.46 => ( 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))
% 28.12/28.46 <=> 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))) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_pos__less__divide__eq,axiom,
% 28.12/28.46 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 28.12/28.46 ( class_Fields_Olinordered__field(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.12/28.46 => ( 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)))
% 28.12/28.46 <=> 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)) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_divide__less__eq,axiom,
% 28.12/28.46 ! [V_a_2,V_c_2,V_b_2,T_b] :
% 28.12/28.46 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 28.12/28.46 => ( 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))
% 28.12/28.46 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.12/28.46 => 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))) )
% 28.12/28.46 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.12/28.46 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.12/28.46 => 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)) )
% 28.12/28.46 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.12/28.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_less__divide__eq,axiom,
% 28.12/28.46 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 28.12/28.46 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 28.12/28.46 => ( 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)))
% 28.12/28.46 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.12/28.46 => 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)) )
% 28.12/28.46 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.12/28.46 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.12/28.46 => 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))) )
% 28.12/28.46 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.12/28.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_add__num__frac,axiom,
% 28.12/28.46 ! [V_x,V_z,V_y,T_a] :
% 28.12/28.46 ( class_Fields_Ofield__inverse__zero(T_a)
% 28.12/28.46 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 28.12/28.46 => 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) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_add__divide__eq__iff,axiom,
% 28.12/28.46 ! [V_y,V_x,V_z,T_a] :
% 28.12/28.46 ( class_Fields_Ofield(T_a)
% 28.12/28.46 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 28.12/28.46 => 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) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_add__frac__num,axiom,
% 28.12/28.46 ! [V_z,V_x,V_y,T_a] :
% 28.12/28.46 ( class_Fields_Ofield__inverse__zero(T_a)
% 28.12/28.46 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 28.12/28.46 => 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) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_divide__add__eq__iff,axiom,
% 28.12/28.46 ! [V_y,V_x,V_z,T_a] :
% 28.12/28.46 ( class_Fields_Ofield(T_a)
% 28.12/28.46 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 28.12/28.46 => 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) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_add__frac__eq,axiom,
% 28.12/28.46 ! [V_w,V_x,V_z,V_y,T_a] :
% 28.12/28.46 ( class_Fields_Ofield(T_a)
% 28.12/28.46 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 28.12/28.46 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 28.12/28.46 => 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)) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_diff__divide__eq__iff,axiom,
% 28.12/28.46 ! [V_y,V_x,V_z,T_a] :
% 28.12/28.46 ( class_Fields_Ofield(T_a)
% 28.12/28.46 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 28.12/28.46 => 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) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_divide__diff__eq__iff,axiom,
% 28.12/28.46 ! [V_y,V_x,V_z,T_a] :
% 28.12/28.46 ( class_Fields_Ofield(T_a)
% 28.12/28.46 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 28.12/28.46 => 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) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_diff__frac__eq,axiom,
% 28.12/28.46 ! [V_w,V_x,V_z,V_y,T_a] :
% 28.12/28.46 ( class_Fields_Ofield(T_a)
% 28.12/28.46 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 28.12/28.46 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 28.12/28.46 => 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)) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_less__half__sum,axiom,
% 28.12/28.46 ! [V_b,V_a,T_a] :
% 28.12/28.46 ( class_Fields_Olinordered__field(T_a)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 28.12/28.46 => 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))))) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_gt__half__sum,axiom,
% 28.12/28.46 ! [V_b,V_a,T_a] :
% 28.12/28.46 ( class_Fields_Olinordered__field(T_a)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 28.12/28.46 => 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)) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_abs__div__pos,axiom,
% 28.12/28.46 ! [V_x,V_y,T_a] :
% 28.12/28.46 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 28.12/28.46 => 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)) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_divide__left__mono__neg,axiom,
% 28.12/28.46 ! [V_c,V_b,V_a,T_a] :
% 28.12/28.46 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 28.12/28.46 => ( 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)))
% 28.12/28.46 => 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))) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_divide__left__mono,axiom,
% 28.12/28.46 ! [V_c,V_a,V_b,T_a] :
% 28.12/28.46 ( class_Fields_Olinordered__field(T_a)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 28.12/28.46 => ( 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)))
% 28.12/28.46 => 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))) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_neg__divide__le__eq,axiom,
% 28.12/28.46 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 28.12/28.46 ( class_Fields_Olinordered__field(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.12/28.46 => ( 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))
% 28.12/28.46 <=> 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)) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_neg__le__divide__eq,axiom,
% 28.12/28.46 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 28.12/28.46 ( class_Fields_Olinordered__field(T_b)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.12/28.46 => ( 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)))
% 28.12/28.46 <=> 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))) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_mult__imp__le__div__pos,axiom,
% 28.12/28.46 ! [V_x,V_z,V_y,T_a] :
% 28.12/28.46 ( class_Fields_Olinordered__field(T_a)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 28.12/28.46 => ( 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))
% 28.12/28.46 => 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))) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_mult__imp__div__pos__le,axiom,
% 28.12/28.46 ! [V_z,V_x,V_y,T_a] :
% 28.12/28.46 ( class_Fields_Olinordered__field(T_a)
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 28.12/28.46 => ( 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)))
% 28.12/28.46 => 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)) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_setprod__Un,axiom,
% 28.12/28.46 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 28.12/28.46 ( class_Fields_Ofield(T_c)
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.12/28.46 => ( ! [B_x] :
% 28.12/28.46 ( 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)))
% 28.12/28.46 => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c) )
% 28.12/28.46 => 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))) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_power__power__power,axiom,
% 28.12/28.46 ! [T_b] :
% 28.12/28.46 ( class_Power_Opower(T_b)
% 28.12/28.46 => 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)) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_int__power__div__base,axiom,
% 28.12/28.46 ! [V_k,V_m] :
% 28.12/28.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 28.12/28.46 => 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)))) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_min__max_OInf__fin_Ohom__commute,axiom,
% 28.12/28.46 ! [V_N_2,V_h_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( ! [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))
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 28.12/28.46 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => 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)) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_zdiv__zero,axiom,
% 28.12/28.46 ! [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) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_zdiv__zminus2,axiom,
% 28.12/28.46 ! [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) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_zdiv__zminus__zminus,axiom,
% 28.12/28.46 ! [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) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_div__0,axiom,
% 28.12/28.46 ! [V_a,T_a] :
% 28.12/28.46 ( class_Divides_Osemiring__div(T_a)
% 28.12/28.46 => 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) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_div__by__0,axiom,
% 28.12/28.46 ! [V_a,T_a] :
% 28.12/28.46 ( class_Divides_Osemiring__div(T_a)
% 28.12/28.46 => 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) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom,
% 28.12/28.46 ! [V_y,V_x] :
% 28.12/28.46 ( c_Nat__Transfer_Ois__nat(V_x)
% 28.12/28.46 => ( c_Nat__Transfer_Ois__nat(V_y)
% 28.12/28.46 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_div__by__1,axiom,
% 28.12/28.46 ! [V_a,T_a] :
% 28.12/28.46 ( class_Divides_Osemiring__div(T_a)
% 28.12/28.46 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
% 28.12/28.46 ! [V_y,V_x] :
% 28.12/28.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 28.12/28.46 => 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))) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_div__neg__pos__less0,axiom,
% 28.12/28.46 ! [V_b,V_a] :
% 28.12/28.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 28.12/28.46 => 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))) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_neg__imp__zdiv__neg__iff,axiom,
% 28.12/28.46 ! [V_a_2,V_b_2] :
% 28.12/28.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.12/28.46 => ( 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)))
% 28.12/28.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_pos__imp__zdiv__neg__iff,axiom,
% 28.12/28.46 ! [V_a_2,V_b_2] :
% 28.12/28.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 28.12/28.46 => ( 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)))
% 28.12/28.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_zdiv__self,axiom,
% 28.12/28.46 ! [V_a] :
% 28.12/28.46 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.12/28.46 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_div__mult__mult1__if,axiom,
% 28.12/28.46 ! [V_b,V_a,V_c,T_a] :
% 28.12/28.46 ( class_Divides_Osemiring__div(T_a)
% 28.12/28.46 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a)
% 28.12/28.46 => 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) )
% 28.12/28.46 & ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 28.12/28.46 => 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) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_div__mult__self2__is__id,axiom,
% 28.12/28.46 ! [V_a,V_b,T_a] :
% 28.12/28.46 ( class_Divides_Osemiring__div(T_a)
% 28.12/28.46 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 28.12/28.46 => 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 ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_div__mult__self1__is__id,axiom,
% 28.12/28.46 ! [V_a,V_b,T_a] :
% 28.12/28.46 ( class_Divides_Osemiring__div(T_a)
% 28.12/28.46 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 28.12/28.46 => 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 ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_div__mult__mult2,axiom,
% 28.12/28.46 ! [V_b,V_a,V_c,T_a] :
% 28.12/28.46 ( class_Divides_Osemiring__div(T_a)
% 28.12/28.46 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 28.12/28.46 => 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) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_div__mult__mult1,axiom,
% 28.12/28.46 ! [V_b,V_a,V_c,T_a] :
% 28.12/28.46 ( class_Divides_Osemiring__div(T_a)
% 28.12/28.46 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 28.12/28.46 => 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) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_div__self,axiom,
% 28.12/28.46 ! [V_a,T_a] :
% 28.12/28.46 ( class_Divides_Osemiring__div(T_a)
% 28.12/28.46 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 28.12/28.46 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_zdiv__eq__0__iff,axiom,
% 28.12/28.46 ! [V_k_2,V_i_2] :
% 28.12/28.46 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.12/28.46 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.12/28.46 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2))
% 28.12/28.46 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) )
% 28.12/28.46 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.12/28.46 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
% 28.12/28.46 ! [V_a_2,V_b_2] :
% 28.12/28.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 28.12/28.46 => ( 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)))
% 28.12/28.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_pos__imp__zdiv__pos__iff,axiom,
% 28.12/28.46 ! [V_i_2,V_k_2] :
% 28.12/28.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 28.12/28.46 => ( 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)))
% 28.12/28.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
% 28.12/28.46 ! [V_b_2,V_a_2] :
% 28.12/28.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))
% 28.12/28.46 => ( 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)))
% 28.12/28.46 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2))
% 28.12/28.46 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_zdiv__mono2,axiom,
% 28.12/28.46 ! [V_b,V_b_H,V_a] :
% 28.12/28.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 28.12/28.46 => 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))) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_div__nonneg__neg__le0,axiom,
% 28.12/28.46 ! [V_b,V_a] :
% 28.12/28.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.12/28.46 => 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))) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_div__pos__pos__trivial,axiom,
% 28.12/28.46 ! [V_b,V_a] :
% 28.12/28.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 28.12/28.46 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
% 28.12/28.46 ! [V_a_2,V_b_2] :
% 28.12/28.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.12/28.46 => ( 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)))
% 28.12/28.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_div__nonpos__pos__le0,axiom,
% 28.12/28.46 ! [V_b,V_a] :
% 28.12/28.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 28.12/28.46 => 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))) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_zdiv__mono2__neg,axiom,
% 28.12/28.46 ! [V_b,V_b_H,V_a] :
% 28.12/28.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 28.12/28.46 => 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))) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_div__neg__neg__trivial,axiom,
% 28.12/28.46 ! [V_b,V_a] :
% 28.12/28.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 28.12/28.46 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_zdiv__mono1,axiom,
% 28.12/28.46 ! [V_b,V_a_H,V_a] :
% 28.12/28.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 28.12/28.46 => 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))) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_zdiv__mono1__neg,axiom,
% 28.12/28.46 ! [V_b,V_a_H,V_a] :
% 28.12/28.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.12/28.46 => 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))) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_int__div__less__self,axiom,
% 28.12/28.46 ! [V_k,V_x] :
% 28.12/28.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k))
% 28.12/28.46 => 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)) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_zdiv__zmult2__eq,axiom,
% 28.12/28.46 ! [V_b,V_a,V_c] :
% 28.12/28.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 28.12/28.46 => 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) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_power_Opower_Opower__0,axiom,
% 28.12/28.46 ! [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 ).
% 28.12/28.46
% 28.12/28.46 fof(fact_power_Opower_Opower__Suc,axiom,
% 28.12/28.46 ! [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)) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_div__mult__self1,axiom,
% 28.12/28.46 ! [V_c,V_a,V_b,T_a] :
% 28.12/28.46 ( class_Divides_Osemiring__div(T_a)
% 28.12/28.46 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 28.12/28.46 => 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)) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_div__mult__self2,axiom,
% 28.12/28.46 ! [V_c,V_a,V_b,T_a] :
% 28.12/28.46 ( class_Divides_Osemiring__div(T_a)
% 28.12/28.46 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 28.12/28.46 => 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)) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_div__add__self1,axiom,
% 28.12/28.46 ! [V_a,V_b,T_a] :
% 28.12/28.46 ( class_Divides_Osemiring__div(T_a)
% 28.12/28.46 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 28.12/28.46 => 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)) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_div__add__self2,axiom,
% 28.12/28.46 ! [V_a,V_b,T_a] :
% 28.12/28.46 ( class_Divides_Osemiring__div(T_a)
% 28.12/28.46 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 28.12/28.46 => 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)) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_divmod__int__rel__div__eq,axiom,
% 28.12/28.46 ! [V_r_1,V_y,V_b_1,V_a_1] :
% 28.12/28.46 ( 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)
% 28.12/28.46 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1))
% 28.12/28.46 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1)) ) )
% 28.12/28.46 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1))
% 28.12/28.46 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 28.12/28.46 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.12/28.46 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_split__zdiv,axiom,
% 28.12/28.46 ! [V_k_2,V_n_2,V_P_2] :
% 28.12/28.46 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)))
% 28.12/28.46 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.12/28.46 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 28.12/28.46 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 28.12/28.46 => ! [B_i] :
% 28.12/28.46 ( ? [B_j] :
% 28.12/28.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 28.12/28.46 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 28.12/28.46 & 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) )
% 28.12/28.46 => hBOOL(hAPP(V_P_2,B_i)) ) )
% 28.12/28.46 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.12/28.46 => ! [B_i] :
% 28.12/28.46 ( ? [B_j] :
% 28.12/28.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 28.12/28.46 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.12/28.46 & 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) )
% 28.12/28.46 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_z3div__def,axiom,
% 28.12/28.46 ! [V_k,V_l] :
% 28.12/28.46 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 28.12/28.46 => c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l) )
% 28.12/28.46 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 28.12/28.46 => 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))) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_Max_Ohom__commute,axiom,
% 28.12/28.46 ! [V_N_2,V_h_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( ! [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))
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 28.12/28.46 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => 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)) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_Min_Ohom__commute,axiom,
% 28.12/28.46 ! [V_N_2,V_h_2,T_b] :
% 28.12/28.46 ( class_Orderings_Olinorder(T_b)
% 28.12/28.46 => ( ! [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))
% 28.12/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 28.12/28.46 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.12/28.46 => 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)) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_strong__setprod__reindex__cong,axiom,
% 28.12/28.46 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 28.12/28.46 ( class_Groups_Ocomm__monoid__mult(T_d)
% 28.12/28.46 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 28.12/28.46 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 28.12/28.46 => ( ! [B_x] :
% 28.12/28.46 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.12/28.46 => 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) )
% 28.12/28.46 => 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) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_div__mult2__eq,axiom,
% 28.12/28.46 ! [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) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_div__le__mono,axiom,
% 28.12/28.46 ! [V_k,V_n,V_m] :
% 28.12/28.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 28.12/28.46 => 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))) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_div__le__dividend,axiom,
% 28.12/28.46 ! [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)) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_div__1,axiom,
% 28.12/28.46 ! [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 ).
% 28.12/28.46
% 28.12/28.46 fof(fact_div__less,axiom,
% 28.12/28.46 ! [V_n,V_m] :
% 28.12/28.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 28.12/28.46 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_nat__mult__div__cancel__disj,axiom,
% 28.12/28.46 ! [V_n,V_m,V_k] :
% 28.12/28.46 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.12/28.46 => 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) )
% 28.12/28.46 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.12/28.46 => 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) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_zdiv__int,axiom,
% 28.12/28.46 ! [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)) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom,
% 28.12/28.46 ! [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)) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_div__le__mono2,axiom,
% 28.12/28.46 ! [V_k,V_n,V_m] :
% 28.12/28.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 28.12/28.46 => 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))) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_nat__mult__div__cancel1,axiom,
% 28.12/28.46 ! [V_n,V_m,V_k] :
% 28.12/28.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 28.12/28.46 => 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) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_div__mult__self1__is__m,axiom,
% 28.12/28.46 ! [V_m,V_n] :
% 28.12/28.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 28.12/28.46 => 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 ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_div__mult__self__is__m,axiom,
% 28.12/28.46 ! [V_m,V_n] :
% 28.12/28.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 28.12/28.46 => 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 ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_div__less__dividend,axiom,
% 28.12/28.46 ! [V_m,V_n] :
% 28.12/28.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 28.12/28.46 => 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)) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_div__geq,axiom,
% 28.12/28.46 ! [V_m,V_n] :
% 28.12/28.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 28.12/28.46 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 28.12/28.46 => 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)) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_div__if,axiom,
% 28.12/28.46 ! [V_m,V_n] :
% 28.12/28.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 28.12/28.46 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 28.12/28.46 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 28.12/28.46 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 28.12/28.46 => 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)) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_split__div,axiom,
% 28.12/28.46 ! [V_k_2,V_n_2,V_P_2] :
% 28.12/28.46 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2)))
% 28.12/28.46 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.12/28.46 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 28.12/28.46 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.12/28.46 => ! [B_i,B_j] :
% 28.12/28.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 28.12/28.46 => ( 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)
% 28.12/28.46 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_nat__div__distrib,axiom,
% 28.12/28.46 ! [V_y,V_x] :
% 28.12/28.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 28.12/28.46 => 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)) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom,
% 28.12/28.46 ! [V_y,V_x] :
% 28.12/28.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 28.12/28.46 => 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)) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_le__div__geq,axiom,
% 28.12/28.46 ! [V_m,V_n] :
% 28.12/28.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 28.12/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 28.12/28.46 => 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)) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_split__div_H,axiom,
% 28.12/28.46 ! [V_n_2,V_m_2,V_P_2] :
% 28.12/28.46 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2)))
% 28.12/28.46 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.12/28.46 & hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 28.12/28.46 | ? [B_q] :
% 28.12/28.46 ( 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))
% 28.12/28.46 & 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))))
% 28.12/28.46 & hBOOL(hAPP(V_P_2,B_q)) ) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_split__div__lemma,axiom,
% 28.12/28.46 ! [V_m_2,V_q_2,V_n_2] :
% 28.12/28.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 28.12/28.46 => ( ( 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))
% 28.12/28.46 & 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)))) )
% 28.12/28.46 <=> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2) ) ) ).
% 28.12/28.46
% 28.12/28.46 fof(fact_Nitpick_Onat__lcm__def,axiom,
% 28.12/28.46 ! [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)) ).
% 28.12/28.46
% 28.45/28.46 fof(fact_setprod__mono__one__left,axiom,
% 28.45/28.46 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 28.45/28.46 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.45/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 28.45/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 28.45/28.46 => ( ! [B_x] :
% 28.45/28.46 ( 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)))
% 28.45/28.46 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 28.45/28.46 => 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) ) ) ) ) ).
% 28.45/28.46
% 28.45/28.46 fof(fact_setprod__mono__one__right,axiom,
% 28.45/28.46 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 28.45/28.46 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.45/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 28.45/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 28.45/28.46 => ( ! [B_x] :
% 28.45/28.46 ( 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)))
% 28.45/28.46 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 28.45/28.46 => 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) ) ) ) ) ).
% 28.45/28.46
% 28.45/28.46 fof(fact_card__partition,axiom,
% 28.45/28.46 ! [V_k_2,V_C_2,T_b] :
% 28.45/28.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_C_2))
% 28.45/28.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
% 28.45/28.46 => ( ! [B_c] :
% 28.45/28.46 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c),V_C_2))
% 28.45/28.46 => hAPP(c_Finite__Set_Ocard(T_b),B_c) = V_k_2 )
% 28.45/28.46 => ( ! [B_c1] :
% 28.45/28.46 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c1),V_C_2))
% 28.45/28.46 => ! [B_c2] :
% 28.45/28.46 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c2),V_C_2))
% 28.45/28.46 => ( B_c1 != B_c2
% 28.45/28.46 => 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)) ) ) )
% 28.45/28.46 => 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)) ) ) ) ) ).
% 28.45/28.46
% 28.45/28.46 fof(fact_Nitpick_Oint__gcd__def,axiom,
% 28.45/28.46 ! [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)))) ).
% 28.45/28.46
% 28.45/28.46 fof(fact_field__le__mult__one__interval,axiom,
% 28.45/28.46 ! [V_y,V_x,T_a] :
% 28.45/28.46 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 28.45/28.46 => ( ! [B_z] :
% 28.45/28.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z))
% 28.45/28.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a)))
% 28.45/28.46 => 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)) ) )
% 28.45/28.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 28.45/28.46
% 28.45/28.46 fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom,
% 28.45/28.46 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
% 28.45/28.46 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 28.45/28.46 & class_Groups_Ocomm__monoid__mult(T_b) )
% 28.45/28.46 => ( V_A_2 = V_B_2
% 28.45/28.46 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 28.45/28.46 => ( ! [B_x] :
% 28.45/28.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 28.45/28.46 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 28.45/28.46 => 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) ) ) ) ) ).
% 28.45/28.46
% 28.45/28.46 fof(fact_split__neg__lemma,axiom,
% 28.45/28.46 ! [V_n_2,V_P_2,V_k_2] :
% 28.45/28.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.45/28.46 => ( 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)))
% 28.45/28.46 <=> ! [B_i,B_j] :
% 28.45/28.46 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 28.45/28.46 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.45/28.46 & 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) )
% 28.45/28.46 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ).
% 28.45/28.46
% 28.45/28.46 fof(fact_zpower__zmod,axiom,
% 28.45/28.46 ! [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) ).
% 28.45/28.46
% 28.45/28.46 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom,
% 28.45/28.46 ! [V_y,V_x] :
% 28.45/28.46 ( c_Nat__Transfer_Ois__nat(V_x)
% 28.45/28.46 => ( c_Nat__Transfer_Ois__nat(V_y)
% 28.45/28.46 => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ).
% 28.45/28.46
% 28.45/28.46 fof(fact_zdiff__zmod__right,axiom,
% 28.45/28.46 ! [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) ).
% 28.45/28.46
% 28.45/28.46 fof(fact_zdiff__zmod__left,axiom,
% 28.45/28.46 ! [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) ).
% 28.45/28.46
% 28.45/28.46 fof(fact_zminus__zmod,axiom,
% 28.45/28.46 ! [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) ).
% 28.45/28.46
% 28.45/28.46 fof(fact_zmod__zminus__zminus,axiom,
% 28.45/28.46 ! [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)) ).
% 28.45/28.46
% 28.45/28.46 fof(fact_zmod__zminus2,axiom,
% 28.45/28.46 ! [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)) ).
% 28.45/28.46
% 28.45/28.46 fof(fact_mod__add__cong,axiom,
% 28.45/28.46 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 28.45/28.46 ( class_Divides_Osemiring__div(T_a)
% 28.45/28.46 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 28.45/28.46 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 28.45/28.46 => 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) ) ) ) ).
% 28.45/28.46
% 28.45/28.46 fof(fact_zmod__simps_I1_J,axiom,
% 28.45/28.46 ! [V_b,V_c,V_a,T_a] :
% 28.45/28.46 ( class_Divides_Osemiring__div(T_a)
% 28.45/28.46 => 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) ) ).
% 28.45/28.46
% 28.45/28.46 fof(fact_zmod__simps_I2_J,axiom,
% 28.45/28.46 ! [V_c,V_b,V_a,T_a] :
% 28.45/28.46 ( class_Divides_Osemiring__div(T_a)
% 28.45/28.46 => 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) ) ).
% 28.45/28.46
% 28.45/28.46 fof(fact_mod__add__eq,axiom,
% 28.45/28.46 ! [V_c,V_b,V_a,T_a] :
% 28.45/28.46 ( class_Divides_Osemiring__div(T_a)
% 28.45/28.46 => 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) ) ).
% 28.45/28.46
% 28.45/28.46 fof(fact_mod__add__left__eq,axiom,
% 28.45/28.46 ! [V_c,V_b,V_a,T_a] :
% 28.45/28.46 ( class_Divides_Osemiring__div(T_a)
% 28.45/28.46 => 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) ) ).
% 28.45/28.46
% 28.45/28.46 fof(fact_mod__add__right__eq,axiom,
% 28.45/28.46 ! [V_c,V_b,V_a,T_a] :
% 28.45/28.46 ( class_Divides_Osemiring__div(T_a)
% 28.45/28.46 => 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) ) ).
% 28.45/28.46
% 28.45/28.46 fof(fact_mod__add__self1,axiom,
% 28.45/28.46 ! [V_a,V_b,T_a] :
% 28.45/28.46 ( class_Divides_Osemiring__div(T_a)
% 28.45/28.46 => 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) ) ).
% 28.45/28.46
% 28.45/28.46 fof(fact_mod__add__self2,axiom,
% 28.45/28.46 ! [V_b,V_a,T_a] :
% 28.45/28.46 ( class_Divides_Osemiring__div(T_a)
% 28.45/28.46 => 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) ) ).
% 28.45/28.46
% 28.45/28.46 fof(fact_mod__mult__cong,axiom,
% 28.45/28.46 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 28.45/28.46 ( class_Divides_Osemiring__div(T_a)
% 28.45/28.46 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 28.45/28.46 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 28.45/28.46 => 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) ) ) ) ).
% 28.45/28.46
% 28.45/28.46 fof(fact_zmod__simps_I4_J,axiom,
% 28.45/28.46 ! [V_b,V_c,V_a,T_a] :
% 28.45/28.46 ( class_Divides_Osemiring__div(T_a)
% 28.45/28.46 => 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) ) ).
% 28.45/28.46
% 28.45/28.46 fof(fact_mod__mult__mult2,axiom,
% 28.45/28.46 ! [V_b,V_c,V_a,T_a] :
% 28.45/28.46 ( class_Divides_Osemiring__div(T_a)
% 28.45/28.46 => 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) ) ).
% 28.45/28.46
% 28.45/28.46 fof(fact_mod__mult__mult1,axiom,
% 28.45/28.46 ! [V_b,V_a,V_c,T_a] :
% 28.45/28.46 ( class_Divides_Osemiring__div(T_a)
% 28.45/28.46 => 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)) ) ).
% 28.45/28.46
% 28.45/28.46 fof(fact_mod__mult__eq,axiom,
% 28.45/28.46 ! [V_c,V_b,V_a,T_a] :
% 28.45/28.46 ( class_Divides_Osemiring__div(T_a)
% 28.45/28.46 => 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) ) ).
% 28.45/28.46
% 28.45/28.46 fof(fact_mod__mult__left__eq,axiom,
% 28.45/28.46 ! [V_c,V_b,V_a,T_a] :
% 28.45/28.46 ( class_Divides_Osemiring__div(T_a)
% 28.45/28.46 => 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) ) ).
% 28.45/28.46
% 28.45/28.46 fof(fact_mod__mult__right__eq,axiom,
% 28.45/28.46 ! [V_c,V_b,V_a,T_a] :
% 28.45/28.46 ( class_Divides_Osemiring__div(T_a)
% 28.45/28.46 => 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) ) ).
% 28.45/28.46
% 28.45/28.46 fof(fact_mod__diff__right__eq,axiom,
% 28.45/28.46 ! [V_c,V_b,V_a,T_a] :
% 28.45/28.46 ( class_Divides_Oring__div(T_a)
% 28.45/28.46 => 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) ) ).
% 28.45/28.46
% 28.45/28.46 fof(fact_mod__diff__left__eq,axiom,
% 28.45/28.46 ! [V_c,V_b,V_a,T_a] :
% 28.45/28.46 ( class_Divides_Oring__div(T_a)
% 28.45/28.46 => 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) ) ).
% 28.45/28.46
% 28.45/28.46 fof(fact_mod__diff__eq,axiom,
% 28.45/28.46 ! [V_c,V_b,V_a,T_a] :
% 28.45/28.46 ( class_Divides_Oring__div(T_a)
% 28.45/28.46 => 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) ) ).
% 28.45/28.46
% 28.45/28.46 fof(fact_mod__diff__cong,axiom,
% 28.45/28.46 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 28.45/28.46 ( class_Divides_Oring__div(T_a)
% 28.45/28.46 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 28.45/28.46 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 28.45/28.46 => 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) ) ) ) ).
% 28.45/28.46
% 28.45/28.46 fof(fact_mod__minus__eq,axiom,
% 28.45/28.46 ! [V_b,V_a,T_a] :
% 28.45/28.46 ( class_Divides_Oring__div(T_a)
% 28.45/28.46 => 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) ) ).
% 28.45/28.46
% 28.45/28.46 fof(fact_mod__minus__cong,axiom,
% 28.45/28.46 ! [V_a_H,V_b,V_a,T_a] :
% 28.45/28.46 ( class_Divides_Oring__div(T_a)
% 28.45/28.46 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b)
% 28.45/28.46 => 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) ) ) ).
% 28.45/28.46
% 28.45/28.46 fof(fact_zmod__self,axiom,
% 28.45/28.47 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_zmod__zero,axiom,
% 28.45/28.47 ! [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) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mod__self,axiom,
% 28.45/28.47 ! [V_a,T_a] :
% 28.45/28.47 ( class_Divides_Osemiring__div(T_a)
% 28.45/28.47 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mod__by__0,axiom,
% 28.45/28.47 ! [V_a,T_a] :
% 28.45/28.47 ( class_Divides_Osemiring__div(T_a)
% 28.45/28.47 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mod__0,axiom,
% 28.45/28.47 ! [V_a,T_a] :
% 28.45/28.47 ( class_Divides_Osemiring__div(T_a)
% 28.45/28.47 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mod__mod__trivial,axiom,
% 28.45/28.47 ! [V_b,V_a,T_a] :
% 28.45/28.47 ( class_Divides_Osemiring__div(T_a)
% 28.45/28.47 => 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) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_zmod__simps_I3_J,axiom,
% 28.45/28.47 ! [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) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_zmod__zmult1__eq,axiom,
% 28.45/28.47 ! [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) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mod__mult__self1__is__0,axiom,
% 28.45/28.47 ! [V_a,V_b,T_a] :
% 28.45/28.47 ( class_Divides_Osemiring__div(T_a)
% 28.45/28.47 => 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) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mod__mult__self2__is__0,axiom,
% 28.45/28.47 ! [V_b,V_a,T_a] :
% 28.45/28.47 ( class_Divides_Osemiring__div(T_a)
% 28.45/28.47 => 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) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mod__mult__self2,axiom,
% 28.45/28.47 ! [V_c,V_b,V_a,T_a] :
% 28.45/28.47 ( class_Divides_Osemiring__div(T_a)
% 28.45/28.47 => 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) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mod__mult__self1,axiom,
% 28.45/28.47 ! [V_b,V_c,V_a,T_a] :
% 28.45/28.47 ( class_Divides_Osemiring__div(T_a)
% 28.45/28.47 => 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) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mod__by__1,axiom,
% 28.45/28.47 ! [V_a,T_a] :
% 28.45/28.47 ( class_Divides_Osemiring__div(T_a)
% 28.45/28.47 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mod__div__trivial,axiom,
% 28.45/28.47 ! [V_b,V_a,T_a] :
% 28.45/28.47 ( class_Divides_Osemiring__div(T_a)
% 28.45/28.47 => 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) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_zmod__le__nonneg__dividend,axiom,
% 28.45/28.47 ! [V_k,V_m] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))
% 28.45/28.47 => 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)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom,
% 28.45/28.47 ! [V_y,V_x] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 28.45/28.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 28.45/28.47 => 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))) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_pos__mod__bound,axiom,
% 28.45/28.47 ! [V_a,V_b] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 28.45/28.47 => 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)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_neg__mod__bound,axiom,
% 28.45/28.47 ! [V_a,V_b] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.45/28.47 => 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))) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_zmod__eq__0__iff,axiom,
% 28.45/28.47 ! [V_d_2,V_m_2] :
% 28.45/28.47 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.45/28.47 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_zmod__zminus1__not__zero,axiom,
% 28.45/28.47 ! [V_l,V_k] :
% 28.45/28.47 ( 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)
% 28.45/28.47 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_zmod__zminus2__not__zero,axiom,
% 28.45/28.47 ! [V_l,V_k] :
% 28.45/28.47 ( 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)
% 28.45/28.47 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_zmod__zdiv__trivial,axiom,
% 28.45/28.47 ! [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) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_DIVISION__BY__ZERO,axiom,
% 28.45/28.47 ! [V_a] :
% 28.45/28.47 ( 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)
% 28.45/28.47 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_zdiv__zadd1__eq,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_semiring__div__class_Omod__div__equality_H,axiom,
% 28.45/28.47 ! [V_b,V_a,T_a] :
% 28.45/28.47 ( class_Divides_Osemiring__div(T_a)
% 28.45/28.47 => 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 ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mod__div__equality2,axiom,
% 28.45/28.47 ! [V_a,V_b,T_a] :
% 28.45/28.47 ( class_Divides_Osemiring__div(T_a)
% 28.45/28.47 => 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 ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mod__div__equality,axiom,
% 28.45/28.47 ! [V_b,V_a,T_a] :
% 28.45/28.47 ( class_Divides_Osemiring__div(T_a)
% 28.45/28.47 => 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 ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_div__mod__equality2,axiom,
% 28.45/28.47 ! [V_c,V_a,V_b,T_a] :
% 28.45/28.47 ( class_Divides_Osemiring__div(T_a)
% 28.45/28.47 => 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) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_div__mod__equality,axiom,
% 28.45/28.47 ! [V_c,V_b,V_a,T_a] :
% 28.45/28.47 ( class_Divides_Osemiring__div(T_a)
% 28.45/28.47 => 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) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mod__neg__neg__trivial,axiom,
% 28.45/28.47 ! [V_b,V_a] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.45/28.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 28.45/28.47 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_neg__mod__conj,axiom,
% 28.45/28.47 ! [V_a,V_b] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.45/28.47 => ( 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)))
% 28.45/28.47 & 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))) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_neg__mod__sign,axiom,
% 28.45/28.47 ! [V_a,V_b] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.45/28.47 => 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))) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mod__pos__pos__trivial,axiom,
% 28.45/28.47 ! [V_b,V_a] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 28.45/28.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 28.45/28.47 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_pos__mod__conj,axiom,
% 28.45/28.47 ! [V_a,V_b] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 28.45/28.47 => ( 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)))
% 28.45/28.47 & 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)) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_pos__mod__sign,axiom,
% 28.45/28.47 ! [V_a,V_b] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 28.45/28.47 => 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))) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_zmod__zminus2__eq__if,axiom,
% 28.45/28.47 ! [V_b,V_a] :
% 28.45/28.47 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.45/28.47 => 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) )
% 28.45/28.47 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.45/28.47 => 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) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_zmod__zminus1__eq__if,axiom,
% 28.45/28.47 ! [V_b,V_a] :
% 28.45/28.47 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.45/28.47 => 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) )
% 28.45/28.47 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.45/28.47 => 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)) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_zmod__zdiv__equality,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_zdiv__zmult1__eq,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_zdiv__zmod__equality,axiom,
% 28.45/28.47 ! [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) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_zdiv__zmod__equality2,axiom,
% 28.45/28.47 ! [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) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_zmult__div__cancel,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_zmod__zdiv__equality_H,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mod__pos__neg__trivial,axiom,
% 28.45/28.47 ! [V_b,V_a] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 28.45/28.47 => ( 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)))
% 28.45/28.47 => 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) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_split__zmod,axiom,
% 28.45/28.47 ! [V_k_2,V_n_2,V_P_2] :
% 28.45/28.47 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 28.45/28.47 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.45/28.47 => hBOOL(hAPP(V_P_2,V_n_2)) )
% 28.45/28.47 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 28.45/28.47 => ! [B_i,B_j] :
% 28.45/28.47 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 28.45/28.47 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 28.45/28.47 & 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) )
% 28.45/28.47 => hBOOL(hAPP(V_P_2,B_j)) ) )
% 28.45/28.47 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.45/28.47 => ! [B_i,B_j] :
% 28.45/28.47 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 28.45/28.47 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.45/28.47 & 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) )
% 28.45/28.47 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_zmult2__lemma__aux3,axiom,
% 28.45/28.47 ! [V_q,V_b,V_r,V_c] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 28.45/28.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 28.45/28.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 28.45/28.47 => 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))) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_zmult2__lemma__aux4,axiom,
% 28.45/28.47 ! [V_q,V_b,V_r,V_c] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 28.45/28.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 28.45/28.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 28.45/28.47 => 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))) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_zmult2__lemma__aux1,axiom,
% 28.45/28.47 ! [V_q,V_r,V_b,V_c] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 28.45/28.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 28.45/28.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.45/28.47 => 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))) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_zmult2__lemma__aux2,axiom,
% 28.45/28.47 ! [V_q,V_r,V_b,V_c] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 28.45/28.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 28.45/28.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.45/28.47 => 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))) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_divmod__int__rel__mod__eq,axiom,
% 28.45/28.47 ! [V_y,V_q_1,V_b_1,V_a_1] :
% 28.45/28.47 ( 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)
% 28.45/28.47 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 28.45/28.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 28.45/28.47 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1)) ) )
% 28.45/28.47 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 28.45/28.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y))
% 28.45/28.47 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 28.45/28.47 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.45/28.47 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_zmod__zmult2__eq,axiom,
% 28.45/28.47 ! [V_b,V_a,V_c] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 28.45/28.47 => 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)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_zdiv__zminus2__eq__if,axiom,
% 28.45/28.47 ! [V_a,V_b] :
% 28.45/28.47 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.45/28.47 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.45/28.47 => 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)) )
% 28.45/28.47 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.45/28.47 => 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)) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_zdiv__zminus1__eq__if,axiom,
% 28.45/28.47 ! [V_a,V_b] :
% 28.45/28.47 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.45/28.47 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.45/28.47 => 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)) )
% 28.45/28.47 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.45/28.47 => 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)) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_split__pos__lemma,axiom,
% 28.45/28.47 ! [V_n_2,V_P_2,V_k_2] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 28.45/28.47 => ( 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)))
% 28.45/28.47 <=> ! [B_i,B_j] :
% 28.45/28.47 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 28.45/28.47 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 28.45/28.47 & 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) )
% 28.45/28.47 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_z3mod__def,axiom,
% 28.45/28.47 ! [V_k,V_l] :
% 28.45/28.47 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 28.45/28.47 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) )
% 28.45/28.47 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 28.45/28.47 => 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)) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_setprod__pos__nat,axiom,
% 28.45/28.47 ! [V_f_2,V_S_2,T_b] :
% 28.45/28.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 28.45/28.47 => ( ! [B_x] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 28.45/28.47 => 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))) )
% 28.45/28.47 => 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))) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_card__quotient__disjoint,axiom,
% 28.45/28.47 ! [V_r_2,V_A_2,T_b] :
% 28.45/28.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.47 => ( 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)
% 28.45/28.47 => 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) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_ex__bij__betw__finite__nat,axiom,
% 28.45/28.47 ! [V_M_2,T_b] :
% 28.45/28.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2))
% 28.45/28.47 => ? [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))) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mod__Suc__eq__Suc__mod,axiom,
% 28.45/28.47 ! [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) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mod__less,axiom,
% 28.45/28.47 ! [V_n,V_m] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 28.45/28.47 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mod__mult__distrib,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mod__mult__distrib2,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mod__less__eq__dividend,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_quotient__empty,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_quotient__is__empty2,axiom,
% 28.45/28.47 ! [V_r_2,V_A_2,T_b] :
% 28.45/28.47 ( 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)
% 28.45/28.47 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_quotient__is__empty,axiom,
% 28.45/28.47 ! [V_r_2,V_A_2,T_b] :
% 28.45/28.47 ( 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))
% 28.45/28.47 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mod__1,axiom,
% 28.45/28.47 ! [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) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mod__Suc,axiom,
% 28.45/28.47 ! [V_n,V_m] :
% 28.45/28.47 ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n
% 28.45/28.47 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 28.45/28.47 & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n
% 28.45/28.47 => 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)) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mod__less__divisor,axiom,
% 28.45/28.47 ! [V_m,V_n] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 28.45/28.47 => 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)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mod__eq__0__iff,axiom,
% 28.45/28.47 ! [V_d_2,V_m_2] :
% 28.45/28.47 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.45/28.47 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mod__if,axiom,
% 28.45/28.47 ! [V_n,V_m] :
% 28.45/28.47 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 28.45/28.47 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m )
% 28.45/28.47 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 28.45/28.47 => 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) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mod__geq,axiom,
% 28.45/28.47 ! [V_n,V_m] :
% 28.45/28.47 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 28.45/28.47 => 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) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mod__mult__self3,axiom,
% 28.45/28.47 ! [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) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_le__mod__geq,axiom,
% 28.45/28.47 ! [V_m,V_n] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 28.45/28.47 => 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) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_zmod__int,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_div__add1__eq,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_nat__gcd_Osimps,axiom,
% 28.45/28.47 ! [V_x,V_y] :
% 28.45/28.47 ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.45/28.47 => c_Nitpick_Onat__gcd(V_x,V_y) = V_x )
% 28.45/28.47 & ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.45/28.47 => 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)) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mod__le__divisor,axiom,
% 28.45/28.47 ! [V_m,V_n] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 28.45/28.47 => 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)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mod__mult__self4,axiom,
% 28.45/28.47 ! [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) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mod__mult2__eq,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_div__mult1__eq,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_div__mod__equality_H,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mult__div__cancel,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_Divides_Omod__div__equality_H,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_quotient__diff1,axiom,
% 28.45/28.47 ! [V_a_2,V_A_2,V_r_2,T_b] :
% 28.45/28.47 ( 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)
% 28.45/28.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.45/28.47 => 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)) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_split__mod,axiom,
% 28.45/28.47 ! [V_k_2,V_n_2,V_P_2] :
% 28.45/28.47 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))
% 28.45/28.47 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.45/28.47 => hBOOL(hAPP(V_P_2,V_n_2)) )
% 28.45/28.47 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.45/28.47 => ! [B_i,B_j] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 28.45/28.47 => ( 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)
% 28.45/28.47 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mod__lemma,axiom,
% 28.45/28.47 ! [V_q,V_b,V_r,V_c] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 28.45/28.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b))
% 28.45/28.47 => 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))) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_Suc__times__mod__eq,axiom,
% 28.45/28.47 ! [V_m,V_k] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k))
% 28.45/28.47 => 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) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom,
% 28.45/28.47 ! [V_y,V_x] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 28.45/28.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 28.45/28.47 => 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)) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_nat__mod__distrib,axiom,
% 28.45/28.47 ! [V_y,V_x] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 28.45/28.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 28.45/28.47 => 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)) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_quotient__def,axiom,
% 28.45/28.47 ! [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)))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_singleton__quotient,axiom,
% 28.45/28.47 ! [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))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_quotientI,axiom,
% 28.45/28.47 ! [V_r_2,V_A_2,V_x_2,T_b] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.45/28.47 => 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))) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_fold__image__1,axiom,
% 28.45/28.47 ! [V_f_2,V_S_2,T_b,T_c] :
% 28.45/28.47 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.45/28.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 28.45/28.47 => ( ! [B_x] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 28.45/28.47 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 28.45/28.47 => 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) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_Image__eq__UN,axiom,
% 28.45/28.47 ! [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))))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_Image__INT__subset,axiom,
% 28.45/28.47 ! [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)))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_Image__Int__subset,axiom,
% 28.45/28.47 ! [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)))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_Image__UN,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_Image__empty,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_Image__mono,axiom,
% 28.45/28.47 ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_c,T_b] :
% 28.45/28.47 ( 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))
% 28.45/28.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_H_2),V_A_2))
% 28.45/28.47 => 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))) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_Image__Un,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_Un__Image,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_quotientE,axiom,
% 28.45/28.47 ! [V_r_2,V_A_2,V_X_2,T_b] :
% 28.45/28.47 ( 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)))
% 28.45/28.47 => ~ ! [B_x] :
% 28.45/28.47 ( 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))))
% 28.45/28.47 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_nat__mod__eq__lemma,axiom,
% 28.45/28.47 ! [V_y,V_n,V_x] :
% 28.45/28.47 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n)
% 28.45/28.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x))
% 28.45/28.47 => ? [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)) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_card_Oneutral,axiom,
% 28.45/28.47 ! [V_A_2,T_b] :
% 28.45/28.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.47 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.45/28.47 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 28.45/28.47 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mod__induct__0,axiom,
% 28.45/28.47 ! [V_i_2,V_P_2,V_p_2] :
% 28.45/28.47 ( ! [B_i] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2))
% 28.45/28.47 => ( hBOOL(hAPP(V_P_2,B_i))
% 28.45/28.47 => hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) )
% 28.45/28.47 => ( hBOOL(hAPP(V_P_2,V_i_2))
% 28.45/28.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2))
% 28.45/28.47 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_less__by__empty,axiom,
% 28.45/28.47 ! [V_B_2,T_b,V_A_2] :
% 28.45/28.47 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 28.45/28.47 => 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)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_fold__image__cong,axiom,
% 28.45/28.47 ! [V_z_2,V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 28.45/28.47 ( class_Groups_Oab__semigroup__mult(T_c)
% 28.45/28.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.47 => ( ! [B_x] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.45/28.47 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) )
% 28.45/28.47 => 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) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_Max__eqI,axiom,
% 28.45/28.47 ! [V_x_2,V_A_2,T_b] :
% 28.45/28.47 ( class_Orderings_Olinorder(T_b)
% 28.45/28.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.47 => ( ! [B_y] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 28.45/28.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_y),V_x_2)) )
% 28.45/28.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.45/28.47 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 ) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_Min__eqI,axiom,
% 28.45/28.47 ! [V_x_2,V_A_2,T_b] :
% 28.45/28.47 ( class_Orderings_Olinorder(T_b)
% 28.45/28.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.47 => ( ! [B_y] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 28.45/28.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_y)) )
% 28.45/28.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.45/28.47 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 ) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_expand__Suc,axiom,
% 28.45/28.47 ! [V_v] :
% 28.45/28.47 ( 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)))
% 28.45/28.47 => 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))) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_of__nat__number__of__lemma,axiom,
% 28.45/28.47 ! [V_v,T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => ( ( 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)))
% 28.45/28.47 => 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) )
% 28.45/28.47 & ( ~ 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)))
% 28.45/28.47 => 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) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_number__of__eq,axiom,
% 28.45/28.47 ! [V_k,T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_eq__number__of,axiom,
% 28.45/28.47 ! [V_y_2,V_x_2,T_b] :
% 28.45/28.47 ( ( class_Int_Onumber__ring(T_b)
% 28.45/28.47 & class_Int_Oring__char__0(T_b) )
% 28.45/28.47 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 28.45/28.47 <=> V_x_2 = V_y_2 ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_number__of__reorient,axiom,
% 28.45/28.47 ! [V_x_2,V_w_2,T_b] :
% 28.45/28.47 ( class_Int_Onumber(T_b)
% 28.45/28.47 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = V_x_2
% 28.45/28.47 <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_of__int__number__of__eq,axiom,
% 28.45/28.47 ! [V_v,T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => 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) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_of__nat__number__of__eq,axiom,
% 28.45/28.47 ! [V_v,T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 28.45/28.47 => 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) )
% 28.45/28.47 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 28.45/28.47 => 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) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_le__number__of__eq__not__less,axiom,
% 28.45/28.47 ! [V_w_2,V_v_2,T_b] :
% 28.45/28.47 ( ( class_Int_Onumber(T_b)
% 28.45/28.47 & class_Orderings_Olinorder(T_b) )
% 28.45/28.47 => ( 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)))
% 28.45/28.47 <=> ~ 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))) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_left__distrib__number__of,axiom,
% 28.45/28.47 ! [V_v,V_b,V_a,T_b] :
% 28.45/28.47 ( ( class_Int_Onumber(T_b)
% 28.45/28.47 & class_Rings_Osemiring(T_b) )
% 28.45/28.47 => 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))) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_right__distrib__number__of,axiom,
% 28.45/28.47 ! [V_c,V_b,V_v,T_b] :
% 28.45/28.47 ( ( class_Int_Onumber(T_b)
% 28.45/28.47 & class_Rings_Osemiring(T_b) )
% 28.45/28.47 => 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)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_right__diff__distrib__number__of,axiom,
% 28.45/28.47 ! [V_c,V_b,V_v,T_b] :
% 28.45/28.47 ( ( class_Int_Onumber(T_b)
% 28.45/28.47 & class_Rings_Oring(T_b) )
% 28.45/28.47 => 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)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_left__diff__distrib__number__of,axiom,
% 28.45/28.47 ! [V_v,V_b,V_a,T_b] :
% 28.45/28.47 ( ( class_Int_Onumber(T_b)
% 28.45/28.47 & class_Rings_Oring(T_b) )
% 28.45/28.47 => 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))) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_le__number__of,axiom,
% 28.45/28.47 ! [V_y_2,V_x_2,T_b] :
% 28.45/28.47 ( ( class_Int_Onumber__ring(T_b)
% 28.45/28.47 & class_Rings_Olinordered__idom(T_b) )
% 28.45/28.47 => ( 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)))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_less__number__of,axiom,
% 28.45/28.47 ! [V_y_2,V_x_2,T_b] :
% 28.45/28.47 ( ( class_Int_Onumber__ring(T_b)
% 28.45/28.47 & class_Rings_Olinordered__idom(T_b) )
% 28.45/28.47 => ( 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)))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_min__number__of,axiom,
% 28.45/28.47 ! [V_v,V_u,T_b] :
% 28.45/28.47 ( ( class_Int_Onumber(T_b)
% 28.45/28.47 & class_Orderings_Oord(T_b) )
% 28.45/28.47 => ( ( 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)))
% 28.45/28.47 => 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) )
% 28.45/28.47 & ( ~ 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)))
% 28.45/28.47 => 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) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_max__number__of,axiom,
% 28.45/28.47 ! [V_v,V_u,T_b] :
% 28.45/28.47 ( ( class_Int_Onumber(T_b)
% 28.45/28.47 & class_Orderings_Oord(T_b) )
% 28.45/28.47 => ( ( 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)))
% 28.45/28.47 => 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) )
% 28.45/28.47 & ( ~ 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)))
% 28.45/28.47 => 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) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_number__of__add,axiom,
% 28.45/28.47 ! [V_w,V_v,T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => 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)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_add__number__of__eq,axiom,
% 28.45/28.47 ! [V_w,V_v,T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => 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)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_add__number__of__left,axiom,
% 28.45/28.47 ! [V_z,V_w,V_v,T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => 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) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_number__of__mult,axiom,
% 28.45/28.47 ! [V_w,V_v,T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => 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)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_arith__simps_I32_J,axiom,
% 28.45/28.47 ! [V_w,V_v,T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => 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)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mult__number__of__left,axiom,
% 28.45/28.47 ! [V_z,V_w,V_v,T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => 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) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_number__of__diff,axiom,
% 28.45/28.47 ! [V_w,V_v,T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => 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)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_number__of__minus,axiom,
% 28.45/28.47 ! [V_w,T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => 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)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_arith__simps_I30_J,axiom,
% 28.45/28.47 ! [V_w,T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => 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)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_Ints__number__of,axiom,
% 28.45/28.47 ! [V_w_2,T_b] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_b)
% 28.45/28.47 => 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))) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_divide__eq__eq__number__of1,axiom,
% 28.45/28.47 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 28.45/28.47 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 28.45/28.47 & class_Int_Onumber(T_b) )
% 28.45/28.47 => ( 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
% 28.45/28.47 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
% 28.45/28.47 => 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)) )
% 28.45/28.47 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
% 28.45/28.47 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_divide__eq__eq__number__of,axiom,
% 28.45/28.47 ! [V_w_2,V_c_2,V_b_2,T_b] :
% 28.45/28.47 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 28.45/28.47 & class_Int_Onumber(T_b) )
% 28.45/28.47 => ( 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)
% 28.45/28.47 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 28.45/28.47 => 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) )
% 28.45/28.47 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 28.45/28.47 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_eq__divide__eq__number__of,axiom,
% 28.45/28.47 ! [V_c_2,V_b_2,V_w_2,T_b] :
% 28.45/28.47 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 28.45/28.47 & class_Int_Onumber(T_b) )
% 28.45/28.47 => ( 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)
% 28.45/28.47 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 28.45/28.47 => 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 )
% 28.45/28.47 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 28.45/28.47 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_eq__divide__eq__number__of1,axiom,
% 28.45/28.47 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 28.45/28.47 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 28.45/28.47 & class_Int_Onumber(T_b) )
% 28.45/28.47 => ( 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))
% 28.45/28.47 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
% 28.45/28.47 => 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 )
% 28.45/28.47 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
% 28.45/28.47 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_add__number__of__diff1,axiom,
% 28.45/28.47 ! [V_c,V_w,V_v,T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => 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) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_minus__number__of__mult,axiom,
% 28.45/28.47 ! [V_z,V_w,T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => 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) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_diff__number__of__eq,axiom,
% 28.45/28.47 ! [V_w,V_v,T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => 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))) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_divide__less__eq__number__of1,axiom,
% 28.45/28.47 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 28.45/28.47 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 28.45/28.47 & class_Int_Onumber(T_b) )
% 28.45/28.47 => ( 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))
% 28.45/28.47 <=> ( ( 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)))
% 28.45/28.47 => 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)))) )
% 28.45/28.47 & ( ~ 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)))
% 28.45/28.47 => ( ( 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)))
% 28.45/28.47 => 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)) )
% 28.45/28.47 & ( ~ 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)))
% 28.45/28.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_divide__less__eq__number__of,axiom,
% 28.45/28.47 ! [V_w_2,V_c_2,V_b_2,T_b] :
% 28.45/28.47 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 28.45/28.47 & class_Int_Onumber(T_b) )
% 28.45/28.47 => ( 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)))
% 28.45/28.47 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.45/28.47 => 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))) )
% 28.45/28.47 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.45/28.47 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.45/28.47 => 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)) )
% 28.45/28.47 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.45/28.47 => 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))) ) ) ) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_less__divide__eq__number__of,axiom,
% 28.45/28.47 ! [V_c_2,V_b_2,V_w_2,T_b] :
% 28.45/28.47 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 28.45/28.47 & class_Int_Onumber(T_b) )
% 28.45/28.47 => ( 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)))
% 28.45/28.47 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.45/28.47 => 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)) )
% 28.45/28.47 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.45/28.47 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.45/28.47 => 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))) )
% 28.45/28.47 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.45/28.47 => 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))) ) ) ) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_less__divide__eq__number__of1,axiom,
% 28.45/28.47 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 28.45/28.47 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 28.45/28.47 & class_Int_Onumber(T_b) )
% 28.45/28.47 => ( 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))))
% 28.45/28.47 <=> ( ( 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)))
% 28.45/28.47 => 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)) )
% 28.45/28.47 & ( ~ 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)))
% 28.45/28.47 => ( ( 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)))
% 28.45/28.47 => 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)))) )
% 28.45/28.47 & ( ~ 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)))
% 28.45/28.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_abs__number__of,axiom,
% 28.45/28.47 ! [V_x,T_a] :
% 28.45/28.47 ( ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 & class_Rings_Olinordered__idom(T_a) )
% 28.45/28.47 => ( ( 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)))
% 28.45/28.47 => 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)) )
% 28.45/28.47 & ( ~ 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)))
% 28.45/28.47 => 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) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_add__number__of__diff2,axiom,
% 28.45/28.47 ! [V_w,V_c,V_v,T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => 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) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_divide__le__eq__number__of1,axiom,
% 28.45/28.47 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 28.45/28.47 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 28.45/28.47 & class_Int_Onumber(T_b) )
% 28.45/28.47 => ( 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))
% 28.45/28.47 <=> ( ( 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)))
% 28.45/28.47 => 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)))) )
% 28.45/28.47 & ( ~ 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)))
% 28.45/28.47 => ( ( 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)))
% 28.45/28.47 => 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)) )
% 28.45/28.47 & ( ~ 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)))
% 28.45/28.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_divide__le__eq__number__of,axiom,
% 28.45/28.47 ! [V_w_2,V_c_2,V_b_2,T_b] :
% 28.45/28.47 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 28.45/28.47 & class_Int_Onumber(T_b) )
% 28.45/28.47 => ( 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)))
% 28.45/28.47 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.45/28.47 => 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))) )
% 28.45/28.47 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.45/28.47 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.45/28.47 => 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)) )
% 28.45/28.47 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.45/28.47 => 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))) ) ) ) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_le__divide__eq__number__of,axiom,
% 28.45/28.47 ! [V_c_2,V_b_2,V_w_2,T_b] :
% 28.45/28.47 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 28.45/28.47 & class_Int_Onumber(T_b) )
% 28.45/28.47 => ( 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)))
% 28.45/28.47 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.45/28.47 => 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)) )
% 28.45/28.47 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.45/28.47 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.45/28.47 => 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))) )
% 28.45/28.47 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.45/28.47 => 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))) ) ) ) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_le__divide__eq__number__of1,axiom,
% 28.45/28.47 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 28.45/28.47 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 28.45/28.47 & class_Int_Onumber(T_b) )
% 28.45/28.47 => ( 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))))
% 28.45/28.47 <=> ( ( 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)))
% 28.45/28.47 => 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)) )
% 28.45/28.47 & ( ~ 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)))
% 28.45/28.47 => ( ( 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)))
% 28.45/28.47 => 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)))) )
% 28.45/28.47 & ( ~ 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)))
% 28.45/28.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_one__mod__nat__number__of,axiom,
% 28.45/28.47 ! [V_v_H] :
% 28.45/28.47 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 28.45/28.47 => 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)) )
% 28.45/28.47 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 28.45/28.47 => 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))) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_one__div__nat__number__of,axiom,
% 28.45/28.47 ! [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))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_power__number__of__odd__number__of,axiom,
% 28.45/28.47 ! [V_v_2,V_w_2,T_b] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_b)
% 28.45/28.47 => ( ( 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)))
% 28.45/28.47 => 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))) )
% 28.45/28.47 & ( ~ 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)))
% 28.45/28.47 => 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) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_power__nat__number__of__number__of,axiom,
% 28.45/28.47 ! [V_w,V_v] :
% 28.45/28.47 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 28.45/28.47 => 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)) )
% 28.45/28.47 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 28.45/28.47 => 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))) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_less__eq__number__of__int__code,axiom,
% 28.45/28.47 ! [V_l_2,V_k_2] :
% 28.45/28.47 ( 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)))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_number__of__is__id,axiom,
% 28.45/28.47 ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k ).
% 28.45/28.47
% 28.45/28.47 fof(fact_less__number__of__int__code,axiom,
% 28.45/28.47 ! [V_l_2,V_k_2] :
% 28.45/28.47 ( 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)))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_times__numeral__code_I5_J,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_plus__numeral__code_I9_J,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_minus__numeral__code_I5_J,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_neg__number__of__Bit1,axiom,
% 28.45/28.47 ! [V_w_2] :
% 28.45/28.47 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2))))
% 28.45/28.47 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_rel__simps_I51_J,axiom,
% 28.45/28.47 ! [V_l_2,V_k_2] :
% 28.45/28.47 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2)
% 28.45/28.47 <=> V_k_2 = V_l_2 ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_rel__simps_I17_J,axiom,
% 28.45/28.47 ! [V_l_2,V_k_2] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_less__int__code_I16_J,axiom,
% 28.45/28.47 ! [V_k2_2,V_k1_2] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_less__eq__int__code_I16_J,axiom,
% 28.45/28.47 ! [V_k2_2,V_k1_2] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_rel__simps_I34_J,axiom,
% 28.45/28.47 ! [V_l_2,V_k_2] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_int__number__of__def,axiom,
% 28.45/28.47 ! [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) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_bin__less__0__simps_I4_J,axiom,
% 28.45/28.47 ! [V_w_2] :
% 28.45/28.47 ( 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)))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_Bit1__def,axiom,
% 28.45/28.47 ! [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) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_nat__number__of,axiom,
% 28.45/28.47 ! [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) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_nat__number__of__def,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_nat__number__of__Bit1,axiom,
% 28.45/28.47 ! [V_w_2] :
% 28.45/28.47 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 28.45/28.47 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 28.45/28.47 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 28.45/28.47 => 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)))) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_number__of__Bit1,axiom,
% 28.45/28.47 ! [V_w,T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => 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)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_power__number__of__odd,axiom,
% 28.45/28.47 ! [V_z_2,V_w_2,T_b] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_b)
% 28.45/28.47 => ( ( 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)))
% 28.45/28.47 => 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))) )
% 28.45/28.47 & ( ~ 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)))
% 28.45/28.47 => 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) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_zpower__number__of__odd,axiom,
% 28.45/28.47 ! [V_z_2,V_w_2] :
% 28.45/28.47 ( ( 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)))
% 28.45/28.47 => 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))) )
% 28.45/28.47 & ( ~ 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)))
% 28.45/28.47 => 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) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_minus__numeral__code_I6_J,axiom,
% 28.45/28.47 ! [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))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_neg__imp__number__of__eq__0,axiom,
% 28.45/28.47 ! [V_v] :
% 28.45/28.47 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 28.45/28.47 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_int__eq__iff__number__of,axiom,
% 28.45/28.47 ! [V_v_2,V_m_2] :
% 28.45/28.47 ( 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)
% 28.45/28.47 <=> ( V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))
% 28.45/28.47 & 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))) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_eq__nat__number__of,axiom,
% 28.45/28.47 ! [V_v_H_2,V_v_2] :
% 28.45/28.47 ( 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)
% 28.45/28.47 <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 28.45/28.47 => 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))) )
% 28.45/28.47 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 28.45/28.47 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 28.45/28.47 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 28.45/28.47 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 28.45/28.47 => V_v_2 = V_v_H_2 ) ) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_nat__number__of__add__left,axiom,
% 28.45/28.47 ! [V_k,V_v_H,V_v] :
% 28.45/28.47 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 28.45/28.47 => 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) )
% 28.45/28.47 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 28.45/28.47 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 28.45/28.47 => 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) )
% 28.45/28.47 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 28.45/28.47 => 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) ) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_int__nat__number__of,axiom,
% 28.45/28.47 ! [V_v] :
% 28.45/28.47 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 28.45/28.47 => 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) )
% 28.45/28.47 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 28.45/28.47 => 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) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mod__nat__number__of,axiom,
% 28.45/28.47 ! [V_v_H,V_v] :
% 28.45/28.47 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 28.45/28.47 => 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) )
% 28.45/28.47 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 28.45/28.47 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 28.45/28.47 => 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) )
% 28.45/28.47 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 28.45/28.47 => 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))) ) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_div__nat__number__of,axiom,
% 28.45/28.47 ! [V_v_H,V_v] :
% 28.45/28.47 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 28.45/28.47 => 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) )
% 28.45/28.47 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 28.45/28.47 => 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))) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_power__nat__number__of,axiom,
% 28.45/28.47 ! [V_n,V_v] :
% 28.45/28.47 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 28.45/28.47 => 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) )
% 28.45/28.47 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 28.45/28.47 => 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)) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_Suc__nat__number__of__add,axiom,
% 28.45/28.47 ! [V_n,V_v] :
% 28.45/28.47 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 28.45/28.47 => 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) )
% 28.45/28.47 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 28.45/28.47 => 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) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_diff__nat__number__of,axiom,
% 28.45/28.47 ! [V_v_2,V_v_H_2] :
% 28.45/28.47 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 28.45/28.47 => 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) )
% 28.45/28.47 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 28.45/28.47 => 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)) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_min__Suc__number__of,axiom,
% 28.45/28.47 ! [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)))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_min__number__of__Suc,axiom,
% 28.45/28.47 ! [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)))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_succ__Pls,axiom,
% 28.45/28.47 c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_rel__simps_I39_J,axiom,
% 28.45/28.47 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_rel__simps_I46_J,axiom,
% 28.45/28.47 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ).
% 28.45/28.47
% 28.45/28.47 fof(fact_rel__simps_I19_J,axiom,
% 28.45/28.47 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_diff__bin__simps_I1_J,axiom,
% 28.45/28.47 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 28.45/28.47
% 28.45/28.47 fof(fact_minus__Pls,axiom,
% 28.45/28.47 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls ).
% 28.45/28.47
% 28.45/28.47 fof(fact_succ__pred,axiom,
% 28.45/28.47 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ).
% 28.45/28.47
% 28.45/28.47 fof(fact_rel__simps_I2_J,axiom,
% 28.45/28.47 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_Pls__def,axiom,
% 28.45/28.47 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mult__Pls,axiom,
% 28.45/28.47 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ).
% 28.45/28.47
% 28.45/28.47 fof(fact_add__Pls,axiom,
% 28.45/28.47 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k ).
% 28.45/28.47
% 28.45/28.47 fof(fact_add__Pls__right,axiom,
% 28.45/28.47 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 28.45/28.47
% 28.45/28.47 fof(fact_number__of__Pls,axiom,
% 28.45/28.47 ! [T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_semiring__norm_I112_J,axiom,
% 28.45/28.47 ! [T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_add__numeral__0__right,axiom,
% 28.45/28.47 ! [V_a,T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => 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 ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_add__numeral__0,axiom,
% 28.45/28.47 ! [V_a,T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => 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 ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_bin__less__0__simps_I1_J,axiom,
% 28.45/28.47 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_nat__number__of__Pls,axiom,
% 28.45/28.47 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_semiring__norm_I113_J,axiom,
% 28.45/28.47 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_zero__is__num__zero,axiom,
% 28.45/28.47 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_rel__simps_I22_J,axiom,
% 28.45/28.47 ! [V_k_2] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_rel__simps_I12_J,axiom,
% 28.45/28.47 ! [V_k_2] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_Suc__diff__number__of,axiom,
% 28.45/28.47 ! [V_m,V_v] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v))
% 28.45/28.47 => 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))) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_not__neg__number__of__Pls,axiom,
% 28.45/28.47 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_nat__number__of__add__1,axiom,
% 28.45/28.47 ! [V_v] :
% 28.45/28.47 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 28.45/28.47 => 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) )
% 28.45/28.47 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 28.45/28.47 => 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)) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_nat__1__add__number__of,axiom,
% 28.45/28.47 ! [V_v] :
% 28.45/28.47 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 28.45/28.47 => 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) )
% 28.45/28.47 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 28.45/28.47 => 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)) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_le__iff__pred__less,axiom,
% 28.45/28.47 ! [V_l_2,V_k_2] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_minus__Bit1,axiom,
% 28.45/28.47 ! [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))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_pred__def,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_nat__number__of__diff__1,axiom,
% 28.45/28.47 ! [V_v] :
% 28.45/28.47 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 28.45/28.47 => 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) )
% 28.45/28.47 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 28.45/28.47 => 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)) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mult__numeral__1,axiom,
% 28.45/28.47 ! [V_a,T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => 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 ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mult__numeral__1__right,axiom,
% 28.45/28.47 ! [V_a,T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => 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 ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_divide__Numeral0,axiom,
% 28.45/28.47 ! [V_x,T_a] :
% 28.45/28.47 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 28.45/28.47 & class_Int_Onumber__ring(T_a) )
% 28.45/28.47 => 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) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_numeral__1__eq__1,axiom,
% 28.45/28.47 ! [T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_semiring__norm_I110_J,axiom,
% 28.45/28.47 ! [T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_eq__0__number__of,axiom,
% 28.45/28.47 ! [V_v_2] :
% 28.45/28.47 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_eq__number__of__0,axiom,
% 28.45/28.47 ! [V_v_2] :
% 28.45/28.47 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_number__of2,axiom,
% 28.45/28.47 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))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_rel__simps_I5_J,axiom,
% 28.45/28.47 ! [V_k_2] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_rel__simps_I29_J,axiom,
% 28.45/28.47 ! [V_k_2] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_less__nat__number__of,axiom,
% 28.45/28.47 ! [V_v_H_2,V_v_2] :
% 28.45/28.47 ( 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)))
% 28.45/28.47 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2))
% 28.45/28.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) )
% 28.45/28.47 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_divide__Numeral1,axiom,
% 28.45/28.47 ! [V_x,T_a] :
% 28.45/28.47 ( ( class_Fields_Ofield(T_a)
% 28.45/28.47 & class_Int_Onumber__ring(T_a) )
% 28.45/28.47 => 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 ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_divide__numeral__1,axiom,
% 28.45/28.47 ! [V_a,T_a] :
% 28.45/28.47 ( ( class_Fields_Ofield(T_a)
% 28.45/28.47 & class_Int_Onumber__ring(T_a) )
% 28.45/28.47 => 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 ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_le__nat__number__of,axiom,
% 28.45/28.47 ! [V_v_H_2,V_v_2] :
% 28.45/28.47 ( 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)))
% 28.45/28.47 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2))
% 28.45/28.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_one__is__num__one,axiom,
% 28.45/28.47 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_nat__numeral__1__eq__1,axiom,
% 28.45/28.47 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_Numeral1__eq1__nat,axiom,
% 28.45/28.47 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom,
% 28.45/28.47 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_succ__def,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_le__special_I3_J,axiom,
% 28.45/28.47 ! [V_x_2,T_b] :
% 28.45/28.47 ( ( class_Int_Onumber__ring(T_b)
% 28.45/28.47 & class_Rings_Olinordered__idom(T_b) )
% 28.45/28.47 => ( 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)))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_le__special_I1_J,axiom,
% 28.45/28.47 ! [V_y_2,T_b] :
% 28.45/28.47 ( ( class_Int_Onumber__ring(T_b)
% 28.45/28.47 & class_Rings_Olinordered__idom(T_b) )
% 28.45/28.47 => ( 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)))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_less__special_I1_J,axiom,
% 28.45/28.47 ! [V_y_2,T_b] :
% 28.45/28.47 ( ( class_Int_Onumber__ring(T_b)
% 28.45/28.47 & class_Rings_Olinordered__idom(T_b) )
% 28.45/28.47 => ( 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)))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_less__special_I3_J,axiom,
% 28.45/28.47 ! [V_x_2,T_b] :
% 28.45/28.47 ( ( class_Int_Onumber__ring(T_b)
% 28.45/28.47 & class_Rings_Olinordered__idom(T_b) )
% 28.45/28.47 => ( 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)))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_less__0__number__of,axiom,
% 28.45/28.47 ! [V_v_2] :
% 28.45/28.47 ( 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)))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_numeral__3__eq__3,axiom,
% 28.45/28.47 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)))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_numeral__1__eq__Suc__0,axiom,
% 28.45/28.47 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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_power3__eq__cube,axiom,
% 28.45/28.47 ! [V_a,T_a] :
% 28.45/28.47 ( class_Groups_Omonoid__mult(T_a)
% 28.45/28.47 => 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) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
% 28.45/28.47 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))))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_Suc3__eq__add__3,axiom,
% 28.45/28.47 ! [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) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_add__nat__number__of,axiom,
% 28.45/28.47 ! [V_v_H,V_v] :
% 28.45/28.47 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 28.45/28.47 => 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) )
% 28.45/28.47 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 28.45/28.47 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 28.45/28.47 => 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) )
% 28.45/28.47 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 28.45/28.47 => 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)) ) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_transfer__int__nat__numerals_I4_J,axiom,
% 28.45/28.47 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)))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_transfer__nat__int__numerals_I4_J,axiom,
% 28.45/28.47 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)))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_number__of__succ,axiom,
% 28.45/28.47 ! [V_k,T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => 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)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_number__of__pred,axiom,
% 28.45/28.47 ! [V_w,T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => 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)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_le__special_I4_J,axiom,
% 28.45/28.47 ! [V_x_2,T_b] :
% 28.45/28.47 ( ( class_Int_Onumber__ring(T_b)
% 28.45/28.47 & class_Rings_Olinordered__idom(T_b) )
% 28.45/28.47 => ( 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)))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_le__special_I2_J,axiom,
% 28.45/28.47 ! [V_y_2,T_b] :
% 28.45/28.47 ( ( class_Int_Onumber__ring(T_b)
% 28.45/28.47 & class_Rings_Olinordered__idom(T_b) )
% 28.45/28.47 => ( 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)))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_less__special_I4_J,axiom,
% 28.45/28.47 ! [V_x_2,T_b] :
% 28.45/28.47 ( ( class_Int_Onumber__ring(T_b)
% 28.45/28.47 & class_Rings_Olinordered__idom(T_b) )
% 28.45/28.47 => ( 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)))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_less__special_I2_J,axiom,
% 28.45/28.47 ! [V_y_2,T_b] :
% 28.45/28.47 ( ( class_Int_Onumber__ring(T_b)
% 28.45/28.47 & class_Rings_Olinordered__idom(T_b) )
% 28.45/28.47 => ( 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)))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_add__special_I3_J,axiom,
% 28.45/28.47 ! [V_v,T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => 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))) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_add__special_I2_J,axiom,
% 28.45/28.47 ! [V_w,T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => 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)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_Suc__diff__eq__diff__pred,axiom,
% 28.45/28.47 ! [V_m,V_n] :
% 28.45/28.47 ( 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))
% 28.45/28.47 => 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)))) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_nat__number__of__mult__left,axiom,
% 28.45/28.47 ! [V_k,V_v_H,V_v] :
% 28.45/28.47 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 28.45/28.47 => 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) )
% 28.45/28.47 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 28.45/28.47 => 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) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mult__nat__number__of,axiom,
% 28.45/28.47 ! [V_v_H,V_v] :
% 28.45/28.47 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 28.45/28.47 => 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) )
% 28.45/28.47 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 28.45/28.47 => 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)) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_neg__number__of__pred__iff__0,axiom,
% 28.45/28.47 ! [V_v_2] :
% 28.45/28.47 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))))
% 28.45/28.47 <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mod__Suc__eq__mod__add3,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_Suc__mod__eq__add3__mod,axiom,
% 28.45/28.47 ! [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) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_Suc__mod__eq__add3__mod__number__of,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_div__Suc__eq__div__add3,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_Suc__div__eq__add3__div,axiom,
% 28.45/28.47 ! [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) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_Suc__div__eq__add3__div__number__of,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_diff__special_I1_J,axiom,
% 28.45/28.47 ! [V_w,T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => 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))) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_diff__special_I2_J,axiom,
% 28.45/28.47 ! [V_v,T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => 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)))) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_Suc__eq__number__of,axiom,
% 28.45/28.47 ! [V_v_2,V_n_2] :
% 28.45/28.47 ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 28.45/28.47 <=> 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))))) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_eq__number__of__Suc,axiom,
% 28.45/28.47 ! [V_n_2,V_v_2] :
% 28.45/28.47 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2)
% 28.45/28.47 <=> 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))))) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_nat__case__number__of,axiom,
% 28.45/28.47 ! [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))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_less__number__of__Suc,axiom,
% 28.45/28.47 ! [V_n_2,V_v_2] :
% 28.45/28.47 ( 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)))
% 28.45/28.47 <=> 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)))) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_less__Suc__number__of,axiom,
% 28.45/28.47 ! [V_v_2,V_n_2] :
% 28.45/28.47 ( 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)))
% 28.45/28.47 <=> 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))))) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_le__Suc__number__of,axiom,
% 28.45/28.47 ! [V_v_2,V_n_2] :
% 28.45/28.47 ( 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)))
% 28.45/28.47 <=> 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))))) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_le__number__of__Suc,axiom,
% 28.45/28.47 ! [V_n_2,V_v_2] :
% 28.45/28.47 ( 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)))
% 28.45/28.47 <=> 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)))) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_Suc__nat__number__of,axiom,
% 28.45/28.47 ! [V_v] :
% 28.45/28.47 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 28.45/28.47 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 28.45/28.47 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 28.45/28.47 => 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)) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_max__Suc__number__of,axiom,
% 28.45/28.47 ! [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)))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_max__number__of__Suc,axiom,
% 28.45/28.47 ! [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)))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_nat__case__add__eq__if,axiom,
% 28.45/28.47 ! [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)))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_nat__rec__add__eq__if,axiom,
% 28.45/28.47 ! [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))))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_eq__special_I2_J,axiom,
% 28.45/28.47 ! [V_y_2,T_b] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_b)
% 28.45/28.47 => ( c_Groups_Oone__class_Oone(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 28.45/28.47 <=> 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)))) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_eq__special_I4_J,axiom,
% 28.45/28.47 ! [V_x_2,T_b] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_b)
% 28.45/28.47 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Oone__class_Oone(T_b)
% 28.45/28.47 <=> 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))))) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_nat__rec__number__of,axiom,
% 28.45/28.47 ! [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)))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_iszero__def,axiom,
% 28.45/28.47 ! [V_z_2,T_b] :
% 28.45/28.47 ( class_Rings_Osemiring__1(T_b)
% 28.45/28.47 => ( c_Int_Oiszero(T_b,V_z_2)
% 28.45/28.47 <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_iszero__0,axiom,
% 28.45/28.47 ! [T_a] :
% 28.45/28.47 ( class_Rings_Osemiring__1(T_a)
% 28.45/28.47 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_not__iszero__1,axiom,
% 28.45/28.47 ! [T_a] :
% 28.45/28.47 ( class_Rings_Osemiring__1(T_a)
% 28.45/28.47 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_nat__rec__0,axiom,
% 28.45/28.47 ! [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 ).
% 28.45/28.47
% 28.45/28.47 fof(fact_nat__rec__Suc,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_iszero__Numeral0,axiom,
% 28.45/28.47 ! [T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_iszero__number__of__Bit1,axiom,
% 28.45/28.47 ! [V_w,T_a] :
% 28.45/28.47 ( ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 & class_Int_Oring__char__0(T_a) )
% 28.45/28.47 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_not__iszero__Numeral1,axiom,
% 28.45/28.47 ! [T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_eq__number__of__eq,axiom,
% 28.45/28.47 ! [V_y_2,V_x_2,T_b] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_b)
% 28.45/28.47 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 28.45/28.47 <=> 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)))) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_eq__special_I1_J,axiom,
% 28.45/28.47 ! [V_y_2,T_b] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_b)
% 28.45/28.47 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 28.45/28.47 <=> 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)))) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_eq__special_I3_J,axiom,
% 28.45/28.47 ! [V_x_2,T_b] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_b)
% 28.45/28.47 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Ozero__class_Ozero(T_b)
% 28.45/28.47 <=> 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)))) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_neg__zmod__mult__2,axiom,
% 28.45/28.47 ! [V_b,V_a] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.45/28.47 => 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)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_zmod__number__of__Bit1,axiom,
% 28.45/28.47 ! [V_v,V_w] :
% 28.45/28.47 ( ( 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)))
% 28.45/28.47 => 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)) )
% 28.45/28.47 & ( ~ 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)))
% 28.45/28.47 => 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)) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_arith__series__int,axiom,
% 28.45/28.47 ! [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)))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_rel__simps_I49_J,axiom,
% 28.45/28.47 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_rel__simps_I50_J,axiom,
% 28.45/28.47 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_rel__simps_I31_J,axiom,
% 28.45/28.47 ! [V_l_2,V_k_2] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_less__eq__int__code_I13_J,axiom,
% 28.45/28.47 ! [V_k2_2,V_k1_2] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_diff__bin__simps_I7_J,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mult__Bit0,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_less__int__code_I13_J,axiom,
% 28.45/28.47 ! [V_k2_2,V_k1_2] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_rel__simps_I14_J,axiom,
% 28.45/28.47 ! [V_l_2,V_k_2] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_Bit0__def,axiom,
% 28.45/28.47 ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_add__Bit0__Bit0,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_rel__simps_I48_J,axiom,
% 28.45/28.47 ! [V_l_2,V_k_2] :
% 28.45/28.47 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2)
% 28.45/28.47 <=> V_k_2 = V_l_2 ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_minus__Bit0,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_Bit0__Pls,axiom,
% 28.45/28.47 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ).
% 28.45/28.47
% 28.45/28.47 fof(fact_rel__simps_I38_J,axiom,
% 28.45/28.47 ! [V_l_2] :
% 28.45/28.47 ( c_Int_OPls = c_Int_OBit0(V_l_2)
% 28.45/28.47 <=> c_Int_OPls = V_l_2 ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_rel__simps_I44_J,axiom,
% 28.45/28.47 ! [V_k_2] :
% 28.45/28.47 ( c_Int_OBit0(V_k_2) = c_Int_OPls
% 28.45/28.47 <=> V_k_2 = c_Int_OPls ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_bin__less__0__simps_I3_J,axiom,
% 28.45/28.47 ! [V_w_2] :
% 28.45/28.47 ( 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)))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_rel__simps_I27_J,axiom,
% 28.45/28.47 ! [V_k_2] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_rel__simps_I21_J,axiom,
% 28.45/28.47 ! [V_k_2] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_less__eq__int__code_I14_J,axiom,
% 28.45/28.47 ! [V_k2_2,V_k1_2] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_rel__simps_I32_J,axiom,
% 28.45/28.47 ! [V_l_2,V_k_2] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_rel__simps_I4_J,axiom,
% 28.45/28.47 ! [V_k_2] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_rel__simps_I10_J,axiom,
% 28.45/28.47 ! [V_k_2] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_rel__simps_I16_J,axiom,
% 28.45/28.47 ! [V_l_2,V_k_2] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_less__int__code_I15_J,axiom,
% 28.45/28.47 ! [V_k2_2,V_k1_2] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_add__Bit0__Bit1,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_add__Bit1__Bit0,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_diff__bin__simps_I3_J,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_diff__bin__simps_I10_J,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_diff__bin__simps_I9_J,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_zdiv__number__of__Bit0,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_neg__number__of__Bit0,axiom,
% 28.45/28.47 ! [V_w_2] :
% 28.45/28.47 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2))))
% 28.45/28.47 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_pred__Bit1,axiom,
% 28.45/28.47 ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_pred__Bit0,axiom,
% 28.45/28.47 ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_iszero__number__of__Bit0,axiom,
% 28.45/28.47 ! [V_w_2,T_b] :
% 28.45/28.47 ( ( class_Int_Onumber__ring(T_b)
% 28.45/28.47 & class_Int_Oring__char__0(T_b) )
% 28.45/28.47 => ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(V_w_2)))
% 28.45/28.47 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_succ__Bit0,axiom,
% 28.45/28.47 ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_succ__Bit1,axiom,
% 28.45/28.47 ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_nat__number__of__Bit0,axiom,
% 28.45/28.47 ! [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))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_number__of__Bit0,axiom,
% 28.45/28.47 ! [V_w,T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => 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)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_rel__simps_I15_J,axiom,
% 28.45/28.47 ! [V_l_2,V_k_2] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_less__int__code_I14_J,axiom,
% 28.45/28.47 ! [V_k2_2,V_k1_2] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_rel__simps_I33_J,axiom,
% 28.45/28.47 ! [V_l_2,V_k_2] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_less__eq__int__code_I15_J,axiom,
% 28.45/28.47 ! [V_k2_2,V_k1_2] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_card__UNIV__bool,axiom,
% 28.45/28.47 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))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mult__Bit1,axiom,
% 28.45/28.47 ! [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) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_diff__bin__simps_I8_J,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_add__Bit1__Bit1,axiom,
% 28.45/28.47 ! [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))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_power__number__of__even,axiom,
% 28.45/28.47 ! [V_w_2,V_z_2,T_b] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_b)
% 28.45/28.47 => 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))) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_zpower__number__of__even,axiom,
% 28.45/28.47 ! [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))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_double__number__of__Bit0,axiom,
% 28.45/28.47 ! [V_w,T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => 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)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_number__of1,axiom,
% 28.45/28.47 ! [V_n] :
% 28.45/28.47 ( 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)))
% 28.45/28.47 => ( 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))))
% 28.45/28.47 & 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)))) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom,
% 28.45/28.47 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_power__number__of__even__number__of,axiom,
% 28.45/28.47 ! [V_w_2,V_v_2,T_b] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_b)
% 28.45/28.47 => 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))) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mult__2__right,axiom,
% 28.45/28.47 ! [V_z,T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => 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) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mult__2,axiom,
% 28.45/28.47 ! [V_z,T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => 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) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_one__add__one__is__two,axiom,
% 28.45/28.47 ! [T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => 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))) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_zero__power2,axiom,
% 28.45/28.47 ! [T_a] :
% 28.45/28.47 ( class_Rings_Osemiring__1(T_a)
% 28.45/28.47 => 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) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_zero__eq__power2,axiom,
% 28.45/28.47 ! [V_a_2,T_b] :
% 28.45/28.47 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 28.45/28.47 => ( 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)
% 28.45/28.47 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_numeral__2__eq__2,axiom,
% 28.45/28.47 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))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_semiring__norm_I115_J,axiom,
% 28.45/28.47 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))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
% 28.45/28.47 ! [V_x,T_a] :
% 28.45/28.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.45/28.47 => 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)))) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_power2__eq__square,axiom,
% 28.45/28.47 ! [V_a,T_a] :
% 28.45/28.47 ( class_Groups_Omonoid__mult(T_a)
% 28.45/28.47 => 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) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom,
% 28.45/28.47 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))))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_add__2__eq__Suc_H,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_add__2__eq__Suc,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_one__power2,axiom,
% 28.45/28.47 ! [T_a] :
% 28.45/28.47 ( class_Rings_Osemiring__1(T_a)
% 28.45/28.47 => 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) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_power2__minus,axiom,
% 28.45/28.47 ! [V_a,T_a] :
% 28.45/28.47 ( class_Rings_Oring__1(T_a)
% 28.45/28.47 => 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)))) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_nat__mult__2__right,axiom,
% 28.45/28.47 ! [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) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_nat__mult__2,axiom,
% 28.45/28.47 ! [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) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_power__even__eq,axiom,
% 28.45/28.47 ! [V_n,V_a,T_a] :
% 28.45/28.47 ( class_Groups_Omonoid__mult(T_a)
% 28.45/28.47 => 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)))) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_transfer__int__nat__numerals_I3_J,axiom,
% 28.45/28.47 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)))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_transfer__nat__int__numerals_I3_J,axiom,
% 28.45/28.47 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)))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_abs__power2,axiom,
% 28.45/28.47 ! [V_a,T_a] :
% 28.45/28.47 ( class_Rings_Olinordered__idom(T_a)
% 28.45/28.47 => 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)))) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_power2__abs,axiom,
% 28.45/28.47 ! [V_a,T_a] :
% 28.45/28.47 ( class_Rings_Olinordered__idom(T_a)
% 28.45/28.47 => 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)))) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_nat__1__add__1,axiom,
% 28.45/28.47 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))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mod2__Suc__Suc,axiom,
% 28.45/28.47 ! [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)))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_div2__Suc__Suc,axiom,
% 28.45/28.47 ! [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))))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_zmod__number__of__Bit0,axiom,
% 28.45/28.47 ! [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))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_add__self__div__2,axiom,
% 28.45/28.47 ! [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 ).
% 28.45/28.47
% 28.45/28.47 fof(fact_half__gt__zero,axiom,
% 28.45/28.47 ! [V_r,T_a] :
% 28.45/28.47 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 28.45/28.47 & class_Int_Onumber__ring(T_a) )
% 28.45/28.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r))
% 28.45/28.47 => 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)))))) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_half__gt__zero__iff,axiom,
% 28.45/28.47 ! [V_r_2,T_b] :
% 28.45/28.47 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 28.45/28.47 & class_Int_Onumber__ring(T_b) )
% 28.45/28.47 => ( 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))))))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_r_2)) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_power2__eq__imp__eq,axiom,
% 28.45/28.47 ! [V_y,V_x,T_a] :
% 28.45/28.47 ( class_Rings_Olinordered__semidom(T_a)
% 28.45/28.47 => ( 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))))
% 28.45/28.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 28.45/28.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 28.45/28.47 => V_x = V_y ) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_power2__le__imp__le,axiom,
% 28.45/28.47 ! [V_y,V_x,T_a] :
% 28.45/28.47 ( class_Rings_Olinordered__semidom(T_a)
% 28.45/28.47 => ( 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))))))
% 28.45/28.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 28.45/28.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_zero__le__power2,axiom,
% 28.45/28.47 ! [V_a,T_a] :
% 28.45/28.47 ( class_Rings_Olinordered__idom(T_a)
% 28.45/28.47 => 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)))))) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_power2__less__0,axiom,
% 28.45/28.47 ! [V_a,T_a] :
% 28.45/28.47 ( class_Rings_Olinordered__idom(T_a)
% 28.45/28.47 => ~ 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))) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_zero__less__power2,axiom,
% 28.45/28.47 ! [V_a_2,T_b] :
% 28.45/28.47 ( class_Rings_Olinordered__idom(T_b)
% 28.45/28.47 => ( 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))))))
% 28.45/28.47 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_sum__power2__eq__zero__iff,axiom,
% 28.45/28.47 ! [V_y_2,V_x_2,T_b] :
% 28.45/28.47 ( class_Rings_Olinordered__idom(T_b)
% 28.45/28.47 => ( 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)
% 28.45/28.47 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 28.45/28.47 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_power2__eq__square__number__of,axiom,
% 28.45/28.47 ! [V_w,T_b] :
% 28.45/28.47 ( ( class_Groups_Omonoid__mult(T_b)
% 28.45/28.47 & class_Int_Onumber(T_b) )
% 28.45/28.47 => 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)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_less__2__cases,axiom,
% 28.45/28.47 ! [V_n] :
% 28.45/28.47 ( 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)))))
% 28.45/28.47 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.45/28.47 | V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_nat__2,axiom,
% 28.45/28.47 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))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_power2__eq__1__iff,axiom,
% 28.45/28.47 ! [V_a_2,T_b] :
% 28.45/28.47 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 28.45/28.47 => ( 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)
% 28.45/28.47 <=> ( V_a_2 = c_Groups_Oone__class_Oone(T_b)
% 28.45/28.47 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
% 28.45/28.47 ! [V_n,V_x,T_a] :
% 28.45/28.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.45/28.47 => 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)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_power__minus__even,axiom,
% 28.45/28.47 ! [V_n,V_a,T_a] :
% 28.45/28.47 ( class_Rings_Oring__1(T_a)
% 28.45/28.47 => 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)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_power2__less__imp__less,axiom,
% 28.45/28.47 ! [V_y,V_x,T_a] :
% 28.45/28.47 ( class_Rings_Olinordered__semidom(T_a)
% 28.45/28.47 => ( 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))))))
% 28.45/28.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 28.45/28.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_sum__power2__ge__zero,axiom,
% 28.45/28.47 ! [V_y,V_x,T_a] :
% 28.45/28.47 ( class_Rings_Olinordered__idom(T_a)
% 28.45/28.47 => 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))))))) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_sum__power2__le__zero__iff,axiom,
% 28.45/28.47 ! [V_y_2,V_x_2,T_b] :
% 28.45/28.47 ( class_Rings_Olinordered__idom(T_b)
% 28.45/28.47 => ( 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)))
% 28.45/28.47 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 28.45/28.47 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_sum__power2__gt__zero__iff,axiom,
% 28.45/28.47 ! [V_y_2,V_x_2,T_b] :
% 28.45/28.47 ( class_Rings_Olinordered__idom(T_b)
% 28.45/28.47 => ( 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)))))))
% 28.45/28.47 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b)
% 28.45/28.47 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_not__sum__power2__lt__zero,axiom,
% 28.45/28.47 ! [V_y,V_x,T_a] :
% 28.45/28.47 ( class_Rings_Olinordered__idom(T_a)
% 28.45/28.47 => ~ 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))) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_power2__sum,axiom,
% 28.45/28.47 ! [V_y,V_x,T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => 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)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_zero__le__even__power_H,axiom,
% 28.45/28.47 ! [V_n,V_a,T_a] :
% 28.45/28.47 ( class_Rings_Olinordered__idom(T_a)
% 28.45/28.47 => 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)))) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_power__odd__eq,axiom,
% 28.45/28.47 ! [V_n,V_a,T_a] :
% 28.45/28.47 ( class_Groups_Omonoid__mult(T_a)
% 28.45/28.47 => 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))))) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom,
% 28.45/28.47 ! [V_n,V_x,T_a] :
% 28.45/28.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.45/28.47 => 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))) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_power__minus1__even,axiom,
% 28.45/28.47 ! [V_n,T_a] :
% 28.45/28.47 ( class_Rings_Oring__1(T_a)
% 28.45/28.47 => 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) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_zdiv__number__of__Bit1,axiom,
% 28.45/28.47 ! [V_v,V_w] :
% 28.45/28.47 ( ( 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)))
% 28.45/28.47 => 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)) )
% 28.45/28.47 & ( ~ 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)))
% 28.45/28.47 => 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)) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mod2__gr__0,axiom,
% 28.45/28.47 ! [V_m_2] :
% 28.45/28.47 ( 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))))))
% 28.45/28.47 <=> 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) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_div__2__gt__zero,axiom,
% 28.45/28.47 ! [V_n] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 28.45/28.47 => 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)))))) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_power2__diff,axiom,
% 28.45/28.47 ! [V_y,V_x,T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => 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)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_odd__0__le__power__imp__0__le,axiom,
% 28.45/28.47 ! [V_n,V_a,T_a] :
% 28.45/28.47 ( class_Rings_Olinordered__idom(T_a)
% 28.45/28.47 => ( 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)))))
% 28.45/28.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_odd__power__less__zero,axiom,
% 28.45/28.47 ! [V_n,V_a,T_a] :
% 28.45/28.47 ( class_Rings_Olinordered__idom(T_a)
% 28.45/28.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 28.45/28.47 => 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))) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_power__minus1__odd,axiom,
% 28.45/28.47 ! [V_n,T_a] :
% 28.45/28.47 ( class_Rings_Oring__1(T_a)
% 28.45/28.47 => 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)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_Suc__n__div__2__gt__zero,axiom,
% 28.45/28.47 ! [V_n] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 28.45/28.47 => 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)))))) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_of__nat__double,axiom,
% 28.45/28.47 ! [V_x,T_a] :
% 28.45/28.47 ( class_Rings_Osemiring__1(T_a)
% 28.45/28.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 28.45/28.47 => 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))) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_pos__zmod__mult__2,axiom,
% 28.45/28.47 ! [V_b,V_a] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 28.45/28.47 => 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))) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_pos__zdiv__mult__2,axiom,
% 28.45/28.47 ! [V_b,V_a] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 28.45/28.47 => 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) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_neg__zdiv__mult__2,axiom,
% 28.45/28.47 ! [V_b,V_a] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.45/28.47 => 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) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_int__of__code,axiom,
% 28.45/28.47 ! [V_k] :
% 28.45/28.47 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 28.45/28.47 => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 28.45/28.47 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 28.45/28.47 => ( ( 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)
% 28.45/28.47 => 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)))))) )
% 28.45/28.47 & ( 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)
% 28.45/28.47 => 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)) ) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_of__int__num,axiom,
% 28.45/28.47 ! [V_k_2,T_b] :
% 28.45/28.47 ( class_Rings_Oring__1(T_b)
% 28.45/28.47 => ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.45/28.47 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = c_Groups_Ozero__class_Ozero(T_b) )
% 28.45/28.47 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.45/28.47 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.45/28.47 => 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))) )
% 28.45/28.47 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.45/28.47 => 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))))) ) ) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_power__m1__odd,axiom,
% 28.45/28.47 ! [V_n,T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => 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) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_rel__simps_I45_J,axiom,
% 28.45/28.47 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ).
% 28.45/28.47
% 28.45/28.47 fof(fact_rel__simps_I42_J,axiom,
% 28.45/28.47 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_rel__simps_I37_J,axiom,
% 28.45/28.47 c_Int_OPls != c_Int_OMin ).
% 28.45/28.47
% 28.45/28.47 fof(fact_rel__simps_I40_J,axiom,
% 28.45/28.47 c_Int_OMin != c_Int_OPls ).
% 28.45/28.47
% 28.45/28.47 fof(fact_rel__simps_I7_J,axiom,
% 28.45/28.47 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_code__numeral__zero__minus__one,axiom,
% 28.45/28.47 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) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_rel__simps_I24_J,axiom,
% 28.45/28.47 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_rel__simps_I47_J,axiom,
% 28.45/28.47 ! [V_k_2] :
% 28.45/28.47 ( c_Int_OBit1(V_k_2) = c_Int_OMin
% 28.45/28.47 <=> V_k_2 = c_Int_OMin ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_rel__simps_I43_J,axiom,
% 28.45/28.47 ! [V_l_2] :
% 28.45/28.47 ( c_Int_OMin = c_Int_OBit1(V_l_2)
% 28.45/28.47 <=> c_Int_OMin = V_l_2 ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_Bit1__Min,axiom,
% 28.45/28.47 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ).
% 28.45/28.47
% 28.45/28.47 fof(fact_bin__less__0__simps_I2_J,axiom,
% 28.45/28.47 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_rel__simps_I23_J,axiom,
% 28.45/28.47 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_rel__simps_I20_J,axiom,
% 28.45/28.47 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_rel__simps_I26_J,axiom,
% 28.45/28.47 ! [V_k_2] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_rel__simps_I30_J,axiom,
% 28.45/28.47 ! [V_k_2] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_rel__simps_I3_J,axiom,
% 28.45/28.47 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_rel__simps_I6_J,axiom,
% 28.45/28.47 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_rel__simps_I13_J,axiom,
% 28.45/28.47 ! [V_k_2] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_rel__simps_I9_J,axiom,
% 28.45/28.47 ! [V_k_2] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_rel__simps_I28_J,axiom,
% 28.45/28.47 ! [V_k_2] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_rel__simps_I8_J,axiom,
% 28.45/28.47 ! [V_k_2] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_eq__number__of__Pls__Min,axiom,
% 28.45/28.47 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) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_Int_OMin__def,axiom,
% 28.45/28.47 c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mult__Min,axiom,
% 28.45/28.47 ! [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) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_neg__number__of__Min,axiom,
% 28.45/28.47 hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_pred__Pls,axiom,
% 28.45/28.47 c_Int_Opred(c_Int_OPls) = c_Int_OMin ).
% 28.45/28.47
% 28.45/28.47 fof(fact_add__Min__right,axiom,
% 28.45/28.47 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_add__Min,axiom,
% 28.45/28.47 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_pred__Min,axiom,
% 28.45/28.47 c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_nonzero__number__of__Min,axiom,
% 28.45/28.47 ! [T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_succ__Min,axiom,
% 28.45/28.47 c_Int_Osucc(c_Int_OMin) = c_Int_OPls ).
% 28.45/28.47
% 28.45/28.47 fof(fact_diff__bin__simps_I2_J,axiom,
% 28.45/28.47 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mult__minus1,axiom,
% 28.45/28.47 ! [V_z,T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => 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) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_mult__minus1__right,axiom,
% 28.45/28.47 ! [V_z,T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => 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) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_number__of__Min,axiom,
% 28.45/28.47 ! [T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => 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)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_arith__simps_I31_J,axiom,
% 28.45/28.47 ! [T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => 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) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_abs__minus__one,axiom,
% 28.45/28.47 ! [T_a] :
% 28.45/28.47 ( ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 & class_Rings_Olinordered__idom(T_a) )
% 28.45/28.47 => 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) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_divide__minus1,axiom,
% 28.45/28.47 ! [V_x,T_a] :
% 28.45/28.47 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 28.45/28.47 & class_Int_Onumber__ring(T_a) )
% 28.45/28.47 => 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) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_rel__simps_I11_J,axiom,
% 28.45/28.47 ! [V_k_2] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_rel__simps_I25_J,axiom,
% 28.45/28.47 ! [V_k_2] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 28.45/28.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_zmod__minus1__right,axiom,
% 28.45/28.47 ! [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) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_diff__bin__simps_I4_J,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_minus__Min,axiom,
% 28.45/28.47 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_pos__zmult__eq__1__iff__lemma,axiom,
% 28.45/28.47 ! [V_n,V_m] :
% 28.45/28.47 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 28.45/28.47 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 28.45/28.47 | V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_zmult__eq__1__iff,axiom,
% 28.45/28.47 ! [V_n_2,V_m_2] :
% 28.45/28.47 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 28.45/28.47 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 28.45/28.47 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 28.45/28.47 | ( V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
% 28.45/28.47 & V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_diff__bin__simps_I6_J,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_diff__bin__simps_I5_J,axiom,
% 28.45/28.47 ! [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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_of__int__m1,axiom,
% 28.45/28.47 ! [T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => 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) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_zdiv__minus1__right,axiom,
% 28.45/28.47 ! [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) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_zero__code__numeral__code,axiom,
% 28.45/28.47 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) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_minus1__divide,axiom,
% 28.45/28.47 ! [V_x,T_a] :
% 28.45/28.47 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 28.45/28.47 & class_Int_Onumber__ring(T_a) )
% 28.45/28.47 => 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)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_abs__power__minus__one,axiom,
% 28.45/28.47 ! [V_n,T_a] :
% 28.45/28.47 ( ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 & class_Rings_Olinordered__idom(T_a) )
% 28.45/28.47 => 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) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_div__eq__minus1,axiom,
% 28.45/28.47 ! [V_b] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 28.45/28.47 => 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) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_div__pos__neg__trivial,axiom,
% 28.45/28.47 ! [V_b,V_a] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 28.45/28.47 => ( 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)))
% 28.45/28.47 => 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) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_zmod__minus1,axiom,
% 28.45/28.47 ! [V_b] :
% 28.45/28.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 28.45/28.47 => 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)) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_one__code__numeral__code,axiom,
% 28.45/28.47 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)) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_power__m1__even,axiom,
% 28.45/28.47 ! [V_n,T_a] :
% 28.45/28.47 ( class_Int_Onumber__ring(T_a)
% 28.45/28.47 => 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) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_Nitpick_OFrac__def,axiom,
% 28.45/28.47 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)))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_int__ge__less__than2__def,axiom,
% 28.45/28.47 ! [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)))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_int__ge__less__than__def,axiom,
% 28.45/28.47 ! [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)))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_inj__graph,axiom,
% 28.45/28.47 ! [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))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_Nitpick_Oprod__def,axiom,
% 28.45/28.47 ! [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)))) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_nat__of__aux__code,axiom,
% 28.45/28.47 ! [V_n,V_i] :
% 28.45/28.47 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 28.45/28.47 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n )
% 28.45/28.47 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 28.45/28.47 => 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)) ) ) ).
% 28.45/28.47
% 28.45/28.47 fof(fact_divmod__int__rel__def,axiom,
% 28.45/28.47 ! [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))))))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_divmod__int__correct,axiom,
% 28.45/28.48 ! [V_a,V_b] :
% 28.45/28.48 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.45/28.48 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_zmult2__lemma,axiom,
% 28.45/28.48 ! [V_c,V_r,V_q,V_b,V_a] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 28.45/28.48 => 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)))) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_code__numeral_Osize_I1_J,axiom,
% 28.45/28.48 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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Nats__number__of,axiom,
% 28.45/28.48 ! [V_w_2,T_b] :
% 28.45/28.48 ( class_Int_Onumber__ring(T_b)
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2))
% 28.45/28.48 => 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))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_bot__empty__eq2,axiom,
% 28.45/28.48 ! [V_y_2,V_x_2,T_c,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 <=> 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)))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_pred__equals__eq2,axiom,
% 28.45/28.48 ! [V_S_2,V_R_2,T_c,T_b] :
% 28.45/28.48 ( 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)
% 28.45/28.48 <=> V_R_2 = V_S_2 ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_inf__Int__eq2,axiom,
% 28.45/28.48 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 <=> 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))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_pred__subset__eq2,axiom,
% 28.45/28.48 ! [V_S_2,V_R_2,T_c,T_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 <=> 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)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_sup__Un__eq2,axiom,
% 28.45/28.48 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 <=> 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))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_enum__ex__prod__def,axiom,
% 28.45/28.48 ! [V_P_2,T_b,T_c] :
% 28.45/28.48 ( ( class_Enum_Oenum(T_c)
% 28.45/28.48 & class_Enum_Oenum(T_b) )
% 28.45/28.48 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_b,T_c)),V_P_2))
% 28.45/28.48 <=> 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))))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_enum__all__prod__def,axiom,
% 28.45/28.48 ! [V_P_2,T_b,T_c] :
% 28.45/28.48 ( ( class_Enum_Oenum(T_c)
% 28.45/28.48 & class_Enum_Oenum(T_b) )
% 28.45/28.48 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_b,T_c)),V_P_2))
% 28.45/28.48 <=> 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))))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Image__iff,axiom,
% 28.45/28.48 ! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
% 28.45/28.48 <=> ? [B_x] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 28.45/28.48 & 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)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rev__ImageI,axiom,
% 28.45/28.48 ! [V_r_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.45/28.48 => ( 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))
% 28.45/28.48 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_unique__remainder,axiom,
% 28.45/28.48 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ( 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)))
% 28.45/28.48 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.45/28.48 => V_r = V_r_H ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_unique__quotient,axiom,
% 28.45/28.48 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ( 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)))
% 28.45/28.48 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.45/28.48 => V_q = V_q_H ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_self__remainder,axiom,
% 28.45/28.48 ! [V_r,V_q,V_a] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.45/28.48 => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_divmod__int__rel__0,axiom,
% 28.45/28.48 ! [V_b] :
% 28.45/28.48 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.45/28.48 => 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)))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_SUP__UN__eq2,axiom,
% 28.45/28.48 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 <=> 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))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_INF__INT__eq2,axiom,
% 28.45/28.48 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 <=> 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))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_self__quotient,axiom,
% 28.45/28.48 ! [V_r,V_q,V_a] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.45/28.48 => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_divmod__int__rel__mod,axiom,
% 28.45/28.48 ! [V_r,V_q,V_b,V_a] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.45/28.48 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_divmod__int__rel__div,axiom,
% 28.45/28.48 ! [V_r,V_q,V_b,V_a] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.45/28.48 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Nats__0,axiom,
% 28.45/28.48 ! [T_b] :
% 28.45/28.48 ( class_Rings_Osemiring__1(T_b)
% 28.45/28.48 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_divmod__int__mod__div,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Nats__add,axiom,
% 28.45/28.48 ! [V_b_2,V_a_2,T_b] :
% 28.45/28.48 ( class_Rings_Osemiring__1(T_b)
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 28.45/28.48 => 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))) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Nats__mult,axiom,
% 28.45/28.48 ! [V_b_2,V_a_2,T_b] :
% 28.45/28.48 ( class_Rings_Osemiring__1(T_b)
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 28.45/28.48 => 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))) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Nats__1,axiom,
% 28.45/28.48 ! [T_b] :
% 28.45/28.48 ( class_Rings_Osemiring__1(T_b)
% 28.45/28.48 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_of__nat__in__Nats,axiom,
% 28.45/28.48 ! [V_n_2,T_b] :
% 28.45/28.48 ( class_Rings_Osemiring__1(T_b)
% 28.45/28.48 => 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))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Image__singleton__iff,axiom,
% 28.45/28.48 ! [V_a_2,V_r_2,T_c,V_b_2,T_b] :
% 28.45/28.48 ( 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))))))
% 28.45/28.48 <=> 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)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_divmod__int__rel__div__mod,axiom,
% 28.45/28.48 ! [V_a,V_b] :
% 28.45/28.48 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.45/28.48 => 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)))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Image__singleton,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_zadd1__lemma,axiom,
% 28.45/28.48 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ( 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)))
% 28.45/28.48 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.45/28.48 => 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)))) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_zminus1__lemma,axiom,
% 28.45/28.48 ! [V_r_2,V_q_2,V_b_2,V_a_2] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => 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))))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_divmod__int__relI,axiom,
% 28.45/28.48 ! [V_r,V_q,V_b,V_a] :
% 28.45/28.48 ( 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)
% 28.45/28.48 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 28.45/28.48 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) ) )
% 28.45/28.48 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 28.45/28.48 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 28.45/28.48 => 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))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_zmult1__lemma,axiom,
% 28.45/28.48 ! [V_a,V_r,V_q,V_c,V_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.45/28.48 => 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)))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_pair__imageI,axiom,
% 28.45/28.48 ! [V_f_2,T_d,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => 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))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_norm__frac_Osimps,axiom,
% 28.45/28.48 ! [V_a_2,V_b_2] :
% 28.45/28.48 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.45/28.48 => 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)) )
% 28.45/28.48 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.45/28.48 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.45/28.48 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 28.45/28.48 => 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)) )
% 28.45/28.48 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.45/28.48 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 28.45/28.48 => 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))) ) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_adjust__eq,axiom,
% 28.45/28.48 ! [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))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_sup2E,axiom,
% 28.45/28.48 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 28.45/28.48 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_sup2CI,axiom,
% 28.45/28.48 ! [T_c,T_b,V_A_2,V_y_2,V_x_2,V_B_2] :
% 28.45/28.48 ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 28.45/28.48 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) )
% 28.45/28.48 => 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)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_inf2I,axiom,
% 28.45/28.48 ! [T_c,T_b,V_B_2,V_y_2,V_x_2,V_A_2] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 28.45/28.48 => 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)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_inf2E,axiom,
% 28.45/28.48 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 28.45/28.48 => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_mem__splitI,axiom,
% 28.45/28.48 ! [T_d,T_c,V_b_2,V_a_2,V_c_2,V_z_2,T_b] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_c_2,V_a_2),V_b_2)))
% 28.45/28.48 => 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)))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_splitI,axiom,
% 28.45/28.48 ! [T_c,T_b,V_b_2,V_a_2,V_f_2] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2))
% 28.45/28.48 => 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))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_prod__caseI,axiom,
% 28.45/28.48 ! [T_c,T_b,V_b_2,V_a_2,V_f1_2] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2))
% 28.45/28.48 => 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))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_bot2E,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_swap__inj__on,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_splitD_H,axiom,
% 28.45/28.48 ! [V_c_2,V_b_2,V_a_2,V_R_2,T_d,T_c,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_c_2)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_inf2D1,axiom,
% 28.45/28.48 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_inf2D2,axiom,
% 28.45/28.48 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_sup2I1,axiom,
% 28.45/28.48 ! [V_B_2,T_c,T_b,V_y_2,V_x_2,V_A_2] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 28.45/28.48 => 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)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_sup2I2,axiom,
% 28.45/28.48 ! [V_A_2,T_c,T_b,V_y_2,V_x_2,V_B_2] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 28.45/28.48 => 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)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rev__predicate2D,axiom,
% 28.45/28.48 ! [V_Q_2,T_c,T_b,V_y_2,V_x_2,V_P_2] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 28.45/28.48 => ( 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))
% 28.45/28.48 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_predicate2D,axiom,
% 28.45/28.48 ! [V_y_2,V_x_2,V_Q_2,V_P_2,T_c,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 28.45/28.48 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Pair__inject,axiom,
% 28.45/28.48 ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] :
% 28.45/28.48 ( 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)
% 28.45/28.48 => ~ ( V_a = V_a_H
% 28.45/28.48 => V_b != V_b_H ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Pair__eq,axiom,
% 28.45/28.48 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 28.45/28.48 ( 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)
% 28.45/28.48 <=> ( V_a_2 = V_a_H_2
% 28.45/28.48 & V_b_2 = V_b_H_2 ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_split__paired__All,axiom,
% 28.45/28.48 ! [T_c,T_b,V_P_2] :
% 28.45/28.48 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 28.45/28.48 <=> ! [B_a,B_b] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_split__weak__cong,axiom,
% 28.45/28.48 ! [V_c_2,T_d,T_c,T_b,V_q_2,V_p_2] :
% 28.45/28.48 ( V_p_2 = V_q_2
% 28.45/28.48 => 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) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_split__twice,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_split__conv,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_prod_Osimps_I2_J,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_splitD,axiom,
% 28.45/28.48 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_split__eta,axiom,
% 28.45/28.48 ! [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 ).
% 28.45/28.48
% 28.45/28.48 fof(fact_The__split__eq,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_split__paired__The,axiom,
% 28.45/28.48 ! [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)))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_adjust__def,axiom,
% 28.45/28.48 ! [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))))))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_in__rel__def,axiom,
% 28.45/28.48 ! [V_y_2,V_x_2,V_R_2,T_c,T_b] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_b,T_c,V_R_2),V_x_2),V_y_2))
% 28.45/28.48 <=> 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)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_div__mod__code__numeral__def,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_negDivAlg__eqn__1__number__of,axiom,
% 28.45/28.48 ! [V_w] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ( ( 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))))
% 28.45/28.48 => 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))) )
% 28.45/28.48 & ( ~ 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))))
% 28.45/28.48 => 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)))) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_negDivAlg__correct,axiom,
% 28.45/28.48 ! [V_b,V_a] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 28.45/28.48 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_negDivAlg__div__mod,axiom,
% 28.45/28.48 ! [V_l,V_k] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 28.45/28.48 => 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)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_negDivAlg__minus1,axiom,
% 28.45/28.48 ! [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))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_negDivAlg_Osimps,axiom,
% 28.45/28.48 ! [V_b,V_a] :
% 28.45/28.48 ( ( ( 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)))
% 28.45/28.48 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 28.45/28.48 => 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)) )
% 28.45/28.48 & ( ~ ( 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)))
% 28.45/28.48 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 28.45/28.48 => 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))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_negDivAlg__eqn__number__of,axiom,
% 28.45/28.48 ! [V_w,V_v] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ( ( 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))))
% 28.45/28.48 => 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))) )
% 28.45/28.48 & ( ~ 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))))
% 28.45/28.48 => 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)))) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_negDivAlg__eqn,axiom,
% 28.45/28.48 ! [V_a,V_b] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 28.45/28.48 => ( ( 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)))
% 28.45/28.48 => 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)) )
% 28.45/28.48 & ( ~ 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)))
% 28.45/28.48 => 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))) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Nitpick_Orefl_H__def,axiom,
% 28.45/28.48 ! [V_r_2,T_b] :
% 28.45/28.48 ( c_Nitpick_Orefl_H(T_b,V_r_2)
% 28.45/28.48 <=> ! [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)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_posDivAlg__eqn__1__number__of,axiom,
% 28.45/28.48 ! [V_w] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ( ( 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)))
% 28.45/28.48 => 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)) )
% 28.45/28.48 & ( ~ 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)))
% 28.45/28.48 => 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)))) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_posDivAlg_Osimps,axiom,
% 28.45/28.48 ! [V_b,V_a] :
% 28.45/28.48 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 28.45/28.48 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 28.45/28.48 => 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) )
% 28.45/28.48 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 28.45/28.48 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 28.45/28.48 => 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))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_posDivAlg__0,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_posDivAlg__correct,axiom,
% 28.45/28.48 ! [V_b,V_a] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 28.45/28.48 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_posDivAlg__div__mod,axiom,
% 28.45/28.48 ! [V_l,V_k] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 28.45/28.48 => 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)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_posDivAlg__eqn__number__of,axiom,
% 28.45/28.48 ! [V_w,V_v] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ( ( 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)))
% 28.45/28.48 => 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)) )
% 28.45/28.48 & ( ~ 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)))
% 28.45/28.48 => 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)))) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_posDivAlg__eqn,axiom,
% 28.45/28.48 ! [V_a,V_b] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 28.45/28.48 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 28.45/28.48 => 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) )
% 28.45/28.48 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 28.45/28.48 => 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))) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_divmod__int__def,axiom,
% 28.45/28.48 ! [V_b,V_a] :
% 28.45/28.48 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 28.45/28.48 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 28.45/28.48 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) )
% 28.45/28.48 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 28.45/28.48 => ( ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.45/28.48 => 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)) )
% 28.45/28.48 & ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.45/28.48 => 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))) ) ) ) ) )
% 28.45/28.48 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 28.45/28.48 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 28.45/28.48 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) )
% 28.45/28.48 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 28.45/28.48 => 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))) ) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_divmod__nat__step,axiom,
% 28.45/28.48 ! [V_m,V_n] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 28.45/28.48 => 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)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_divmod__int__pdivmod,axiom,
% 28.45/28.48 ! [V_l_2,V_k_2] :
% 28.45/28.48 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.45/28.48 => 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)) )
% 28.45/28.48 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.45/28.48 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.45/28.48 => 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) )
% 28.45/28.48 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.45/28.48 => 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)))) ) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_apsnd__compose,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_negateSnd__def,axiom,
% 28.45/28.48 c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_apsnd__conv,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_divmod__nat__zero,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_divmod__nat__base,axiom,
% 28.45/28.48 ! [V_n,V_m] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 28.45/28.48 => 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) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_negateSnd__eq,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_divmod__nat__div__mod,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_divmod__int__rel__neg,axiom,
% 28.45/28.48 ! [V_qr,V_b,V_a] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_divmod__nat__if,axiom,
% 28.45/28.48 ! [V_m_2,V_n_2] :
% 28.45/28.48 ( ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.45/28.48 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 28.45/28.48 => 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) )
% 28.45/28.48 & ( ~ ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.45/28.48 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 28.45/28.48 => 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)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_pdivmod__def,axiom,
% 28.45/28.48 ! [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))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_pdivmod__posDivAlg,axiom,
% 28.45/28.48 ! [V_k,V_l] :
% 28.45/28.48 ( ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.45/28.48 => 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)) )
% 28.45/28.48 & ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.45/28.48 => 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)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_divmod__int__code,axiom,
% 28.45/28.48 ! [V_l_2,V_k_2] :
% 28.45/28.48 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.45/28.48 => 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)) )
% 28.45/28.48 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.45/28.48 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.45/28.48 => 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) )
% 28.45/28.48 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.45/28.48 => 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)))) ) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_divmod__nat__rel__mult1__eq,axiom,
% 28.45/28.48 ! [V_a,V_r,V_q,V_c,V_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 28.45/28.48 => 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)))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_divmod__nat__rel__mult2__eq,axiom,
% 28.45/28.48 ! [V_c,V_r,V_q,V_b,V_a] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b))
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 28.45/28.48 => 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)))) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_negDivAlg_Opsimps,axiom,
% 28.45/28.48 ! [V_b_2,V_a_2] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ( ( ( 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)))
% 28.45/28.48 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 28.45/28.48 => 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)) )
% 28.45/28.48 & ( ~ ( 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)))
% 28.45/28.48 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 28.45/28.48 => 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))) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_divmod__nat__rel__unique,axiom,
% 28.45/28.48 ! [V_qr_H,V_qr,V_n,V_m] :
% 28.45/28.48 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 28.45/28.48 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H))
% 28.45/28.48 => V_qr = V_qr_H ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_divmod__nat__rel__divmod__nat,axiom,
% 28.45/28.48 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_divmod__nat__eq,axiom,
% 28.45/28.48 ! [V_qr,V_n,V_m] :
% 28.45/28.48 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 28.45/28.48 => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_divmod__nat__def,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_mod__eq,axiom,
% 28.45/28.48 ! [V_r,V_q,V_n,V_m] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_div__eq,axiom,
% 28.45/28.48 ! [V_r,V_q,V_n,V_m] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_divmod__nat__rel,axiom,
% 28.45/28.48 ! [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)))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_divmod__nat__rel__add1__eq,axiom,
% 28.45/28.48 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ( 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)))
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 28.45/28.48 => 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)))) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_posDivAlg_Opsimps,axiom,
% 28.45/28.48 ! [V_b_2,V_a_2] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 28.45/28.48 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 28.45/28.48 => 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) )
% 28.45/28.48 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 28.45/28.48 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 28.45/28.48 => 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))) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_norm__frac_Opsimps,axiom,
% 28.45/28.48 ! [V_b_2,V_a_2] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.45/28.48 => 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)) )
% 28.45/28.48 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.45/28.48 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.45/28.48 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 28.45/28.48 => 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)) )
% 28.45/28.48 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.45/28.48 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 28.45/28.48 => 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))) ) ) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_negDivAlg_Opinduct,axiom,
% 28.45/28.48 ! [V_P_2,V_a1_2,V_a0_2] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ( ! [B_a,B_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ( ( ~ ( 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)))
% 28.45/28.48 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 28.45/28.48 => 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))) )
% 28.45/28.48 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 28.45/28.48 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_posDivAlg_Opinduct,axiom,
% 28.45/28.48 ! [V_P_2,V_a1_2,V_a0_2] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ( ! [B_a,B_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b))
% 28.45/28.48 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 28.45/28.48 => 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))) )
% 28.45/28.48 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 28.45/28.48 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_accp__subset,axiom,
% 28.45/28.48 ! [V_R2_2,V_R1_2,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => 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))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_mod__pos__neg__1__number__of,axiom,
% 28.45/28.48 ! [V_w] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => 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))))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_snd__eqD,axiom,
% 28.45/28.48 ! [V_a,V_y,V_x,T_a,T_b] :
% 28.45/28.48 ( 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
% 28.45/28.48 => V_y = V_a ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_snd__conv,axiom,
% 28.45/28.48 ! [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 ).
% 28.45/28.48
% 28.45/28.48 fof(fact_snd__def,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_snd__apsnd,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_apsnd__eq__conv,axiom,
% 28.45/28.48 ! [V_g_2,V_x_2,V_f_2,T_b,T_c,T_d] :
% 28.45/28.48 ( 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)
% 28.45/28.48 <=> 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)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_mod__int__def,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_accp__downward,axiom,
% 28.45/28.48 ! [V_a_2,V_b_2,V_r_2,T_b] :
% 28.45/28.48 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_b_2))
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 28.45/28.48 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_accp_Oequations,axiom,
% 28.45/28.48 ! [V_a_2,V_r_2,T_b] :
% 28.45/28.48 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
% 28.45/28.48 <=> ! [B_x] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 28.45/28.48 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_accp_Osimps,axiom,
% 28.45/28.48 ! [V_a_2,V_r_2,T_b] :
% 28.45/28.48 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
% 28.45/28.48 <=> ! [B_x] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 28.45/28.48 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_mod__neg__pos,axiom,
% 28.45/28.48 ! [V_b,V_a] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 28.45/28.48 => 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)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_mod__pos__pos,axiom,
% 28.45/28.48 ! [V_b,V_a] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 28.45/28.48 => 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)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_mod__pos__pos__1__number__of,axiom,
% 28.45/28.48 ! [V_w] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => 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))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_mod__pos__neg,axiom,
% 28.45/28.48 ! [V_b,V_a] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.45/28.48 => 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)))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_mod__neg__neg,axiom,
% 28.45/28.48 ! [V_b,V_a] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.45/28.48 => 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)))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_nat__gcd_Opsimps,axiom,
% 28.45/28.48 ! [V_y_2,V_x_2] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.45/28.48 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 )
% 28.45/28.48 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.45/28.48 => 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)) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_nat_Osize_I2_J,axiom,
% 28.45/28.48 ! [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))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_in__measure,axiom,
% 28.45/28.48 ! [V_f_2,V_y_2,V_x_2,T_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 <=> 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))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_mod__nat__def,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_nat_Osize_I1_J,axiom,
% 28.45/28.48 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_irrefl__def,axiom,
% 28.45/28.48 ! [V_r_2,T_b] :
% 28.45/28.48 ( c_Relation_Oirrefl(T_b,V_r_2)
% 28.45/28.48 <=> ! [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)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_norm__frac_Opinduct,axiom,
% 28.45/28.48 ! [V_P_2,V_a1_2,V_a0_2] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ( ! [B_a,B_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.45/28.48 => 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))) )
% 28.45/28.48 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 28.45/28.48 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_div__pos__neg__1__number__of,axiom,
% 28.45/28.48 ! [V_w] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => 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))))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Pair__fst__snd__eq,axiom,
% 28.45/28.48 ! [T_c,T_b,V_t_2,V_s_2] :
% 28.45/28.48 ( V_s_2 = V_t_2
% 28.45/28.48 <=> ( hAPP(c_Product__Type_Ofst(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Ofst(T_b,T_c),V_t_2)
% 28.45/28.48 & hAPP(c_Product__Type_Osnd(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Osnd(T_b,T_c),V_t_2) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_prod__eqI,axiom,
% 28.45/28.48 ! [V_q,V_p,T_b,T_a] :
% 28.45/28.48 ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q)
% 28.45/28.48 => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q)
% 28.45/28.48 => V_p = V_q ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_fst__eqD,axiom,
% 28.45/28.48 ! [V_a,V_y,V_x,T_b,T_a] :
% 28.45/28.48 ( 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
% 28.45/28.48 => V_x = V_a ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_fst__conv,axiom,
% 28.45/28.48 ! [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 ).
% 28.45/28.48
% 28.45/28.48 fof(fact_fst__def,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_fst__apsnd,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_pair__collapse,axiom,
% 28.45/28.48 ! [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 ).
% 28.45/28.48
% 28.45/28.48 fof(fact_surjective__pairing,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_prod__case__beta,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_div__int__def,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_split__beta,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_split__comp__eq,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_split__def,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_split__comp,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_The__split,axiom,
% 28.45/28.48 ! [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))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_div__neg__pos,axiom,
% 28.45/28.48 ! [V_b,V_a] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 28.45/28.48 => 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)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_div__pos__pos,axiom,
% 28.45/28.48 ! [V_b,V_a] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 28.45/28.48 => 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)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_div__pos__pos__1__number__of,axiom,
% 28.45/28.48 ! [V_w] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => 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))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_div__pos__neg,axiom,
% 28.45/28.48 ! [V_b,V_a] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.45/28.48 => 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)))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_div__neg__neg,axiom,
% 28.45/28.48 ! [V_b,V_a] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.45/28.48 => 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)))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_prod__size__simp,axiom,
% 28.45/28.48 ! [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))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_exI__realizer,axiom,
% 28.45/28.48 ! [T_b,T_c,V_x_2,V_y_2,V_P_2] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(V_P_2,V_y_2),V_x_2))
% 28.45/28.48 => 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)))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_conjI__realizer,axiom,
% 28.45/28.48 ! [T_c,T_b,V_q_2,V_Q_2,V_p_2,V_P_2] :
% 28.45/28.48 ( hBOOL(hAPP(V_P_2,V_p_2))
% 28.45/28.48 => ( hBOOL(hAPP(V_Q_2,V_q_2))
% 28.45/28.48 => ( 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))))
% 28.45/28.48 & 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)))) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_div__nat__def,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_divmod__nat__rel__def,axiom,
% 28.45/28.48 ! [V_qr_2,V_n_2,V_m_2] :
% 28.45/28.48 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2))
% 28.45/28.48 <=> ( 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))
% 28.45/28.48 & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.45/28.48 => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 28.45/28.48 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.45/28.48 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 28.45/28.48 => ( 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)))
% 28.45/28.48 & 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)) ) )
% 28.45/28.48 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 28.45/28.48 => ( 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)))
% 28.45/28.48 & 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))) ) ) ) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_nat__def,axiom,
% 28.45/28.48 ! [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)))))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_nat__gcd_Opinduct,axiom,
% 28.45/28.48 ! [V_P_2,V_a1_2,V_a0_2] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ( ! [B_x,B_y] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.45/28.48 => hBOOL(hAPP(hAPP(V_P_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) )
% 28.45/28.48 => hBOOL(hAPP(hAPP(V_P_2,B_x),B_y)) ) )
% 28.45/28.48 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_inv__image__def,axiom,
% 28.45/28.48 ! [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))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Rep__Integ__inject,axiom,
% 28.45/28.48 ! [V_y_2,V_x_2] :
% 28.45/28.48 ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2)
% 28.45/28.48 <=> V_x_2 = V_y_2 ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_in__inv__image,axiom,
% 28.45/28.48 ! [V_f_2,V_r_2,T_c,V_y_2,V_x_2,T_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 <=> 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)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rp__inv__image__def,axiom,
% 28.45/28.48 ! [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))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_equiv__class__nondisjoint,axiom,
% 28.45/28.48 ! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_b] :
% 28.45/28.48 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 28.45/28.48 => ( 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)))))))
% 28.45/28.48 => 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)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_subset__equiv__class,axiom,
% 28.45/28.48 ! [V_a_2,V_b_2,V_r_2,V_A_2,T_b] :
% 28.45/28.48 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 28.45/28.48 => ( 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))))))
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 28.45/28.48 => 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)) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Union__quotient,axiom,
% 28.45/28.48 ! [V_r_2,V_A_2,T_b] :
% 28.45/28.48 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 28.45/28.48 => 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 ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_equiv__class__self,axiom,
% 28.45/28.48 ! [V_a_2,V_r_2,V_A_2,T_b] :
% 28.45/28.48 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.45/28.48 => 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)))))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_quotient__disj,axiom,
% 28.45/28.48 ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 28.45/28.48 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 28.45/28.48 => ( 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)))
% 28.45/28.48 => ( 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)))
% 28.45/28.48 => ( V_X_2 = V_Y_2
% 28.45/28.48 | 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)) ) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_equiv__class__eq,axiom,
% 28.45/28.48 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
% 28.45/28.48 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 28.45/28.48 => ( 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))
% 28.45/28.48 => 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)))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_quotient__eq__iff,axiom,
% 28.45/28.48 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 28.45/28.48 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 28.45/28.48 => ( 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)))
% 28.45/28.48 => ( 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)))
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
% 28.45/28.48 => ( V_X_2 = V_Y_2
% 28.45/28.48 <=> 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)) ) ) ) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_quotient__eqI,axiom,
% 28.45/28.48 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 28.45/28.48 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 28.45/28.48 => ( 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)))
% 28.45/28.48 => ( 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)))
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
% 28.45/28.48 => ( 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))
% 28.45/28.48 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_equiv__class__eq__iff,axiom,
% 28.45/28.48 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 28.45/28.48 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 28.45/28.48 => ( 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))
% 28.45/28.48 <=> ( 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))))
% 28.45/28.48 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.45/28.48 & hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_eq__equiv__class,axiom,
% 28.45/28.48 ! [V_A_2,V_b_2,V_a_2,V_r_2,T_b] :
% 28.45/28.48 ( 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))))
% 28.45/28.48 => ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 28.45/28.48 => 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)) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_eq__equiv__class__iff,axiom,
% 28.45/28.48 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 28.45/28.48 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 28.45/28.48 => ( 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))))
% 28.45/28.48 <=> 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)) ) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_equiv__class__subset,axiom,
% 28.45/28.48 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
% 28.45/28.48 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 28.45/28.48 => ( 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))
% 28.45/28.48 => 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)))))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_eq__equiv__class__iff2,axiom,
% 28.45/28.48 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 28.45/28.48 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 28.45/28.48 => ( 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)
% 28.45/28.48 <=> 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)) ) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_UN__equiv__class,axiom,
% 28.45/28.48 ! [V_a_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 28.45/28.48 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 28.45/28.48 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.45/28.48 => 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) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_UN__equiv__class2,axiom,
% 28.45/28.48 ! [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] :
% 28.45/28.48 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 28.45/28.48 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 28.45/28.48 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a1_2),V_A1_2))
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a2_2),V_A2_2))
% 28.45/28.48 => 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) ) ) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_in__finite__psubset,axiom,
% 28.45/28.48 ! [V_B_2,V_A_2,T_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.45/28.48 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_congruent2__implies__congruent,axiom,
% 28.45/28.48 ! [V_a_2,V_f_2,V_r2_2,T_d,T_c,V_r1_2,V_A_2,T_b] :
% 28.45/28.48 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r1_2)
% 28.45/28.48 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.45/28.48 => c_Equiv__Relations_Ocongruent(T_c,T_d,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_congruent2D,axiom,
% 28.45/28.48 ! [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] :
% 28.45/28.48 ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
% 28.45/28.48 => ( 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))
% 28.45/28.48 => ( 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))
% 28.45/28.48 => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_congruentD,axiom,
% 28.45/28.48 ! [V_z_2,V_y_2,V_f_2,V_r_2,T_c,T_b] :
% 28.45/28.48 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
% 28.45/28.48 => ( 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))
% 28.45/28.48 => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_congruent2__implies__congruent__UN,axiom,
% 28.45/28.48 ! [V_a_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
% 28.45/28.48 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 28.45/28.48 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 28.45/28.48 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A2_2))
% 28.45/28.48 => 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)) ) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_finite__psubset__def,axiom,
% 28.45/28.48 ! [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)))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_UN__equiv__class__inject,axiom,
% 28.45/28.48 ! [V_Y_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 28.45/28.48 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 28.45/28.48 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 28.45/28.48 => ( 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)
% 28.45/28.48 => ( 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)))
% 28.45/28.48 => ( 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)))
% 28.45/28.48 => ( ! [B_x] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.45/28.48 => ! [B_y] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 28.45/28.48 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 28.45/28.48 => 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)) ) ) )
% 28.45/28.48 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_UN__equiv__class__type2,axiom,
% 28.45/28.48 ! [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] :
% 28.45/28.48 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 28.45/28.48 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 28.45/28.48 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 28.45/28.48 => ( 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)))
% 28.45/28.48 => ( 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)))
% 28.45/28.48 => ( ! [B_x1] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x1),V_A1_2))
% 28.45/28.48 => ! [B_x2] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x2),V_A2_2))
% 28.45/28.48 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) )
% 28.45/28.48 => 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)) ) ) ) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_UN__equiv__class__type,axiom,
% 28.45/28.48 ! [V_B_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 28.45/28.48 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 28.45/28.48 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 28.45/28.48 => ( 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)))
% 28.45/28.48 => ( ! [B_x] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.45/28.48 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) )
% 28.45/28.48 => 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)) ) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_mlex__leq,axiom,
% 28.45/28.48 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ( 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))
% 28.45/28.48 => 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))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_code__numeral_Osize_I2_J,axiom,
% 28.45/28.48 ! [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))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_mlex__less,axiom,
% 28.45/28.48 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => 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))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_code__numeral_Oinject,axiom,
% 28.45/28.48 ! [V_code__numeral_H_2,V_code__numeral_2] :
% 28.45/28.48 ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2)
% 28.45/28.48 <=> V_code__numeral_2 = V_code__numeral_H_2 ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_code__numeral_Osimps_I2_J,axiom,
% 28.45/28.48 ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_code__numeral_Osimps_I3_J,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Suc__code__numeral__minus__one,axiom,
% 28.45/28.48 ! [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 ).
% 28.45/28.48
% 28.45/28.48 fof(fact_code__numeral_Osize_I4_J,axiom,
% 28.45/28.48 ! [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))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_nat_Osize_I4_J,axiom,
% 28.45/28.48 ! [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))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_prod_Orecs,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_nat__size,axiom,
% 28.45/28.48 ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n ).
% 28.45/28.48
% 28.45/28.48 fof(fact_nat_Osize_I3_J,axiom,
% 28.45/28.48 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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_code__numeral_Osize_I3_J,axiom,
% 28.45/28.48 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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_lfp__induct2,axiom,
% 28.45/28.48 ! [V_P_2,V_f_2,V_b_2,V_a_2,T_c,T_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ( 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)
% 28.45/28.48 => ( ! [B_a,B_b] :
% 28.45/28.48 ( 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))))))
% 28.45/28.48 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) )
% 28.45/28.48 => hBOOL(hAPP(hAPP(V_P_2,V_a_2),V_b_2)) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_in__lex__prod,axiom,
% 28.45/28.48 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 <=> ( 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))
% 28.45/28.48 | ( V_a_2 = V_a_H_2
% 28.45/28.48 & 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)) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_equivp__equiv,axiom,
% 28.45/28.48 ! [V_A_2,T_b] :
% 28.45/28.48 ( c_Equiv__Relations_Oequiv(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_A_2)
% 28.45/28.48 <=> 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)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_identity__equivp,axiom,
% 28.45/28.48 ! [T_b] : c_Equiv__Relations_Oequivp(T_b,c_fequal) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_equivp__def,axiom,
% 28.45/28.48 ! [V_R_2,T_b] :
% 28.45/28.48 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 28.45/28.48 <=> ! [B_x,B_y] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
% 28.45/28.48 <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_equivp__reflp,axiom,
% 28.45/28.48 ! [V_x_2,V_R_2,T_b] :
% 28.45/28.48 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 28.45/28.48 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_equivp__symp,axiom,
% 28.45/28.48 ! [V_y_2,V_x_2,V_R_2,T_b] :
% 28.45/28.48 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 28.45/28.48 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_equivp__transp,axiom,
% 28.45/28.48 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] :
% 28.45/28.48 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
% 28.45/28.48 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_same__fstI,axiom,
% 28.45/28.48 ! [T_b,V_R_2,V_y_2,V_y_H_2,T_c,V_x_2,V_P_2] :
% 28.45/28.48 ( hBOOL(hAPP(V_P_2,V_x_2))
% 28.45/28.48 => ( 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)))
% 28.45/28.48 => 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))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_apfst__apsnd,axiom,
% 28.45/28.48 ! [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))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_apsnd__apfst,axiom,
% 28.45/28.48 ! [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))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_apfst__conv,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_fst__apfst,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_apfst__eq__conv,axiom,
% 28.45/28.48 ! [V_g_2,V_x_2,V_f_2,T_c,T_b,T_d] :
% 28.45/28.48 ( 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)
% 28.45/28.48 <=> 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)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_snd__apfst,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_apfst__compose,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_apsnd__apfst__commute,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_pair__lessI2,axiom,
% 28.45/28.48 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2))
% 28.45/28.48 => 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)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_ImageE,axiom,
% 28.45/28.48 ! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
% 28.45/28.48 => ~ ! [B_x] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_mlex__prod__def,axiom,
% 28.45/28.48 ! [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))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_pair__less__def,axiom,
% 28.45/28.48 c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_measure__def,axiom,
% 28.45/28.48 ! [T_b] : c_Wellfounded_Omeasure(T_b) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_b),c_Wellfounded_Oless__than) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_less__than__iff,axiom,
% 28.45/28.48 ! [V_y_2,V_x_2] :
% 28.45/28.48 ( 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))
% 28.45/28.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_pair__lessI1,axiom,
% 28.45/28.48 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 28.45/28.48 => 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)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_pair__leqI2,axiom,
% 28.45/28.48 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2))
% 28.45/28.48 => 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)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_smin__insertI,axiom,
% 28.45/28.48 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 28.45/28.48 => ( 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))
% 28.45/28.48 => ( 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))
% 28.45/28.48 => 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)) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_smax__insertI,axiom,
% 28.45/28.48 ! [V_X_2,V_x_2,V_Y_2,V_y_2] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2))
% 28.45/28.48 => ( 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))
% 28.45/28.48 => ( 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))
% 28.45/28.48 => 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)) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_smax__emptyI,axiom,
% 28.45/28.48 ! [V_Y_2] :
% 28.45/28.48 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2))
% 28.45/28.48 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 28.45/28.48 => 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)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_smin__emptyI,axiom,
% 28.45/28.48 ! [V_X_2] :
% 28.45/28.48 ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 28.45/28.48 => 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)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_pair__leqI1,axiom,
% 28.45/28.48 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 28.45/28.48 => 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)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wmax__insertI,axiom,
% 28.45/28.48 ! [V_XS_2,V_x_2,V_YS_2,V_y_2] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))
% 28.45/28.48 => ( 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))
% 28.45/28.48 => ( 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))
% 28.45/28.48 => 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)) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wmin__insertI,axiom,
% 28.45/28.48 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 28.45/28.48 => ( 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))
% 28.45/28.48 => ( 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))
% 28.45/28.48 => 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)) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Field__insert,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Field__Union,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Field__empty,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_mono__Field,axiom,
% 28.45/28.48 ! [V_s_2,V_r_2,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => 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))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Field__Un,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_finite__Field,axiom,
% 28.45/28.48 ! [V_r_2,T_b] :
% 28.45/28.48 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 28.45/28.48 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_OField(T_b),V_r_2))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wmin__emptyI,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wmax__emptyI,axiom,
% 28.45/28.48 ! [V_X_2] :
% 28.45/28.48 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2))
% 28.45/28.48 => 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)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_min__weak__def,axiom,
% 28.45/28.48 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)))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_max__weak__def,axiom,
% 28.45/28.48 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)))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Id__on__def,axiom,
% 28.45/28.48 ! [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)))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Id__on__def_H,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Id__on__empty,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Image__Id__on,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Id__on__iff,axiom,
% 28.45/28.48 ! [V_A_2,V_y_2,V_x_2,T_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 <=> ( V_x_2 = V_y_2
% 28.45/28.48 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Id__on__eqI,axiom,
% 28.45/28.48 ! [V_A_2,T_b,V_b_2,V_a_2] :
% 28.45/28.48 ( V_a_2 = V_b_2
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.45/28.48 => 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))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_max__strict__def,axiom,
% 28.45/28.48 c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_max__ext__additive,axiom,
% 28.45/28.48 ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ( 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)))
% 28.45/28.48 => 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))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_min__strict__def,axiom,
% 28.45/28.48 c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_max__extp__max__ext__eq,axiom,
% 28.45/28.48 ! [V_xa_2,V_x_2,V_R_2,T_b] :
% 28.45/28.48 ( 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)
% 28.45/28.48 <=> 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))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_min__rpair__set,axiom,
% 28.45/28.48 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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_max__rpair__set,axiom,
% 28.45/28.48 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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rp__inv__image__rp,axiom,
% 28.45/28.48 ! [V_f_2,T_c,V_P_2,T_b] :
% 28.45/28.48 ( c_FunDef_Oreduction__pair(T_b,V_P_2)
% 28.45/28.48 => c_FunDef_Oreduction__pair(T_c,hAPP(hAPP(c_FunDef_Orp__inv__image(T_b,T_c),V_P_2),V_f_2)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_equiv__intrel__iff,axiom,
% 28.45/28.48 ! [V_y_2,V_x_2] :
% 28.45/28.48 ( 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))))
% 28.45/28.48 <=> 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)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_intrel__iff,axiom,
% 28.45/28.48 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 28.45/28.48 ( 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))
% 28.45/28.48 <=> 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) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Id__onE,axiom,
% 28.45/28.48 ! [V_A_2,V_c_2,T_b] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_c_2),c_Relation_OId__on(T_b,V_A_2)))
% 28.45/28.48 => ~ ! [B_x] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.45/28.48 => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_equiv__intrel,axiom,
% 28.45/28.48 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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_of__int,axiom,
% 28.45/28.48 ! [V_j_2,V_i_2,T_b] :
% 28.45/28.48 ( class_Rings_Oring__1(T_b)
% 28.45/28.48 => 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)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_One__int__def,axiom,
% 28.45/28.48 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))))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_mult,axiom,
% 28.45/28.48 ! [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))))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Rep__Integ__inverse,axiom,
% 28.45/28.48 ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2 ).
% 28.45/28.48
% 28.45/28.48 fof(fact_minus,axiom,
% 28.45/28.48 ! [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))))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Zero__int__def,axiom,
% 28.45/28.48 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))))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_int__def,axiom,
% 28.45/28.48 ! [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))))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_add,axiom,
% 28.45/28.48 ! [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))))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_nat,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_minus__int__def,axiom,
% 28.45/28.48 ! [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))))))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_less,axiom,
% 28.45/28.48 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 28.45/28.48 ( 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)))))))
% 28.45/28.48 <=> 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))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_le,axiom,
% 28.45/28.48 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 28.45/28.48 ( 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)))))))
% 28.45/28.48 <=> 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))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_eq__Abs__Integ,axiom,
% 28.45/28.48 ! [V_z_2] :
% 28.45/28.48 ~ ! [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))))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Integ__def,axiom,
% 28.45/28.48 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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_code__numeral_Osimps_I5_J,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Rep__Integ,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_code__numeral_Osimps_I4_J,axiom,
% 28.45/28.48 ! [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 ).
% 28.45/28.48
% 28.45/28.48 fof(fact_type__definition__Integ,axiom,
% 28.45/28.48 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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_accp__acc__eq,axiom,
% 28.45/28.48 ! [V_x_2,V_r_2,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rel__comp__def,axiom,
% 28.45/28.48 ! [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))))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rel__compI,axiom,
% 28.45/28.48 ! [V_s_2,V_c_2,T_d,V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => ( 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))
% 28.45/28.48 => 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))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rel__comp__UNION__distrib2,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rel__comp__UNION__distrib,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rel__comp__empty1,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rel__comp__empty2,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rel__comp__distrib,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rel__comp__distrib2,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_O__assoc,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rel__comp__mono,axiom,
% 28.45/28.48 ! [V_s_2,V_s_H_2,T_d,V_r_2,V_r_H_2,T_c,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => ( 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))
% 28.45/28.48 => 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))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_union__comp__emptyR,axiom,
% 28.45/28.48 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => ( 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))
% 28.45/28.48 => 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)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_union__comp__emptyL,axiom,
% 28.45/28.48 ! [V_B_2,V_C_2,V_A_2,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => ( 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))
% 28.45/28.48 => 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)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_acc__subset,axiom,
% 28.45/28.48 ! [V_R2_2,V_R1_2,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => 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))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_acc__downward,axiom,
% 28.45/28.48 ! [V_a_2,V_r_2,V_b_2,T_b] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 28.45/28.48 => ( 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))
% 28.45/28.48 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_acc_Osimps,axiom,
% 28.45/28.48 ! [V_r_2,V_a_2,T_b] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 28.45/28.48 <=> ! [B_x] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_max__ext__compat,axiom,
% 28.45/28.48 ! [V_S_2,V_R_2,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => 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))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_min__ext__compat,axiom,
% 28.45/28.48 ! [V_S_2,V_R_2,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => 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))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_type__definition_OAbs__image,axiom,
% 28.45/28.48 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 28.45/28.48 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 28.45/28.48 => 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)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_type__definition_ORep__range,axiom,
% 28.45/28.48 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 28.45/28.48 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 28.45/28.48 => 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 ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_type__definition_ORep,axiom,
% 28.45/28.48 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 28.45/28.48 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 28.45/28.48 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_Rep_2,V_x_2)),V_A_2)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_type__definition_ORep__inverse,axiom,
% 28.45/28.48 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 28.45/28.48 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 28.45/28.48 => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_type__definition_ORep__inject,axiom,
% 28.45/28.48 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 28.45/28.48 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 28.45/28.48 => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2)
% 28.45/28.48 <=> V_x_2 = V_y_2 ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_type__definition_OAbs__inject,axiom,
% 28.45/28.48 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 28.45/28.48 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
% 28.45/28.48 => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2)
% 28.45/28.48 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_type__definition_OAbs__inverse,axiom,
% 28.45/28.48 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 28.45/28.48 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
% 28.45/28.48 => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_pred__comp__rel__comp__eq,axiom,
% 28.45/28.48 ! [V_y_2,V_x_2,V_s_2,V_r_2,T_d,T_c,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 <=> 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))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_reduction__pairI,axiom,
% 28.45/28.48 ! [V_S_2,V_R_2,T_b] :
% 28.45/28.48 ( c_Wellfounded_Owf(T_b,V_R_2)
% 28.45/28.48 => ( 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))
% 28.45/28.48 => 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)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_max__extp_Oequations,axiom,
% 28.45/28.48 ! [V_a2_2,V_a1_2,V_R_2,T_b] :
% 28.45/28.48 ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2)
% 28.45/28.48 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 28.45/28.48 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 28.45/28.48 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.45/28.48 & ! [B_x] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 28.45/28.48 => ? [B_xa] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 28.45/28.48 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wf__less__than,axiom,
% 28.45/28.48 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_pred__comp_Ointros,axiom,
% 28.45/28.48 ! [T_d,T_c,T_b,V_c_2,V_s_2,V_b_2,V_a_2,V_r_2] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_c_2))
% 28.45/28.48 => 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)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wf__empty,axiom,
% 28.45/28.48 ! [T_b] : c_Wellfounded_Owf(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wf__inv__image,axiom,
% 28.45/28.48 ! [V_f_2,T_c,V_r_2,T_b] :
% 28.45/28.48 ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.45/28.48 => c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wf__lex__prod,axiom,
% 28.45/28.48 ! [V_rb_2,T_c,V_ra_2,T_b] :
% 28.45/28.48 ( c_Wellfounded_Owf(T_b,V_ra_2)
% 28.45/28.48 => ( c_Wellfounded_Owf(T_c,V_rb_2)
% 28.45/28.48 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_ra_2,V_rb_2)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wf__measure,axiom,
% 28.45/28.48 ! [V_f_2,T_b] : c_Wellfounded_Owf(T_b,hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wf__comp__self,axiom,
% 28.45/28.48 ! [V_R_2,T_b] :
% 28.45/28.48 ( c_Wellfounded_Owf(T_b,V_R_2)
% 28.45/28.48 <=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wf__subset,axiom,
% 28.45/28.48 ! [V_p_2,V_r_2,T_b] :
% 28.45/28.48 ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.45/28.48 => ( 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))
% 28.45/28.48 => c_Wellfounded_Owf(T_b,V_p_2) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_min__ext__wf,axiom,
% 28.45/28.48 ! [V_r_2,T_b] :
% 28.45/28.48 ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.45/28.48 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_b,V_r_2)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wf__less,axiom,
% 28.45/28.48 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)))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_pred__comp_Oequations,axiom,
% 28.45/28.48 ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_d,T_c,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 <=> ? [B_b] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b))
% 28.45/28.48 & hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wf__Int2,axiom,
% 28.45/28.48 ! [V_r_H_2,V_r_2,T_b] :
% 28.45/28.48 ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.45/28.48 => 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)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wf__Int1,axiom,
% 28.45/28.48 ! [V_r_H_2,V_r_2,T_b] :
% 28.45/28.48 ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.45/28.48 => 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)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wf__finite__psubset,axiom,
% 28.45/28.48 ! [T_b] : c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wf__mlex,axiom,
% 28.45/28.48 ! [V_f_2,V_R_2,T_b] :
% 28.45/28.48 ( c_Wellfounded_Owf(T_b,V_R_2)
% 28.45/28.48 => c_Wellfounded_Owf(T_b,c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wf__pair__less,axiom,
% 28.45/28.48 c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_max__ext__wf,axiom,
% 28.45/28.48 ! [V_r_2,T_b] :
% 28.45/28.48 ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.45/28.48 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_b,V_r_2)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wf__not__refl,axiom,
% 28.45/28.48 ! [V_a_2,V_r_2,T_b] :
% 28.45/28.48 ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.45/28.48 => ~ 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)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wf__not__sym,axiom,
% 28.45/28.48 ! [V_x_2,V_a_2,V_r_2,T_b] :
% 28.45/28.48 ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.45/28.48 => ( 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))
% 28.45/28.48 => ~ 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)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wf__asym,axiom,
% 28.45/28.48 ! [V_x_2,V_a_2,V_r_2,T_b] :
% 28.45/28.48 ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.45/28.48 => ( 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))
% 28.45/28.48 => ~ 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)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wf__irrefl,axiom,
% 28.45/28.48 ! [V_a_2,V_r_2,T_b] :
% 28.45/28.48 ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.45/28.48 => ~ 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)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wf__int__ge__less__than,axiom,
% 28.45/28.48 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wf__int__ge__less__than2,axiom,
% 28.45/28.48 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wf__acc__iff,axiom,
% 28.45/28.48 ! [V_r_2,T_b] :
% 28.45/28.48 ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.45/28.48 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_acc__wfD,axiom,
% 28.45/28.48 ! [V_x_2,V_r_2,T_b] :
% 28.45/28.48 ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.45/28.48 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wf__no__loop,axiom,
% 28.45/28.48 ! [V_R_2,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wf__union__merge,axiom,
% 28.45/28.48 ! [V_S_2,V_R_2,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 <=> 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)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wf__iff__no__infinite__down__chain,axiom,
% 28.45/28.48 ! [V_r_2,T_b] :
% 28.45/28.48 ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.45/28.48 <=> ~ ? [B_f] :
% 28.45/28.48 ! [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)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wfE__pf,axiom,
% 28.45/28.48 ! [V_A_2,V_R_2,T_b] :
% 28.45/28.48 ( c_Wellfounded_Owf(T_b,V_R_2)
% 28.45/28.48 => ( 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)))
% 28.45/28.48 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wf__union__compatible,axiom,
% 28.45/28.48 ! [V_S_2,V_R_2,T_b] :
% 28.45/28.48 ( c_Wellfounded_Owf(T_b,V_R_2)
% 28.45/28.48 => ( c_Wellfounded_Owf(T_b,V_S_2)
% 28.45/28.48 => ( 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))
% 28.45/28.48 => 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)) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wf,axiom,
% 28.45/28.48 ! [T_b] :
% 28.45/28.48 ( class_Orderings_Owellorder(T_b)
% 28.45/28.48 => 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)))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_reduction__pair__def,axiom,
% 28.45/28.48 ! [V_P_2,T_b] :
% 28.45/28.48 ( c_FunDef_Oreduction__pair(T_b,V_P_2)
% 28.45/28.48 <=> ( 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))
% 28.45/28.48 & 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))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_reduction__pair__lemma,axiom,
% 28.45/28.48 ! [V_S_2,V_R_2,V_P_2,T_b] :
% 28.45/28.48 ( c_FunDef_Oreduction__pair(T_b,V_P_2)
% 28.45/28.48 => ( 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)))
% 28.45/28.48 => ( 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)))
% 28.45/28.48 => ( c_Wellfounded_Owf(T_b,V_S_2)
% 28.45/28.48 => 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)) ) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wf__lenlex,axiom,
% 28.45/28.48 ! [V_r_2,T_b] :
% 28.45/28.48 ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.45/28.48 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olenlex(T_b,V_r_2)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wf__if__measure,axiom,
% 28.45/28.48 ! [T_b,V_g_2,V_f_2,V_P_2] :
% 28.45/28.48 ( ! [B_x] :
% 28.45/28.48 ( hBOOL(hAPP(V_P_2,B_x))
% 28.45/28.48 => 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))) )
% 28.45/28.48 => 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))))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_max__ext_Ointros,axiom,
% 28.45/28.48 ! [V_R_2,V_Y_2,V_X_2,T_b] :
% 28.45/28.48 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2))
% 28.45/28.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2))
% 28.45/28.48 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.45/28.48 => ( ! [B_x] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2))
% 28.45/28.48 => ? [B_xa] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2))
% 28.45/28.48 & 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)) ) )
% 28.45/28.48 => 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))) ) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_pred__nat__def,axiom,
% 28.45/28.48 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))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wf__lex,axiom,
% 28.45/28.48 ! [V_r_2,T_b] :
% 28.45/28.48 ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.45/28.48 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olex(T_b,V_r_2)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wf__lexn,axiom,
% 28.45/28.48 ! [V_n_2,V_r_2,T_b] :
% 28.45/28.48 ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.45/28.48 => c_Wellfounded_Owf(tc_List_Olist(T_b),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_lex__def,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_lexn_Osimps_I1_J,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wf__pred__nat,axiom,
% 28.45/28.48 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wf__same__fst,axiom,
% 28.45/28.48 ! [T_b,V_R_2,T_c,V_P_2] :
% 28.45/28.48 ( ! [B_x] :
% 28.45/28.48 ( hBOOL(hAPP(V_P_2,B_x))
% 28.45/28.48 => c_Wellfounded_Owf(T_c,hAPP(V_R_2,B_x)) )
% 28.45/28.48 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Recdef_Osame__fst(T_b,T_c,V_P_2,V_R_2)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Nitpick_Ozero__frac__def,axiom,
% 28.45/28.48 ! [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))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Range__Collect__split,axiom,
% 28.45/28.48 ! [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))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_RangeI,axiom,
% 28.45/28.48 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Range__Id__on,axiom,
% 28.45/28.48 ! [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 ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Range__Diff__subset,axiom,
% 28.45/28.48 ! [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)))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Range__Union,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Range__empty,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Range__empty__iff,axiom,
% 28.45/28.48 ! [V_r_2,T_b,T_c] :
% 28.45/28.48 ( hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.45/28.48 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Range__Un__eq,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_finite__Range,axiom,
% 28.45/28.48 ! [V_r_2,T_c,T_b] :
% 28.45/28.48 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
% 28.45/28.48 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_snd__eq__Range,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Range__iff,axiom,
% 28.45/28.48 ! [V_r_2,T_c,V_a_2,T_b] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
% 28.45/28.48 <=> ? [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)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Range__insert,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Range__Int__subset,axiom,
% 28.45/28.48 ! [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)))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Nitpick_Oone__frac__def,axiom,
% 28.45/28.48 ! [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))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Nitpick_Onumber__of__frac__def,axiom,
% 28.45/28.48 ! [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))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_RangeP__Range__eq,axiom,
% 28.45/28.48 ! [V_x_2,V_r_2,T_c,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_RangeP_Ointros,axiom,
% 28.45/28.48 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 28.45/28.48 => hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_b_2)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_RangeP_Oequations,axiom,
% 28.45/28.48 ! [V_a2_2,V_r_2,T_c,T_b] :
% 28.45/28.48 ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_a2_2))
% 28.45/28.48 <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Nitpick_Ofrac__def,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_RangeE,axiom,
% 28.45/28.48 ! [V_r_2,T_c,V_b_2,T_b] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
% 28.45/28.48 => ~ ! [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)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wf__Un,axiom,
% 28.45/28.48 ! [V_s_2,V_r_2,T_b] :
% 28.45/28.48 ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.45/28.48 => ( c_Wellfounded_Owf(T_b,V_s_2)
% 28.45/28.48 => ( 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))
% 28.45/28.48 => 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)) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_DomainI,axiom,
% 28.45/28.48 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Domain__Id__on,axiom,
% 28.45/28.48 ! [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 ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Domain__empty,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Domain__empty__iff,axiom,
% 28.45/28.48 ! [V_r_2,T_c,T_b] :
% 28.45/28.48 ( hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.45/28.48 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Domain__mono,axiom,
% 28.45/28.48 ! [V_s_2,V_r_2,T_c,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => 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))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Domain__Un__eq,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_finite__Domain,axiom,
% 28.45/28.48 ! [V_r_2,T_c,T_b] :
% 28.45/28.48 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
% 28.45/28.48 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_fst__eq__Domain,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Domain__iff,axiom,
% 28.45/28.48 ! [V_r_2,T_c,V_a_2,T_b] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
% 28.45/28.48 <=> ? [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)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Domain__insert,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Domain__Int__subset,axiom,
% 28.45/28.48 ! [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)))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Domain__Diff__subset,axiom,
% 28.45/28.48 ! [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)))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Field__def,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Domain__Union,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Domain__Collect__split,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_DomainP__Domain__eq,axiom,
% 28.45/28.48 ! [V_x_2,V_r_2,T_c,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_DomainE,axiom,
% 28.45/28.48 ! [V_r_2,T_c,V_a_2,T_b] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
% 28.45/28.48 => ~ ! [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)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_image__split__eq__Sigma,axiom,
% 28.45/28.48 ! [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))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_DomainP_Ointros,axiom,
% 28.45/28.48 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 28.45/28.48 => hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a_2)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_SigmaI,axiom,
% 28.45/28.48 ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
% 28.45/28.48 => 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))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Sigma__empty1,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Times__eq__cancel2,axiom,
% 28.45/28.48 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
% 28.45/28.48 => ( 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))
% 28.45/28.48 <=> V_A_2 = V_B_2 ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Sigma__Union,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_card__cartesian__product,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_setsum__cartesian__product,axiom,
% 28.45/28.48 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 28.45/28.48 ( class_Groups_Ocomm__monoid__add(T_b)
% 28.45/28.48 => 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))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Sigma__empty2,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Times__empty,axiom,
% 28.45/28.48 ! [V_B_2,V_A_2,T_c,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.45/28.48 | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Compl__Times__UNIV2,axiom,
% 28.45/28.48 ! [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)))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Compl__Times__UNIV1,axiom,
% 28.45/28.48 ! [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))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_setprod__cartesian__product,axiom,
% 28.45/28.48 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 28.45/28.48 ( class_Groups_Ocomm__monoid__mult(T_b)
% 28.45/28.48 => 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))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Sigma__Un__distrib2,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Times__Un__distrib1,axiom,
% 28.45/28.48 ! [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))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Sigma__Un__distrib1,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rel__comp__subset__Sigma,axiom,
% 28.45/28.48 ! [V_C_2,V_s_2,T_d,V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 28.45/28.48 ( 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))))
% 28.45/28.48 => ( 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))))
% 28.45/28.48 => 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)))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_swap__product,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_finite__cartesian__product,axiom,
% 28.45/28.48 ! [V_B_2,T_c,V_A_2,T_b] :
% 28.45/28.48 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 28.45/28.48 => 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)))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_equiv__type,axiom,
% 28.45/28.48 ! [V_r_2,V_A_2,T_b] :
% 28.45/28.48 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 28.45/28.48 => 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)))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Sigma__Int__distrib1,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Times__Int__distrib1,axiom,
% 28.45/28.48 ! [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))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Sigma__Int__distrib2,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Id__on__subset__Times,axiom,
% 28.45/28.48 ! [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)))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Sigma__Diff__distrib2,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Times__Diff__distrib1,axiom,
% 28.45/28.48 ! [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))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Sigma__Diff__distrib1,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_DomainP_Oequations,axiom,
% 28.45/28.48 ! [V_a1_2,V_r_2,T_c,T_b] :
% 28.45/28.48 ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a1_2))
% 28.45/28.48 <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_UNIV__Times__UNIV,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_SigmaE2,axiom,
% 28.45/28.48 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.45/28.48 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_SigmaD2,axiom,
% 28.45/28.48 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_SigmaD1,axiom,
% 28.45/28.48 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_mem__Sigma__iff,axiom,
% 28.45/28.48 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.45/28.48 & hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_card__cartesian__product__singleton,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Times__subset__cancel2,axiom,
% 28.45/28.48 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
% 28.45/28.48 => ( 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))))
% 28.45/28.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Image__subset,axiom,
% 28.45/28.48 ! [V_C_2,V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 28.45/28.48 ( 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))))
% 28.45/28.48 => 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)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_finite__cartesian__productD2,axiom,
% 28.45/28.48 ! [V_B_2,V_A_2,T_c,T_b] :
% 28.45/28.48 ( 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))))
% 28.45/28.48 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.45/28.48 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_finite__cartesian__productD1,axiom,
% 28.45/28.48 ! [V_B_2,V_A_2,T_c,T_b] :
% 28.45/28.48 ( 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))))
% 28.45/28.48 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
% 28.45/28.48 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_SetCompr__Sigma__eq,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Collect__split,axiom,
% 28.45/28.48 ! [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))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_fst__image__times,axiom,
% 28.45/28.48 ! [V_A_2,T_c,T_b,V_B_2] :
% 28.45/28.48 ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.45/28.48 => 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)) )
% 28.45/28.48 & ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.45/28.48 => 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 ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_snd__image__times,axiom,
% 28.45/28.48 ! [V_B_2,T_c,T_b,V_A_2] :
% 28.45/28.48 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.45/28.48 => 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)) )
% 28.45/28.48 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.45/28.48 => 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 ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_insert__times__insert,axiom,
% 28.45/28.48 ! [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)))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_finite__equiv__class,axiom,
% 28.45/28.48 ! [V_X_2,V_r_2,V_A_2,T_b] :
% 28.45/28.48 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.48 => ( 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))))
% 28.45/28.48 => ( 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)))
% 28.45/28.48 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_vimage__Times,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_UN__Times__distrib,axiom,
% 28.45/28.48 ! [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))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Sigma__def,axiom,
% 28.45/28.48 ! [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))))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_finite__quotient,axiom,
% 28.45/28.48 ! [V_r_2,V_A_2,T_b] :
% 28.45/28.48 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.48 => ( 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))))
% 28.45/28.48 => 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))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_setsum__mult__setsum__if__inj,axiom,
% 28.45/28.48 ! [V_B_2,V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] :
% 28.45/28.48 ( class_Rings_Osemiring__0(T_d)
% 28.45/28.48 => ( 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)))
% 28.45/28.48 => 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))))))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Ex__inj__on__UNION__Sigma,axiom,
% 28.45/28.48 ! [V_A_2,V_I_2,T_c,T_b] :
% 28.45/28.48 ? [B_f] :
% 28.45/28.48 ( 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))
% 28.45/28.48 & 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))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_fold__image__Sigma,axiom,
% 28.45/28.48 ! [V_g_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 28.45/28.48 ( class_Groups_Ocomm__monoid__mult(T_d)
% 28.45/28.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.48 => ( ! [B_x] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.45/28.48 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 28.45/28.48 => 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)) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_bij__betw__id,axiom,
% 28.45/28.48 ! [V_A_2,T_b] : c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),V_A_2,V_A_2) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_image__id,axiom,
% 28.45/28.48 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),V_Y_2) = V_Y_2 ).
% 28.45/28.48
% 28.45/28.48 fof(fact_apsnd__id,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_id__def,axiom,
% 28.45/28.48 ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1 ).
% 28.45/28.48
% 28.45/28.48 fof(fact_id__apply,axiom,
% 28.45/28.48 ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x ).
% 28.45/28.48
% 28.45/28.48 fof(fact_vimage__id,axiom,
% 28.45/28.48 ! [V_A_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_Fun_Oid(T_b)),V_A_2) = V_A_2 ).
% 28.45/28.48
% 28.45/28.48 fof(fact_bij__betw__id__iff,axiom,
% 28.45/28.48 ! [V_B_2,V_A_2,T_b] :
% 28.45/28.48 ( c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),V_A_2,V_B_2)
% 28.45/28.48 <=> V_A_2 = V_B_2 ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_inj__on__id,axiom,
% 28.45/28.48 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_Fun_Oid(T_b),V_A_2) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_o__id,axiom,
% 28.45/28.48 ! [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 ).
% 28.45/28.48
% 28.45/28.48 fof(fact_id__o,axiom,
% 28.45/28.48 ! [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 ).
% 28.45/28.48
% 28.45/28.48 fof(fact_o__eq__id__dest,axiom,
% 28.45/28.48 ! [V_v_2,V_c_2,V_b_2,V_a_2,T_b,T_c,T_d] :
% 28.45/28.48 ( 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)
% 28.45/28.48 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_apfst__id,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_of__int__eq__id,axiom,
% 28.45/28.48 c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_surj__id,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_bij__id,axiom,
% 28.45/28.48 ! [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))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_folding_Oempty,axiom,
% 28.45/28.48 ! [V_F_2,V_f_2,T_c,T_b] :
% 28.45/28.48 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 28.45/28.48 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Fun_Oid(T_c) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_split__Pair,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_setsum__reindex__id,axiom,
% 28.45/28.48 ! [V_B_2,V_f_2,T_b,T_c] :
% 28.45/28.48 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.45/28.48 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 28.45/28.48 => 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)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_setprod__reindex__id,axiom,
% 28.45/28.48 ! [V_B_2,V_f_2,T_b,T_c] :
% 28.45/28.48 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.45/28.48 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 28.45/28.48 => 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)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_setprod__Sigma,axiom,
% 28.45/28.48 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 28.45/28.48 ( class_Groups_Ocomm__monoid__mult(T_d)
% 28.45/28.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.48 => ( ! [B_x] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.45/28.48 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 28.45/28.48 => 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)) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_setsum__Sigma,axiom,
% 28.45/28.48 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 28.45/28.48 ( class_Groups_Ocomm__monoid__add(T_d)
% 28.45/28.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.48 => ( ! [B_x] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.45/28.48 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 28.45/28.48 => 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)) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_card__SigmaI,axiom,
% 28.45/28.48 ! [V_B_2,T_c,V_A_2,T_b] :
% 28.45/28.48 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.48 => ( ! [B_x] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.45/28.48 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 28.45/28.48 => 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) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_finite__SigmaI,axiom,
% 28.45/28.48 ! [V_B_2,T_c,V_A_2,T_b] :
% 28.45/28.48 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.48 => ( ! [B_a] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 28.45/28.48 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) )
% 28.45/28.48 => 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))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_SigmaE,axiom,
% 28.45/28.48 ! [V_B_2,V_A_2,V_c_2,T_c,T_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ~ ! [B_x] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.45/28.48 => ! [B_y] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(V_B_2,B_x)))
% 28.45/28.48 => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_map__pair__surj,axiom,
% 28.45/28.48 ! [V_g_2,T_d,T_e,V_f_2,T_b,T_c] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => ( 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))
% 28.45/28.48 => 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)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_map__pair__imageI,axiom,
% 28.45/28.48 ! [V_g_2,V_f_2,T_e,T_d,V_R_2,V_b_2,V_a_2,T_c,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => 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))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_map__pair__simp,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_map__pair__ident,axiom,
% 28.45/28.48 ! [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 ).
% 28.45/28.48
% 28.45/28.48 fof(fact_snd__prod__fun,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_fst__map__pair,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_fst__comp__map__pair,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_snd__comp__map__pair,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_map__pair_Ocomp,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_map__pair__compose,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_map__pair_Ocompositionality,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_map__pair_Oidentity,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_apsnd__def,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_apfst__def,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_map__pair_Oid,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_map__pair__def,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_map__pair__surj__on,axiom,
% 28.45/28.48 ! [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] :
% 28.45/28.48 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2
% 28.45/28.48 => ( hAPP(c_Set_Oimage(T_e,T_d,V_g_2),V_B_2) = V_B_H_2
% 28.45/28.48 => 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)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wf__map__pair__image,axiom,
% 28.45/28.48 ! [V_f_2,T_c,V_r_2,T_b] :
% 28.45/28.48 ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.45/28.48 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 28.45/28.48 => 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)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_map__pair__inj__on,axiom,
% 28.45/28.48 ! [V_B_2,V_g_2,T_e,T_d,V_A_2,V_f_2,T_c,T_b] :
% 28.45/28.48 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 28.45/28.48 => ( c_Fun_Oinj__on(T_d,T_e,V_g_2,V_B_2)
% 28.45/28.48 => 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))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_prod__fun__imageE,axiom,
% 28.45/28.48 ! [V_R_2,V_g_2,V_f_2,T_e,T_d,V_c_2,T_c,T_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ~ ! [B_x,B_y] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => ~ 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)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_refl__on__def,axiom,
% 28.45/28.48 ! [V_r_2,V_A_2,T_b] :
% 28.45/28.48 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 28.45/28.48 <=> ( 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))))
% 28.45/28.48 & ! [B_x] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.45/28.48 => 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)) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wfP__def,axiom,
% 28.45/28.48 ! [V_r_2,T_b] :
% 28.45/28.48 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 28.45/28.48 <=> 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))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wfP__empty,axiom,
% 28.45/28.48 ! [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))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_refl__on__Id__on,axiom,
% 28.45/28.48 ! [V_A_2,T_b] : c_Relation_Orefl__on(T_b,V_A_2,c_Relation_OId__on(T_b,V_A_2)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_accp__wfPD,axiom,
% 28.45/28.48 ! [V_x_2,V_r_2,T_b] :
% 28.45/28.48 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 28.45/28.48 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_x_2)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wfP__accp__iff,axiom,
% 28.45/28.48 ! [V_r_2,T_b] :
% 28.45/28.48 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 28.45/28.48 <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x1)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wfP__subset,axiom,
% 28.45/28.48 ! [V_p_2,V_r_2,T_b] :
% 28.45/28.48 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 28.45/28.48 => ( 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))
% 28.45/28.48 => c_Wellfounded_OwfP(T_b,V_p_2) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_refl__on__empty,axiom,
% 28.45/28.48 ! [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))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_refl__on__Un,axiom,
% 28.45/28.48 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
% 28.45/28.48 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 28.45/28.48 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
% 28.45/28.48 => 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)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_refl__on__Int,axiom,
% 28.45/28.48 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
% 28.45/28.48 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 28.45/28.48 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
% 28.45/28.48 => 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)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_refl__onD2,axiom,
% 28.45/28.48 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 28.45/28.48 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 28.45/28.48 => ( 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))
% 28.45/28.48 => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_refl__onD1,axiom,
% 28.45/28.48 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 28.45/28.48 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 28.45/28.48 => ( 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))
% 28.45/28.48 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_refl__onD,axiom,
% 28.45/28.48 ! [V_a_2,V_r_2,V_A_2,T_b] :
% 28.45/28.48 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.45/28.48 => 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)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wf__in__rel,axiom,
% 28.45/28.48 ! [V_R_2,T_b] :
% 28.45/28.48 ( c_Wellfounded_Owf(T_b,V_R_2)
% 28.45/28.48 => c_Wellfounded_OwfP(T_b,c_FunDef_Oin__rel(T_b,T_b,V_R_2)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wfP__wf__eq,axiom,
% 28.45/28.48 ! [V_r_2,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 <=> c_Wellfounded_Owf(T_b,V_r_2) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_reflp__def,axiom,
% 28.45/28.48 ! [V_r_2,T_b] :
% 28.45/28.48 ( c_Predicate_Oreflp(T_b,V_r_2)
% 28.45/28.48 <=> 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))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_refl__onI,axiom,
% 28.45/28.48 ! [V_A_2,V_r_2,T_b] :
% 28.45/28.48 ( 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))))
% 28.45/28.48 => ( ! [B_x] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.45/28.48 => 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)) )
% 28.45/28.48 => c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wfP__acyclicP,axiom,
% 28.45/28.48 ! [V_r_2,T_b] :
% 28.45/28.48 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 28.45/28.48 => 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))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_reflpE,axiom,
% 28.45/28.48 ! [V_x_2,V_r_2,T_b] :
% 28.45/28.48 ( c_Predicate_Oreflp(T_b,V_r_2)
% 28.45/28.48 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_acyclic__subset,axiom,
% 28.45/28.48 ! [V_r_2,V_s_2,T_b] :
% 28.45/28.48 ( c_Wellfounded_Oacyclic(T_b,V_s_2)
% 28.45/28.48 => ( 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))
% 28.45/28.48 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wf__acyclic,axiom,
% 28.45/28.48 ! [V_r_2,T_b] :
% 28.45/28.48 ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.45/28.48 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wf__iff__acyclic__if__finite,axiom,
% 28.45/28.48 ! [V_r_2,T_b] :
% 28.45/28.48 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 28.45/28.48 => ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.45/28.48 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_finite__acyclic__wf,axiom,
% 28.45/28.48 ! [V_r_2,T_b] :
% 28.45/28.48 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 28.45/28.48 => ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 28.45/28.48 => c_Wellfounded_Owf(T_b,V_r_2) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Nitpick_Owf_H__def,axiom,
% 28.45/28.48 ! [V_r_2,T_b] :
% 28.45/28.48 ( c_Nitpick_Owf_H(T_b,V_r_2)
% 28.45/28.48 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 28.45/28.48 & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 28.45/28.48 | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Rep__Integ__induct,axiom,
% 28.45/28.48 ! [V_P_2,V_y_2] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 28.45/28.48 => ( ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Int_ORep__Integ,B_x)))
% 28.45/28.48 => hBOOL(hAPP(V_P_2,V_y_2)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Rep__Integ__cases,axiom,
% 28.45/28.48 ! [V_y_2] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 28.45/28.48 => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_refl__on__def_H,axiom,
% 28.45/28.48 ! [V_r_2,V_A_2,T_b] :
% 28.45/28.48 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 28.45/28.48 <=> ( ! [B_x] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
% 28.45/28.48 => 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)) )
% 28.45/28.48 & ! [B_x] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.45/28.48 => 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)) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Abs__Integ__induct,axiom,
% 28.45/28.48 ! [V_x_2,V_P_2] :
% 28.45/28.48 ( ! [B_y] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg))
% 28.45/28.48 => hBOOL(hAPP(V_P_2,hAPP(c_Int_OAbs__Integ,B_y))) )
% 28.45/28.48 => hBOOL(hAPP(V_P_2,V_x_2)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Abs__Integ__cases,axiom,
% 28.45/28.48 ! [V_x_2] :
% 28.45/28.48 ~ ! [B_y] :
% 28.45/28.48 ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y)
% 28.45/28.48 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Powp__def,axiom,
% 28.45/28.48 ! [V_B_2,V_A_2,T_b] :
% 28.45/28.48 ( hBOOL(hAPP(c_Predicate_OPowp(T_b,V_A_2),V_B_2))
% 28.45/28.48 <=> ! [B_x] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 28.45/28.48 => hBOOL(hAPP(V_A_2,B_x)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_INFI__bool__eq,axiom,
% 28.45/28.48 ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_HOL_Obool) = c_Set_OBall(T_b) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_ball__empty,axiom,
% 28.45/28.48 ! [V_P_2,T_b,B_x] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 28.45/28.48 => hBOOL(hAPP(V_P_2,B_x)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Collect__ball__eq,axiom,
% 28.45/28.48 ! [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))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_congruent__def,axiom,
% 28.45/28.48 ! [V_f_2,V_r_2,T_c,T_b] :
% 28.45/28.48 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
% 28.45/28.48 <=> ! [B_x] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
% 28.45/28.48 => 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)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_INTER__def,axiom,
% 28.45/28.48 ! [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)))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Inf__Sup,axiom,
% 28.45/28.48 ! [V_A_2,T_b] :
% 28.45/28.48 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.45/28.48 => 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))))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Sup__Inf,axiom,
% 28.45/28.48 ! [V_A_2,T_b] :
% 28.45/28.48 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.45/28.48 => 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)))))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wfP__SUP,axiom,
% 28.45/28.48 ! [T_b,V_r_2,T_c] :
% 28.45/28.48 ( ! [B_i] : c_Wellfounded_OwfP(T_c,hAPP(V_r_2,B_i))
% 28.45/28.48 => ( ! [B_i,B_j] :
% 28.45/28.48 ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j)
% 28.45/28.48 => 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)) )
% 28.45/28.48 => 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)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_mem__splitE,axiom,
% 28.45/28.48 ! [V_p_2,V_c_2,T_d,T_c,V_z_2,T_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ~ ! [B_x,B_y] :
% 28.45/28.48 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y)
% 28.45/28.48 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_c_2,B_x),B_y))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_mem__splitI2,axiom,
% 28.45/28.48 ! [V_c_2,V_z_2,T_d,T_c,T_b,V_p_2] :
% 28.45/28.48 ( ! [B_a,B_b] :
% 28.45/28.48 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)
% 28.45/28.48 => hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(V_c_2,B_a),B_b))) )
% 28.45/28.48 => 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))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Inter__eq,axiom,
% 28.45/28.48 ! [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)))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Eps__split,axiom,
% 28.45/28.48 ! [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))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wfI__pf,axiom,
% 28.45/28.48 ! [V_R_2,T_b] :
% 28.45/28.48 ( ! [B_A] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
% 28.45/28.48 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Sigma__mono,axiom,
% 28.45/28.48 ! [V_D_2,V_B_2,T_c,V_C_2,V_A_2,T_b] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 28.45/28.48 => ( ! [B_x] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.45/28.48 => 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))) )
% 28.45/28.48 => 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))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_some__sym__eq__trivial,axiom,
% 28.45/28.48 ! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 28.45/28.48
% 28.45/28.48 fof(fact_some__eq__trivial,axiom,
% 28.45/28.48 ! [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 ).
% 28.45/28.48
% 28.45/28.48 fof(fact_some__eq__ex,axiom,
% 28.45/28.48 ! [T_b,V_P_2] :
% 28.45/28.48 ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2)))
% 28.45/28.48 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_someI__ex,axiom,
% 28.45/28.48 ! [T_b,V_P_2] :
% 28.45/28.48 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 28.45/28.48 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_someI,axiom,
% 28.45/28.48 ! [T_b,V_x_2,V_P_2] :
% 28.45/28.48 ( hBOOL(hAPP(V_P_2,V_x_2))
% 28.45/28.48 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_tfl__some,axiom,
% 28.45/28.48 ! [T_b,B_P] :
% 28.45/28.48 ( ? [B_x] : hBOOL(hAPP(B_P,B_x))
% 28.45/28.48 => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_b,B_P))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_exE__some,axiom,
% 28.45/28.48 ! [T_b,V_c_2,V_P_2] :
% 28.45/28.48 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 28.45/28.48 => ( V_c_2 = c_Hilbert__Choice_OEps(T_b,V_P_2)
% 28.45/28.48 => hBOOL(hAPP(V_P_2,V_c_2)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_split__paired__Eps,axiom,
% 28.45/28.48 ! [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)))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Eps__split__eq,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_acc_OaccI,axiom,
% 28.45/28.48 ! [V_r_2,V_x_2,T_b] :
% 28.45/28.48 ( ! [B_y] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => hBOOL(hAPP(hAPP(c_member(T_b),B_y),c_Wellfounded_Oacc(T_b,V_r_2))) )
% 28.45/28.48 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_not__acc__down,axiom,
% 28.45/28.48 ! [V_R_2,V_x_2,T_b] :
% 28.45/28.48 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_R_2)))
% 28.45/28.48 => ~ ! [B_z] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => hBOOL(hAPP(hAPP(c_member(T_b),B_z),c_Wellfounded_Oacc(T_b,V_R_2))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_max__ext_Osimps,axiom,
% 28.45/28.48 ! [V_R_2,V_a2_2,V_a1_2,T_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 28.45/28.48 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 28.45/28.48 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.45/28.48 & ! [B_x] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 28.45/28.48 => ? [B_xa] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 28.45/28.48 & 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)) ) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wf__no__infinite__down__chainE,axiom,
% 28.45/28.48 ! [V_f_2,V_r_2,T_b] :
% 28.45/28.48 ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.45/28.48 => ~ ! [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)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_setsum__reindex__cong,axiom,
% 28.45/28.48 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 28.45/28.48 ( class_Groups_Ocomm__monoid__add(T_d)
% 28.45/28.48 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 28.45/28.48 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 28.45/28.48 => ( ! [B_a] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 28.45/28.48 => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) )
% 28.45/28.48 => 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) ) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_scomp__unfold,axiom,
% 28.45/28.48 ! [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))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_scomp__Pair,axiom,
% 28.45/28.48 ! [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 ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Pair__scomp,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_scomp__scomp,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_scomp__apply,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_scomp__def,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_iterate_Osimps,axiom,
% 28.45/28.48 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
% 28.45/28.48 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 28.45/28.48 => 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) )
% 28.45/28.48 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 28.45/28.48 => 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)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_setsum__ivl__cong,axiom,
% 28.45/28.48 ! [V_g_2,V_f_2,V_d_2,V_b_2,V_c_2,V_a_2,T_b,T_c] :
% 28.45/28.48 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 28.45/28.48 & class_Orderings_Oord(T_b) )
% 28.45/28.48 => ( V_a_2 = V_c_2
% 28.45/28.48 => ( V_b_2 = V_d_2
% 28.45/28.48 => ( ! [B_x] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),B_x))
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_d_2))
% 28.45/28.48 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) )
% 28.45/28.48 => 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)) ) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_log_Osimps,axiom,
% 28.45/28.48 ! [V_i,V_b] :
% 28.45/28.48 ( ( ( 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)))
% 28.45/28.48 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 28.45/28.48 => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 28.45/28.48 & ( ~ ( 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)))
% 28.45/28.48 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 28.45/28.48 => 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))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_minus__shift__def,axiom,
% 28.45/28.48 ! [V_r,V_l,V_k] :
% 28.45/28.48 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 28.45/28.48 => 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) )
% 28.45/28.48 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 28.45/28.48 => 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) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_inc__shift__def,axiom,
% 28.45/28.48 ! [V_k,V_v] :
% 28.45/28.48 ( ( V_v = V_k
% 28.45/28.48 => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 28.45/28.48 & ( V_v != V_k
% 28.45/28.48 => 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)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_range,axiom,
% 28.45/28.48 ! [V_s,V_k] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => 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)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_less__eq,axiom,
% 28.45/28.48 ! [V_n_2,V_m_2] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_nat__intermed__int__val,axiom,
% 28.45/28.48 ! [V_k_2,V_f_2,V_n_2,V_m_2] :
% 28.45/28.48 ( ! [B_i] :
% 28.45/28.48 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 28.45/28.48 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) )
% 28.45/28.48 => 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))) )
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2))
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 28.45/28.48 => ? [B_i] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 28.45/28.48 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 28.45/28.48 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wf__trancl,axiom,
% 28.45/28.48 ! [V_r_2,T_b] :
% 28.45/28.48 ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.45/28.48 => c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_less__than__def,axiom,
% 28.45/28.48 c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_acyclic__def,axiom,
% 28.45/28.48 ! [V_r_2,T_b] :
% 28.45/28.48 ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 28.45/28.48 <=> ! [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))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_trancl_Or__into__trancl,axiom,
% 28.45/28.48 ! [V_r_2,V_b_2,V_a_2,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => 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))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_trancl__subset__Field2,axiom,
% 28.45/28.48 ! [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))))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_r__into__trancl_H,axiom,
% 28.45/28.48 ! [V_r_2,V_p_2,T_b] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
% 28.45/28.48 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_trancl__empty,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_trancl__domain,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_trancl__range,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_finite__trancl,axiom,
% 28.45/28.48 ! [V_r_2,T_b] :
% 28.45/28.48 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 28.45/28.48 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_trancl__trans,axiom,
% 28.45/28.48 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ( 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)))
% 28.45/28.48 => 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))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom,
% 28.45/28.48 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ( 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))
% 28.45/28.48 => 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))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_trancl__into__trancl2,axiom,
% 28.45/28.48 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => ( 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)))
% 28.45/28.48 => 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))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_r__r__into__trancl,axiom,
% 28.45/28.48 ! [V_c_2,V_R_2,V_b_2,V_a_2,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => ( 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))
% 28.45/28.48 => 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))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_trancl__mono,axiom,
% 28.45/28.48 ! [V_s_2,V_r_2,V_p_2,T_b] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 28.45/28.48 => ( 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))
% 28.45/28.48 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_s_2))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_trancl__unfold,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_trancl__subset__Sigma,axiom,
% 28.45/28.48 ! [V_A_2,V_r_2,T_b] :
% 28.45/28.48 ( 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))))
% 28.45/28.48 => 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)))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_trancl__Int__subset,axiom,
% 28.45/28.48 ! [V_s_2,V_r_2,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => ( 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))
% 28.45/28.48 => 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)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_trancl__insert,axiom,
% 28.45/28.48 ! [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)))))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_reflcl__set__eq,axiom,
% 28.45/28.48 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 <=> 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)))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_r__into__rtrancl,axiom,
% 28.45/28.48 ! [V_r_2,V_p_2,T_b] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
% 28.45/28.48 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rtrancl_Ortrancl__refl,axiom,
% 28.45/28.48 ! [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))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_IdI,axiom,
% 28.45/28.48 ! [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))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_trancl__into__rtrancl,axiom,
% 28.45/28.48 ! [V_r_2,V_b_2,V_a_2,T_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => 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))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rtrancl__trancl__absorb,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_trancl__rtrancl__absorb,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_reflcl__trancl,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_trancl__reflcl,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_trancl__unfold__left,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_trancl__unfold__right,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Image__closed__trancl,axiom,
% 28.45/28.48 ! [V_X_2,V_r_2,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => hAPP(c_Relation_OImage(T_b,T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_X_2) = V_X_2 ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rtrancl__Un__subset,axiom,
% 28.45/28.48 ! [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)))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rtrancl__mono,axiom,
% 28.45/28.48 ! [V_s_2,V_r_2,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => 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))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rtrancl__subset,axiom,
% 28.45/28.48 ! [V_S_2,V_R_2,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => ( 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)))
% 28.45/28.48 => c_Transitive__Closure_Ortrancl(T_b,V_S_2) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rtrancl__subset__rtrancl,axiom,
% 28.45/28.48 ! [V_s_2,V_r_2,T_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => 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))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rtrancl__Int__subset,axiom,
% 28.45/28.48 ! [V_r_2,V_s_2,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => ( 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))
% 28.45/28.48 => 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)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Domain__rtrancl,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Range__rtrancl,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rtrancl__empty,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rtrancl__unfold,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_in__rtrancl__UnI,axiom,
% 28.45/28.48 ! [V_S_2,V_R_2,V_x_2,T_b] :
% 28.45/28.48 ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 28.45/28.48 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_S_2))) )
% 28.45/28.48 => 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)))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rtrancl__idemp__self__comp,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_r__comp__rtrancl__eq,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rtrancl__reflcl,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rtrancl__Un__rtrancl,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rtrancl__reflcl__absorb,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rtrancl__idemp,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rtrancl__trans,axiom,
% 28.45/28.48 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ( 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)))
% 28.45/28.48 => 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))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom,
% 28.45/28.48 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ( 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))
% 28.45/28.48 => 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))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_converse__rtrancl__into__rtrancl,axiom,
% 28.45/28.48 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => ( 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)))
% 28.45/28.48 => 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))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rtrancl__r__diff__Id,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_refl__rtrancl,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Image__Id,axiom,
% 28.45/28.48 ! [V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId(T_b)),V_A_2) = V_A_2 ).
% 28.45/28.48
% 28.45/28.48 fof(fact_R__O__Id,axiom,
% 28.45/28.48 ! [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 ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Id__O__R,axiom,
% 28.45/28.48 ! [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 ).
% 28.45/28.48
% 28.45/28.48 fof(fact_pair__in__Id__conv,axiom,
% 28.45/28.48 ! [V_b_2,V_a_2,T_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 <=> V_a_2 = V_b_2 ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rtrancl__trancl__trancl,axiom,
% 28.45/28.48 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ( 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)))
% 28.45/28.48 => 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))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_trancl__rtrancl__trancl,axiom,
% 28.45/28.48 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ( 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)))
% 28.45/28.48 => 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))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rtrancl__into__trancl1,axiom,
% 28.45/28.48 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ( 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))
% 28.45/28.48 => 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))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rtranclD,axiom,
% 28.45/28.48 ! [V_R_2,V_b_2,V_a_2,T_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ( V_a_2 = V_b_2
% 28.45/28.48 | ( V_a_2 != V_b_2
% 28.45/28.48 & 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))) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rtrancl__into__trancl2,axiom,
% 28.45/28.48 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => ( 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)))
% 28.45/28.48 => 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))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rtrancl__eq__or__trancl,axiom,
% 28.45/28.48 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 <=> ( V_x_2 = V_y_2
% 28.45/28.48 | ( V_x_2 != V_y_2
% 28.45/28.48 & 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))) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Domain__Id,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Range__Id,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_refl__Id,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_pair__leq__def,axiom,
% 28.45/28.48 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))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Not__Domain__rtrancl,axiom,
% 28.45/28.48 ! [V_y_2,V_R_2,V_x_2,T_b] :
% 28.45/28.48 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_b),V_R_2)))
% 28.45/28.48 => ( 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)))
% 28.45/28.48 <=> V_x_2 = V_y_2 ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_acc__downwards,axiom,
% 28.45/28.48 ! [V_b_2,V_r_2,V_a_2,T_b] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 28.45/28.48 => ( 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)))
% 28.45/28.48 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_acc__downwards__aux,axiom,
% 28.45/28.48 ! [V_r_2,V_a_2,V_b_2,T_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 28.45/28.48 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wf__insert,axiom,
% 28.45/28.48 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 <=> ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.45/28.48 & ~ 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))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_acyclic__insert,axiom,
% 28.45/28.48 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 28.45/28.48 & ~ 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))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_refl__reflcl,axiom,
% 28.45/28.48 ! [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))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Id__def,axiom,
% 28.45/28.48 ! [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))))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_irrefl__diff__Id,axiom,
% 28.45/28.48 ! [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))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_pred__nat__trancl__eq__le,axiom,
% 28.45/28.48 ! [V_n_2,V_m_2] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_trancl__subset__Sigma__aux,axiom,
% 28.45/28.48 ! [V_A_2,V_r_2,V_b_2,V_a_2,T_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ( 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))))
% 28.45/28.48 => ( V_a_2 = V_b_2
% 28.45/28.48 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_irrefl__tranclI,axiom,
% 28.45/28.48 ! [V_x_2,V_r_2,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => ~ 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))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_sequence__trans,axiom,
% 28.45/28.48 ! [V_k_2,V_i_2,V_r_2,V_f_2,T_b] :
% 28.45/28.48 ( ! [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)))
% 28.45/28.48 => 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))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rtrancl__converse,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_converse__Id,axiom,
% 28.45/28.48 ! [T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId(T_b)) = c_Relation_OId(T_b) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_acyclic__converse,axiom,
% 28.45/28.48 ! [V_r_2,T_b] :
% 28.45/28.48 ( c_Wellfounded_Oacyclic(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 28.45/28.48 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_converse__UNION,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_converseD,axiom,
% 28.45/28.48 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => 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)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_converseI,axiom,
% 28.45/28.48 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => 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))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_converse__iff,axiom,
% 28.45/28.48 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 <=> 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)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_converse__rel__comp,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_converse__Un,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_converse__Id__on,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_converse__inv__image,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_converse__converse,axiom,
% 28.45/28.48 ! [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 ).
% 28.45/28.48
% 28.45/28.48 fof(fact_converse__Int,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_finite__converse,axiom,
% 28.45/28.48 ! [V_r_2,T_c,T_b] :
% 28.45/28.48 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
% 28.45/28.48 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_b)),V_r_2)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Field__converse,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_refl__on__converse,axiom,
% 28.45/28.48 ! [V_r_2,V_A_2,T_b] :
% 28.45/28.48 ( c_Relation_Orefl__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 28.45/28.48 <=> c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_converse__INTER,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_trancl__converse,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wf__converse__trancl,axiom,
% 28.45/28.48 ! [V_r_2,T_b] :
% 28.45/28.48 ( c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 28.45/28.48 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_equiv__comp__eq,axiom,
% 28.45/28.48 ! [V_r_2,V_A_2,T_b] :
% 28.45/28.48 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 28.45/28.48 => 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 ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Range__def,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Domain__converse,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Range__converse,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rtrancl__converseI,axiom,
% 28.45/28.48 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => 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)))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rtrancl__converseD,axiom,
% 28.45/28.48 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 28.45/28.48 ( 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))))
% 28.45/28.48 => 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))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_trancl__converseI,axiom,
% 28.45/28.48 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 28.45/28.48 ( 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))))
% 28.45/28.48 => 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)))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_trancl__converseD,axiom,
% 28.45/28.48 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 28.45/28.48 ( 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))))
% 28.45/28.48 => 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)))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Image__subset__eq,axiom,
% 28.45/28.48 ! [V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 <=> 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))))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_refl__on__comp__subset,axiom,
% 28.45/28.48 ! [V_r_2,V_A_2,T_b] :
% 28.45/28.48 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 28.45/28.48 => 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))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_comp__equivI,axiom,
% 28.45/28.48 ! [V_A_2,V_r_2,T_b] :
% 28.45/28.48 ( 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
% 28.45/28.48 => ( hAPP(c_Relation_ODomain(T_b,T_b),V_r_2) = V_A_2
% 28.45/28.48 => c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_finite__acyclic__wf__converse,axiom,
% 28.45/28.48 ! [V_r_2,T_b] :
% 28.45/28.48 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 28.45/28.48 => ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 28.45/28.48 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_converse__def,axiom,
% 28.45/28.48 ! [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))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Image__INT__eq,axiom,
% 28.45/28.48 ! [V_B_2,T_d,V_A_2,V_r_2,T_c,T_b] :
% 28.45/28.48 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))
% 28.45/28.48 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
% 28.45/28.48 => 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)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_total__on__diff__Id,axiom,
% 28.45/28.48 ! [V_r_2,V_A_2,T_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_single__valued__Id,axiom,
% 28.45/28.48 ! [T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId(T_b)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_single__valued__rel__comp,axiom,
% 28.45/28.48 ! [V_s_2,T_d,V_r_2,T_c,T_b] :
% 28.45/28.48 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 28.45/28.48 => ( c_Relation_Osingle__valued(T_c,T_d,V_s_2)
% 28.45/28.48 => 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)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_single__valued__subset,axiom,
% 28.45/28.48 ! [V_s_2,V_r_2,T_c,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2)
% 28.45/28.48 => c_Relation_Osingle__valued(T_b,T_c,V_r_2) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_single__valued__Id__on,axiom,
% 28.45/28.48 ! [V_A_2,T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_total__on__empty,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_total__on__converse,axiom,
% 28.45/28.48 ! [V_r_2,V_A_2,T_b] :
% 28.45/28.48 ( c_Relation_Ototal__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 28.45/28.48 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_single__valued__def,axiom,
% 28.45/28.48 ! [V_r_2,T_c,T_b] :
% 28.45/28.48 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 28.45/28.48 <=> ! [B_x,B_y] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => ! [B_z] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => B_y = B_z ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_single__valuedD,axiom,
% 28.45/28.48 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_c,T_b] :
% 28.45/28.48 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 28.45/28.48 => ( 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))
% 28.45/28.48 => ( 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))
% 28.45/28.48 => V_y_2 = V_z_2 ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_total__on__def,axiom,
% 28.45/28.48 ! [V_r_2,V_A_2,T_b] :
% 28.45/28.48 ( c_Relation_Ototal__on(T_b,V_A_2,V_r_2)
% 28.45/28.48 <=> ! [B_x] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.45/28.48 => ! [B_xa] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 28.45/28.48 => ( B_x != B_xa
% 28.45/28.48 => ( 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))
% 28.45/28.48 | 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)) ) ) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_single__valued__confluent,axiom,
% 28.45/28.48 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] :
% 28.45/28.48 ( c_Relation_Osingle__valued(T_b,T_b,V_r_2)
% 28.45/28.48 => ( 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)))
% 28.45/28.48 => ( 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)))
% 28.45/28.48 => ( 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)))
% 28.45/28.48 | 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))) ) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_Image__Int__eq,axiom,
% 28.45/28.48 ! [V_B_2,V_A_2,V_R_2,T_c,T_b] :
% 28.45/28.48 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_R_2))
% 28.45/28.48 => 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)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rtrancl__imp__UN__rel__pow,axiom,
% 28.45/28.48 ! [V_R_2,V_p_2,T_b] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 28.45/28.48 => 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)))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_acyclicI,axiom,
% 28.45/28.48 ! [V_r_2,T_b] :
% 28.45/28.48 ( ! [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)))
% 28.45/28.48 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_single__valued__rel__pow,axiom,
% 28.45/28.48 ! [V_n_2,V_R_2,T_b] :
% 28.45/28.48 ( c_Relation_Osingle__valued(T_b,T_b,V_R_2)
% 28.45/28.48 => 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)) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_wf__exp,axiom,
% 28.45/28.48 ! [V_R_2,V_n_2,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_funpow__mult,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_funpow__swap1,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_comp__funpow,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rel__pow__1,axiom,
% 28.45/28.48 ! [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 ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rel__pow__commute,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rel__pow__imp__rtrancl,axiom,
% 28.45/28.48 ! [V_R_2,V_n_2,V_p_2,T_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rtrancl__power,axiom,
% 28.45/28.48 ! [V_R_2,V_p_2,T_b] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 28.45/28.48 <=> ? [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))) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_relpow_Osimps_I2_J,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rel__pow__add,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_relpow_Osimps_I1_J,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rel__pow__0__I,axiom,
% 28.45/28.48 ! [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))) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rel__pow__0__E,axiom,
% 28.45/28.48 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => V_x_2 = V_y_2 ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rel__pow__Suc__I,axiom,
% 28.45/28.48 ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ( 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))
% 28.45/28.48 => 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))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rel__pow__Suc__I2,axiom,
% 28.45/28.48 ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_b] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => ( 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)))
% 28.45/28.48 => 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))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_funpow_Osimps_I2_J,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_funpow__add,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_funpow_Osimps_I1_J,axiom,
% 28.45/28.48 ! [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) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_trancl__power,axiom,
% 28.45/28.48 ! [V_R_2,V_p_2,T_b] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
% 28.45/28.48 <=> ? [B_n] :
% 28.45/28.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 28.45/28.48 & 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))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rtrancl__is__UN__rel__pow,axiom,
% 28.45/28.48 ! [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)) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_funpow__code__def,axiom,
% 28.45/28.48 ! [T_b] : c_Nat_Ofunpow(T_b) = c_Nat_Ocompow(T_b,T_b) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rel__pow__E,axiom,
% 28.45/28.48 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.45/28.48 => V_x_2 != V_z_2 )
% 28.45/28.48 => ~ ! [B_y,B_m] :
% 28.45/28.48 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 28.45/28.48 => ( 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)))
% 28.45/28.48 => ~ 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)) ) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rel__pow__E2,axiom,
% 28.45/28.48 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.45/28.48 => V_x_2 != V_z_2 )
% 28.45/28.48 => ~ ! [B_y,B_m] :
% 28.45/28.48 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 28.45/28.48 => ( 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))
% 28.45/28.48 => ~ 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))) ) ) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rtrancl__Un__separator__converseE,axiom,
% 28.45/28.48 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_b] :
% 28.45/28.48 ( 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))))
% 28.45/28.48 => ( ! [B_x] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ! [B_y] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => B_y = B_x ) )
% 28.45/28.48 => 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))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rtrancl__Un__separatorE,axiom,
% 28.45/28.48 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_b] :
% 28.45/28.48 ( 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))))
% 28.45/28.48 => ( ! [B_x] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ! [B_y] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => B_x = B_y ) )
% 28.45/28.48 => 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))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rel__pow__Suc__E,axiom,
% 28.45/28.48 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ~ ! [B_y] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ~ 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)) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rel__pow__Suc__D2,axiom,
% 28.45/28.48 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ? [B_y] :
% 28.45/28.48 ( 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))
% 28.45/28.48 & 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))) ) ) ).
% 28.45/28.48
% 28.45/28.48 fof(fact_rel__pow__Suc__E2,axiom,
% 28.45/28.48 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 28.45/28.48 ( 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)))
% 28.45/28.48 => ~ ! [B_y] :
% 28.45/28.48 ( 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))
% 28.45/28.48 => ~ 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))) ) ) ).
% 28.45/28.48
% 28.45/28.49 fof(fact_tranclD2,axiom,
% 28.45/28.49 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => ? [B_z] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 & 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)) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_tranclD,axiom,
% 28.45/28.49 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => ? [B_z] :
% 28.45/28.49 ( 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))
% 28.45/28.49 & 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))) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_IdE,axiom,
% 28.45/28.49 ! [V_p_2,T_b] :
% 28.45/28.49 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Relation_OId(T_b)))
% 28.45/28.49 => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom,
% 28.45/28.49 ! [V_x_2,V_A_2,T_b] :
% 28.45/28.49 ( class_Orderings_Olinorder(T_b)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.45/28.49 => 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) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_folding_Oeq__fold,axiom,
% 28.45/28.49 ! [V_s_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 28.45/28.49 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => 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) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_fold__image__def,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_fold__empty,axiom,
% 28.45/28.49 ! [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 ).
% 28.45/28.49
% 28.45/28.49 fof(fact_fold__def,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_union__fold__insert,axiom,
% 28.45/28.49 ! [V_B_2,V_A_2,T_b] :
% 28.45/28.49 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => 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) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_fold__sup__insert,axiom,
% 28.45/28.49 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 28.45/28.49 ( class_Lattices_Osemilattice__sup(T_b)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => 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)) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_fold__inf__insert,axiom,
% 28.45/28.49 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 28.45/28.49 ( class_Lattices_Osemilattice__inf(T_b)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => 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)) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_min__max_Ofold__inf__insert,axiom,
% 28.45/28.49 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 28.45/28.49 ( class_Orderings_Olinorder(T_b)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => 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)) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_min__max_Ofold__sup__insert,axiom,
% 28.45/28.49 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 28.45/28.49 ( class_Orderings_Olinorder(T_b)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => 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)) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_sup__Sup__fold__sup,axiom,
% 28.45/28.49 ! [V_B_2,V_A_2,T_b] :
% 28.45/28.49 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => 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) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_inf__Inf__fold__inf,axiom,
% 28.45/28.49 ! [V_B_2,V_A_2,T_b] :
% 28.45/28.49 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => 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) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom,
% 28.45/28.49 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 28.45/28.49 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => 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)) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom,
% 28.45/28.49 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 28.45/28.49 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => 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) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_sup__SUPR__fold__sup,axiom,
% 28.45/28.49 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 28.45/28.49 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => 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) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_inf__INFI__fold__inf,axiom,
% 28.45/28.49 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 28.45/28.49 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => 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) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom,
% 28.45/28.49 ! [V_a_2,V_A_2,V_F_2,V_f_2,T_b] :
% 28.45/28.49 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => 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) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_sup__le__fold__sup,axiom,
% 28.45/28.49 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 28.45/28.49 ( class_Lattices_Osemilattice__sup(T_b)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.45/28.49 => 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))) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_fold__inf__le__inf,axiom,
% 28.45/28.49 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 28.45/28.49 ( class_Lattices_Osemilattice__inf(T_b)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.45/28.49 => 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))) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_min__max_Ofold__inf__le__inf,axiom,
% 28.45/28.49 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 28.45/28.49 ( class_Orderings_Olinorder(T_b)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.45/28.49 => 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))) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_min__max_Osup__le__fold__sup,axiom,
% 28.45/28.49 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 28.45/28.49 ( class_Orderings_Olinorder(T_b)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.45/28.49 => 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))) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_Sup__fold__sup,axiom,
% 28.45/28.49 ! [V_A_2,T_b] :
% 28.45/28.49 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => 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) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_Inf__fold__inf,axiom,
% 28.45/28.49 ! [V_A_2,T_b] :
% 28.45/28.49 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => 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) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_fold1__eq__fold__idem,axiom,
% 28.45/28.49 ! [V_a_2,V_A_2,T_b] :
% 28.45/28.49 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => 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) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_Sup__fin_Oeq__fold__idem_H,axiom,
% 28.45/28.49 ! [V_a_2,V_A_2,T_b] :
% 28.45/28.49 ( class_Lattices_Olattice(T_b)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => 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) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_Inf__fin_Oeq__fold__idem_H,axiom,
% 28.45/28.49 ! [V_a_2,V_A_2,T_b] :
% 28.45/28.49 ( class_Lattices_Olattice(T_b)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => 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) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_Min_Oeq__fold__idem_H,axiom,
% 28.45/28.49 ! [V_a_2,V_A_2,T_b] :
% 28.45/28.49 ( class_Orderings_Olinorder(T_b)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => 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) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_Max_Oeq__fold__idem_H,axiom,
% 28.45/28.49 ! [V_a_2,V_A_2,T_b] :
% 28.45/28.49 ( class_Orderings_Olinorder(T_b)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => 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) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom,
% 28.45/28.49 ! [V_a_2,V_A_2,T_b] :
% 28.45/28.49 ( class_Orderings_Olinorder(T_b)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => 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) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom,
% 28.45/28.49 ! [V_a_2,V_A_2,T_b] :
% 28.45/28.49 ( class_Orderings_Olinorder(T_b)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => 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) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_minus__fold__remove,axiom,
% 28.45/28.49 ! [V_B_2,V_A_2,T_b] :
% 28.45/28.49 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => 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) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_folding__one_Oeq__fold_H,axiom,
% 28.45/28.49 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 28.45/28.49 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.45/28.49 => 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) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_SUPR__fold__sup,axiom,
% 28.45/28.49 ! [V_f_2,V_A_2,T_b,T_c] :
% 28.45/28.49 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => 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) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_INFI__fold__inf,axiom,
% 28.45/28.49 ! [V_f_2,V_A_2,T_b,T_c] :
% 28.45/28.49 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => 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) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_fold1__eq__fold,axiom,
% 28.45/28.49 ! [V_a_2,V_A_2,T_b] :
% 28.45/28.49 ( class_Groups_Oab__semigroup__mult(T_b)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.45/28.49 => 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) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_Sup__fin_Oeq__fold_H,axiom,
% 28.45/28.49 ! [V_x_2,V_A_2,T_b] :
% 28.45/28.49 ( class_Lattices_Olattice(T_b)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.45/28.49 => 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) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_Inf__fin_Oeq__fold_H,axiom,
% 28.45/28.49 ! [V_x_2,V_A_2,T_b] :
% 28.45/28.49 ( class_Lattices_Olattice(T_b)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.45/28.49 => 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) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_Min_Oeq__fold_H,axiom,
% 28.45/28.49 ! [V_x_2,V_A_2,T_b] :
% 28.45/28.49 ( class_Orderings_Olinorder(T_b)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.45/28.49 => 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) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_Max_Oeq__fold_H,axiom,
% 28.45/28.49 ! [V_x_2,V_A_2,T_b] :
% 28.45/28.49 ( class_Orderings_Olinorder(T_b)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.45/28.49 => 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) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom,
% 28.45/28.49 ! [V_x_2,V_A_2,T_b] :
% 28.45/28.49 ( class_Orderings_Olinorder(T_b)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.45/28.49 => 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) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_fun__left__comm_Ofold__rec,axiom,
% 28.45/28.49 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 28.45/28.49 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.45/28.49 => 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)))))) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_fun__left__comm_Ofold__insert__remove,axiom,
% 28.45/28.49 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 28.45/28.49 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => 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)))))) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_fun__left__comm_Ofun__comp__comm,axiom,
% 28.45/28.49 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 28.45/28.49 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 28.45/28.49 => 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)) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom,
% 28.45/28.49 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 28.45/28.49 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 28.45/28.49 => 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)) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_fun__left__comm,axiom,
% 28.45/28.49 ! [T_b] :
% 28.45/28.49 ( class_Groups_Oab__semigroup__mult(T_b)
% 28.45/28.49 => c_Finite__Set_Ofun__left__comm(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_fun__left__comm_Ofun__left__comm,axiom,
% 28.45/28.49 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 28.45/28.49 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 28.45/28.49 => 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)) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_fun__left__comm_Ofold__graph__determ,axiom,
% 28.45/28.49 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 28.45/28.49 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 28.45/28.49 => V_y_2 = V_x_2 ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_fun__left__comm_Ofold__fun__comm,axiom,
% 28.45/28.49 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 28.45/28.49 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => 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) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_fun__left__comm_Ofold__equality,axiom,
% 28.45/28.49 ! [V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 28.45/28.49 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 28.45/28.49 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = V_y_2 ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_fun__left__comm_Ofold__graph__fold,axiom,
% 28.45/28.49 ! [V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 28.45/28.49 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => 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))) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_fun__left__comm_Ofold__insert2,axiom,
% 28.45/28.49 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 28.45/28.49 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.45/28.49 => 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) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_fun__left__comm_Ofold__insert,axiom,
% 28.45/28.49 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 28.45/28.49 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.45/28.49 => 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)) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom,
% 28.45/28.49 ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 28.45/28.49 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 28.45/28.49 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.45/28.49 => ? [B_y_H] :
% 28.45/28.49 ( V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H)
% 28.45/28.49 & 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)) ) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_fun__left__comm_Ofold__graph__insertE,axiom,
% 28.45/28.49 ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_c,T_b] :
% 28.45/28.49 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 28.45/28.49 => ( 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))
% 28.45/28.49 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.45/28.49 => ~ ! [B_y] :
% 28.45/28.49 ( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y)
% 28.45/28.49 => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_min__max_Ofold__sup__le__sup,axiom,
% 28.45/28.49 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 28.45/28.49 ( class_Orderings_Olinorder(T_b)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => ( ! [B_x] :
% 28.45/28.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.45/28.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) )
% 28.45/28.49 => 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))) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_min__max_Oinf__le__fold__inf,axiom,
% 28.45/28.49 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 28.45/28.49 ( class_Orderings_Olinorder(T_b)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => ( ! [B_x] :
% 28.45/28.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.45/28.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) )
% 28.45/28.49 => 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))) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_inf__le__fold__inf,axiom,
% 28.45/28.49 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 28.45/28.49 ( class_Lattices_Osemilattice__inf(T_b)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => ( ! [B_x] :
% 28.45/28.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.45/28.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) )
% 28.45/28.49 => 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))) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_fold__sup__le__sup,axiom,
% 28.45/28.49 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 28.45/28.49 ( class_Lattices_Osemilattice__sup(T_b)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => ( ! [B_x] :
% 28.45/28.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.45/28.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) )
% 28.45/28.49 => 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))) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_mod__div__decomp,axiom,
% 28.45/28.49 ! [V_b,V_a,T_a] :
% 28.45/28.49 ( class_Divides_Osemiring__div(T_a)
% 28.45/28.49 => 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)) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_wf__eq__minimal,axiom,
% 28.45/28.49 ! [V_r_2,T_b] :
% 28.45/28.49 ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.45/28.49 <=> ! [B_Q] :
% 28.45/28.49 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q))
% 28.45/28.49 => ? [B_x] :
% 28.45/28.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q))
% 28.45/28.49 & ! [B_y] :
% 28.45/28.49 ( 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))
% 28.45/28.49 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_y),B_Q)) ) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_folding__image__simple__idem_Ounion__idem,axiom,
% 28.45/28.49 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 28.45/28.49 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 28.45/28.49 => 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)) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_transfer__nat__int__set__cong,axiom,
% 28.45/28.49 ! [V_P_H_2,V_P_2] :
% 28.45/28.49 ( ! [B_x] :
% 28.45/28.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 28.45/28.49 => ( hBOOL(hAPP(V_P_2,B_x))
% 28.45/28.49 <=> hBOOL(hAPP(V_P_H_2,B_x)) ) )
% 28.45/28.49 => 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)) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_folding__image__simple__idem_Oidem,axiom,
% 28.45/28.49 ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 28.45/28.49 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 28.45/28.49 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_folding__image__simple__idem_Oin__idem,axiom,
% 28.45/28.49 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 28.45/28.49 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 28.45/28.49 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 28.45/28.49 => 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) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom,
% 28.45/28.49 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 28.45/28.49 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 28.45/28.49 => 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)) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_folding__image__simple__idem_Osubset__idem,axiom,
% 28.45/28.49 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 28.45/28.49 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 28.45/28.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))
% 28.45/28.49 => 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) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_Int__Collect__mono,axiom,
% 28.45/28.49 ! [V_Q_2,V_P_2,V_B_2,V_A_2,T_b] :
% 28.45/28.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.45/28.49 => ( ! [B_x] :
% 28.45/28.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.45/28.49 => ( hBOOL(hAPP(V_P_2,B_x))
% 28.45/28.49 => hBOOL(hAPP(V_Q_2,B_x)) ) )
% 28.45/28.49 => 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)))) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_converseE,axiom,
% 28.45/28.49 ! [V_r_2,V_yx_2,T_c,T_b] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => ~ ! [B_x,B_y] :
% 28.45/28.49 ( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_y),B_x)
% 28.45/28.49 => ~ 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)) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_rel__compE,axiom,
% 28.45/28.49 ! [V_s_2,V_r_2,T_d,V_xz_2,T_c,T_b] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => ~ ! [B_x,B_y,B_z] :
% 28.45/28.49 ( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z)
% 28.45/28.49 => ( 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))
% 28.45/28.49 => ~ 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)) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_Nitpick_Oplus__frac__def,axiom,
% 28.45/28.49 ! [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))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_Nitpick_Otimes__frac__def,axiom,
% 28.45/28.49 ! [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))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_Nitpick_Oof__frac__def,axiom,
% 28.45/28.49 ! [V_q,T_a,T_b] :
% 28.45/28.49 ( ( class_Rings_Oinverse(T_b)
% 28.45/28.49 & class_Rings_Oring__1(T_b) )
% 28.45/28.49 => 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))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_Nitpick_Oinverse__frac__def,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_Nitpick_Ouminus__frac__def,axiom,
% 28.45/28.49 ! [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))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_Nitpick_Oless__frac__def,axiom,
% 28.45/28.49 ! [V_r_2,V_q_2,T_b] :
% 28.45/28.49 ( c_Nitpick_Oless__frac(T_b,V_q_2,V_r_2)
% 28.45/28.49 <=> 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))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_Nitpick_Oless__eq__frac__def,axiom,
% 28.45/28.49 ! [V_r_2,V_q_2,T_b] :
% 28.45/28.49 ( c_Nitpick_Oless__eq__frac(T_b,V_q_2,V_r_2)
% 28.45/28.49 <=> 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))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_Nitpick_Onum__def,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_Nitpick_Odenom__def,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_setprod__pos,axiom,
% 28.45/28.49 ! [V_f_2,V_A_2,T_b,T_c] :
% 28.45/28.49 ( class_Rings_Olinordered__semidom(T_c)
% 28.45/28.49 => ( ! [B_x] :
% 28.45/28.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.45/28.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 28.45/28.49 => 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))) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_internal__split__def,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_internal__split__conv,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_setprod__nonneg,axiom,
% 28.45/28.49 ! [V_f_2,V_A_2,T_b,T_c] :
% 28.45/28.49 ( class_Rings_Olinordered__semidom(T_c)
% 28.45/28.49 => ( ! [B_x] :
% 28.45/28.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.45/28.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 28.45/28.49 => 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))) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_bool_Osize_I2_J,axiom,
% 28.45/28.49 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_bool_Osize_I1_J,axiom,
% 28.45/28.49 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_finite__less__ub,axiom,
% 28.45/28.49 ! [V_u_2,V_f_2] :
% 28.45/28.49 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_n),hAPP(V_f_2,B_n)))
% 28.45/28.49 => 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)))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_lenlex__def,axiom,
% 28.45/28.49 ! [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)))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_lexn__length,axiom,
% 28.45/28.49 ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = V_n_2
% 28.45/28.49 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2 ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_neq__if__length__neq,axiom,
% 28.45/28.49 ! [V_ys,V_xs,T_a] :
% 28.45/28.49 ( 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)
% 28.45/28.49 => V_xs != V_ys ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_lenlex__conv,axiom,
% 28.45/28.49 ! [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)))))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_length__sublists,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_length__sublist,axiom,
% 28.45/28.49 ! [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)))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_lexn_Osimps_I2_J,axiom,
% 28.45/28.49 ! [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)))))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_lexord__lex,axiom,
% 28.45/28.49 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 <=> ( 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)))
% 28.45/28.49 & 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) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_lexord__cons__cons,axiom,
% 28.45/28.49 ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_b] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 <=> ( 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))
% 28.45/28.49 | ( V_a_2 = V_b_2
% 28.45/28.49 & 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))) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_impossible__Cons,axiom,
% 28.45/28.49 ! [V_x,V_ys,V_xs,T_a] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_list_Oinject,axiom,
% 28.45/28.49 ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_b] :
% 28.45/28.49 ( 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)
% 28.45/28.49 <=> ( V_a_2 = V_a_H_2
% 28.45/28.49 & V_list_2 = V_list_H_2 ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_not__Cons__self2,axiom,
% 28.45/28.49 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs ).
% 28.45/28.49
% 28.45/28.49 fof(fact_not__Cons__self,axiom,
% 28.45/28.49 ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_list_Osize_I4_J,axiom,
% 28.45/28.49 ! [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))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_Cons__in__lex,axiom,
% 28.45/28.49 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 <=> ( ( 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))
% 28.45/28.49 & 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) )
% 28.45/28.49 | ( V_x_2 = V_y_2
% 28.45/28.49 & 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))) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_set__Cons__def,axiom,
% 28.45/28.49 ! [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)))))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_pick_Osimps,axiom,
% 28.45/28.49 ! [V_xs,V_x,T_a,V_i] :
% 28.45/28.49 ( ( 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)))
% 28.45/28.49 => 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) )
% 28.45/28.49 & ( ~ 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)))
% 28.45/28.49 => 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))) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_select__weight__cons__zero,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_rtrancl__listrel1__ConsI2,axiom,
% 28.45/28.49 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => ( 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))))
% 28.45/28.49 => 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)))) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_Cons__acc__listrel1I,axiom,
% 28.45/28.49 ! [V_xs_2,V_r_2,V_x_2,T_b] :
% 28.45/28.49 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 28.45/28.49 => ( 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))))
% 28.45/28.49 => 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)))) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom,
% 28.45/28.49 ! [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)))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listrel1__converse,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listrel1__mono,axiom,
% 28.45/28.49 ! [V_s_2,V_r_2,T_b] :
% 28.45/28.49 ( 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))
% 28.45/28.49 => 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))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_rtrancl__listrel1__ConsI1,axiom,
% 28.45/28.49 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 28.45/28.49 ( 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))))
% 28.45/28.49 => 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)))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listrel1I2,axiom,
% 28.45/28.49 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => 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))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listrel1__eq__len,axiom,
% 28.45/28.49 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => 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) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_rtrancl__listrel1__eq__len,axiom,
% 28.45/28.49 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 28.45/28.49 ( 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))))
% 28.45/28.49 => 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) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_in__listrel1__converse,axiom,
% 28.45/28.49 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 28.45/28.49 ( 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))))
% 28.45/28.49 <=> 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)))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listrel1I1,axiom,
% 28.45/28.49 ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 28.45/28.49 ( 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))
% 28.45/28.49 => 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))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_Cons__listrel1__Cons,axiom,
% 28.45/28.49 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 <=> ( ( 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))
% 28.45/28.49 & V_xs_2 = V_ys_2 )
% 28.45/28.49 | ( V_x_2 = V_y_2
% 28.45/28.49 & 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))) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_list_Osize_I2_J,axiom,
% 28.45/28.49 ! [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))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listrel__Cons,axiom,
% 28.45/28.49 ! [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))))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listrel__rtrancl__refl,axiom,
% 28.45/28.49 ! [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)))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listrel__mono,axiom,
% 28.45/28.49 ! [V_s_2,V_r_2,T_b] :
% 28.45/28.49 ( 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))
% 28.45/28.49 => 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))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listrel__subset__rtrancl__listrel1,axiom,
% 28.45/28.49 ! [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)))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listrel__eq__len,axiom,
% 28.45/28.49 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => 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) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listrel__rtrancl__trans,axiom,
% 28.45/28.49 ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 28.45/28.49 ( 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))))
% 28.45/28.49 => ( 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))))
% 28.45/28.49 => 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)))) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listrel__reflcl__if__listrel1,axiom,
% 28.45/28.49 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => 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)))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listrel1__subset__listrel,axiom,
% 28.45/28.49 ! [V_r_H_2,V_r_2,T_b] :
% 28.45/28.49 ( 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))
% 28.45/28.49 => ( c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_r_H_2)
% 28.45/28.49 => 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))) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_rtrancl__listrel1__if__listrel,axiom,
% 28.45/28.49 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => 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)))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listrel_OCons,axiom,
% 28.45/28.49 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 28.45/28.49 ( 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))
% 28.45/28.49 => ( 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)))
% 28.45/28.49 => 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))) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listrelp__listrel__eq,axiom,
% 28.45/28.49 ! [V_xa_2,V_x_2,V_r_2,T_b] :
% 28.45/28.49 ( 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)
% 28.45/28.49 <=> 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))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listrel__Cons2,axiom,
% 28.45/28.49 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_b] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => ~ ! [B_x,B_xs] :
% 28.45/28.49 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs)
% 28.45/28.49 => ( 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))
% 28.45/28.49 => ~ 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))) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listrelp_OCons,axiom,
% 28.45/28.49 ! [V_ys_2,V_xs_2,T_b,V_y_2,V_x_2,V_r_2] :
% 28.45/28.49 ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
% 28.45/28.49 => ( c_List_Olistrelp(T_b,V_r_2,V_xs_2,V_ys_2)
% 28.45/28.49 => 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)) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listrelp_Oequations_I2_J,axiom,
% 28.45/28.49 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_b] :
% 28.45/28.49 ( 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))
% 28.45/28.49 <=> ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2))
% 28.45/28.49 & c_List_Olistrelp(T_b,V_r_2,V_a3_2,V_a4_2) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listrel__Cons1,axiom,
% 28.45/28.49 ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_b] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => ~ ! [B_y,B_ys] :
% 28.45/28.49 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_ys)
% 28.45/28.49 => ( 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))
% 28.45/28.49 => ~ 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))) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listrel__subset,axiom,
% 28.45/28.49 ! [V_A_2,V_r_2,T_b] :
% 28.45/28.49 ( 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))))
% 28.45/28.49 => 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))))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_lists__UNIV,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_lists__mono,axiom,
% 28.45/28.49 ! [V_B_2,V_A_2,T_b] :
% 28.45/28.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.45/28.49 => 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))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_equiv__listrel,axiom,
% 28.45/28.49 ! [V_r_2,V_A_2,T_b] :
% 28.45/28.49 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 28.45/28.49 => 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)) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listrel__refl__on,axiom,
% 28.45/28.49 ! [V_r_2,V_A_2,T_b] :
% 28.45/28.49 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 28.45/28.49 => 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)) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_Cons__in__lists__iff,axiom,
% 28.45/28.49 ! [V_A_2,V_xs_2,V_x_2,T_b] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.45/28.49 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_lists__accI,axiom,
% 28.45/28.49 ! [V_r_2,V_xs_2,T_b] :
% 28.45/28.49 ( 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))))
% 28.45/28.49 => 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)))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_lists__accD,axiom,
% 28.45/28.49 ! [V_r_2,V_xs_2,T_b] :
% 28.45/28.49 ( 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))))
% 28.45/28.49 => 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)))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listrel__iff__nth,axiom,
% 28.45/28.49 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 <=> ( 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)
% 28.45/28.49 & ! [B_n] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => 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)) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_lexord__irreflexive,axiom,
% 28.45/28.49 ! [V_y_2,V_r_2,T_b] :
% 28.45/28.49 ( ! [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))
% 28.45/28.49 => ~ 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))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_nth__Cons__0,axiom,
% 28.45/28.49 ! [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 ).
% 28.45/28.49
% 28.45/28.49 fof(fact_nth__Cons__Suc,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_list__eq__iff__nth__eq,axiom,
% 28.45/28.49 ! [T_b,V_ys_2,V_xs_2] :
% 28.45/28.49 ( V_xs_2 = V_ys_2
% 28.45/28.49 <=> ( 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)
% 28.45/28.49 & ! [B_i] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_i) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_infinite__UNIV__listI,axiom,
% 28.45/28.49 ! [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)))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_nth_Osimps,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_nth__Cons_H,axiom,
% 28.45/28.49 ! [V_xs,V_x,T_a,V_n] :
% 28.45/28.49 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.45/28.49 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x )
% 28.45/28.49 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.45/28.49 => 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))) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_nth__Cons__number__of,axiom,
% 28.45/28.49 ! [V_xs,V_x,T_a,V_v] :
% 28.45/28.49 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.45/28.49 => 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 )
% 28.45/28.49 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.45/28.49 => 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))) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_lexord__take__index__conv,axiom,
% 28.45/28.49 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 <=> ( ( 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)))
% 28.45/28.49 & 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 )
% 28.45/28.49 | ? [B_i] :
% 28.45/28.49 ( 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))))
% 28.45/28.49 & hAPP(hAPP(c_List_Otake(T_b),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_b),B_i),V_y_2)
% 28.45/28.49 & 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)) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_lexord__linear,axiom,
% 28.45/28.49 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 28.45/28.49 ( ! [B_a,B_b] :
% 28.45/28.49 ( 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))
% 28.45/28.49 | B_a = B_b
% 28.45/28.49 | 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)) )
% 28.45/28.49 => ( 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)))
% 28.45/28.49 | V_x_2 = V_y_2
% 28.45/28.49 | 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))) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_take__all,axiom,
% 28.45/28.49 ! [V_n,V_xs,T_a] :
% 28.45/28.49 ( 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))
% 28.45/28.49 => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_nth__take,axiom,
% 28.45/28.49 ! [V_xs,T_a,V_n,V_i] :
% 28.45/28.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n))
% 28.45/28.49 => 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) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_sublist__upt__eq__take,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_take__take,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_length__take,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_take__Suc__Cons,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_finite__lists__length__le,axiom,
% 28.45/28.49 ! [V_n_2,V_A_2,T_b] :
% 28.45/28.49 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => 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))))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_set__sublist,axiom,
% 28.45/28.49 ! [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))))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_finite__set,axiom,
% 28.45/28.49 ! [V_xs_2,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_set__take__subset,axiom,
% 28.45/28.49 ! [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))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_in__set__takeD,axiom,
% 28.45/28.49 ! [V_xs_2,V_n_2,V_x_2,T_b] :
% 28.45/28.49 ( 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))))
% 28.45/28.49 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_List_Oset_Osimps_I2_J,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_set__ConsD,axiom,
% 28.45/28.49 ! [V_xs_2,V_x_2,V_y_2,T_b] :
% 28.45/28.49 ( 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))))
% 28.45/28.49 => ( V_y_2 = V_x_2
% 28.45/28.49 | hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_notin__set__sublistI,axiom,
% 28.45/28.49 ! [V_I_2,V_xs_2,V_x_2,T_b] :
% 28.45/28.49 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.45/28.49 => ~ 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)))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_in__set__sublistD,axiom,
% 28.45/28.49 ! [V_I_2,V_xs_2,V_x_2,T_b] :
% 28.45/28.49 ( 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))))
% 28.45/28.49 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_sublists__powset,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_set__subset__Cons,axiom,
% 28.45/28.49 ! [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)))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_set__sublist__subset,axiom,
% 28.45/28.49 ! [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))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_card__length,axiom,
% 28.45/28.49 ! [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))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_all__set__conv__all__nth,axiom,
% 28.45/28.49 ! [V_P_2,V_xs_2,T_b] :
% 28.45/28.49 ( ! [B_x] :
% 28.45/28.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.45/28.49 => hBOOL(hAPP(V_P_2,B_x)) )
% 28.45/28.49 <=> ! [B_i] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_set__take__subset__set__take,axiom,
% 28.45/28.49 ! [V_xs_2,T_b,V_n_2,V_m_2] :
% 28.45/28.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 28.45/28.49 => 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)))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_list__size__estimation,axiom,
% 28.45/28.49 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 28.45/28.49 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.45/28.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 28.45/28.49 => 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))) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_list__size__estimation_H,axiom,
% 28.45/28.49 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 28.45/28.49 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.45/28.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 28.45/28.49 => 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))) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_in__lists__conv__set,axiom,
% 28.45/28.49 ! [V_A_2,V_xs_2,T_b] :
% 28.45/28.49 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
% 28.45/28.49 <=> ! [B_x] :
% 28.45/28.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.45/28.49 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_length__pos__if__in__set,axiom,
% 28.45/28.49 ! [V_xs_2,V_x_2,T_b] :
% 28.45/28.49 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.45/28.49 => 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))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_in__set__conv__nth,axiom,
% 28.45/28.49 ! [V_xs_2,V_x_2,T_b] :
% 28.45/28.49 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.45/28.49 <=> ? [B_i] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 & hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = V_x_2 ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_nth__mem,axiom,
% 28.45/28.49 ! [V_xs_2,T_b,V_n_2] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => 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))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_lists__eq__set,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_set__conv__nth,axiom,
% 28.45/28.49 ! [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))))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_finite__lists__length__eq,axiom,
% 28.45/28.49 ! [V_n_2,V_A_2,T_b] :
% 28.45/28.49 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => 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))))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listrel__iff__zip,axiom,
% 28.45/28.49 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 <=> ( 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)
% 28.45/28.49 & ! [B_x] :
% 28.45/28.49 ( 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))))
% 28.45/28.49 => 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)) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_set__n__lists,axiom,
% 28.45/28.49 ! [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)))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_length__zip,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_take__zip,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_zip__Cons__Cons,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_list__eq__iff__zip__eq,axiom,
% 28.45/28.49 ! [T_b,V_ys_2,V_xs_2] :
% 28.45/28.49 ( V_xs_2 = V_ys_2
% 28.45/28.49 <=> ( 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)
% 28.45/28.49 & ! [B_x] :
% 28.45/28.49 ( 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))))
% 28.45/28.49 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_fequal),B_x)) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_zip__same,axiom,
% 28.45/28.49 ! [V_xs_2,V_b_2,V_a_2,T_b] :
% 28.45/28.49 ( 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))))
% 28.45/28.49 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.45/28.49 & V_a_2 = V_b_2 ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_set__zip__leftD,axiom,
% 28.45/28.49 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 28.45/28.49 ( 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))))
% 28.45/28.49 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_set__zip__rightD,axiom,
% 28.45/28.49 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 28.45/28.49 ( 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))))
% 28.45/28.49 => hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_in__set__zipE,axiom,
% 28.45/28.49 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 28.45/28.49 ( 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))))
% 28.45/28.49 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.45/28.49 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_nth__zip,axiom,
% 28.45/28.49 ! [V_ys,T_b,V_xs,T_a,V_i] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => ( 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)))
% 28.45/28.49 => 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)) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_length__n__lists__elem,axiom,
% 28.45/28.49 ! [V_xs_2,V_n_2,V_ys_2,T_b] :
% 28.45/28.49 ( 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))))
% 28.45/28.49 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2 ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_length__n__lists,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_set__zip,axiom,
% 28.45/28.49 ! [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)))))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_product__list__set,axiom,
% 28.45/28.49 ! [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))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_greaterThanLessThan__upto,axiom,
% 28.45/28.49 ! [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)))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_set__upto,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_atLeastAtMost__upto,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_atLeastLessThan__upto,axiom,
% 28.45/28.49 ! [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)))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_greaterThanAtMost__upto,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_nat__list__def,axiom,
% 28.45/28.49 ! [V_l_2] :
% 28.45/28.49 ( c_List_Onat__list(V_l_2)
% 28.45/28.49 <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listsum__setsum__nth,axiom,
% 28.45/28.49 ! [V_xs_2,T_b] :
% 28.45/28.49 ( class_Groups_Ocomm__monoid__add(T_b)
% 28.45/28.49 => 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))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listsum__eq__0__nat__iff__nat,axiom,
% 28.45/28.49 ! [V_ns_2] :
% 28.45/28.49 ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.45/28.49 <=> ! [B_x] :
% 28.45/28.49 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 28.45/28.49 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listsum__simps_I2_J,axiom,
% 28.45/28.49 ! [V_xs,V_x,T_a] :
% 28.45/28.49 ( class_Groups_Omonoid__add(T_a)
% 28.45/28.49 => 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)) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_elem__le__listsum__nat,axiom,
% 28.45/28.49 ! [V_ns,V_k] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => 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))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_list__size__pointwise,axiom,
% 28.45/28.49 ! [V_g_2,V_f_2,V_xs_2,T_b] :
% 28.45/28.49 ( ! [B_x] :
% 28.45/28.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.45/28.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 28.45/28.49 => 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))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_butlast__take,axiom,
% 28.45/28.49 ! [V_xs,T_a,V_n] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => 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) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_in__set__butlastD,axiom,
% 28.45/28.49 ! [V_xs_2,V_x_2,T_b] :
% 28.45/28.49 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2))))
% 28.45/28.49 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_take__butlast,axiom,
% 28.45/28.49 ! [V_xs,T_a,V_n] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => 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) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_length__butlast,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_butlast__conv__take,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listsum__update__nat,axiom,
% 28.45/28.49 ! [V_n,V_ns,V_k] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => 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)) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_nth__take__lemma,axiom,
% 28.45/28.49 ! [V_ys,V_xs,T_a,V_k] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => ( 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)))
% 28.45/28.49 => ( ! [B_i] :
% 28.45/28.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k))
% 28.45/28.49 => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) )
% 28.45/28.49 => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_list__update__beyond,axiom,
% 28.45/28.49 ! [V_x,V_i,V_xs,T_a] :
% 28.45/28.49 ( 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))
% 28.45/28.49 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_nth__list__update__neq,axiom,
% 28.45/28.49 ! [V_x,V_xs,T_a,V_j,V_i] :
% 28.45/28.49 ( V_i != V_j
% 28.45/28.49 => 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) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_list__update__id,axiom,
% 28.45/28.49 ! [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 ).
% 28.45/28.49
% 28.45/28.49 fof(fact_length__list__update,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_list__update_Osimps_I2_J,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_list__update__code_I2_J,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_list__update__code_I3_J,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_list__update__overwrite,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_list__update__swap,axiom,
% 28.45/28.49 ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] :
% 28.45/28.49 ( V_i != V_i_H
% 28.45/28.49 => 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) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_update__zip,axiom,
% 28.45/28.49 ! [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))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_zip__update,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_set__update__subsetI,axiom,
% 28.45/28.49 ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_b] :
% 28.45/28.49 ( 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))
% 28.45/28.49 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.45/28.49 => 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)) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_set__update__subset__insert,axiom,
% 28.45/28.49 ! [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)))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_nth__list__update__eq,axiom,
% 28.45/28.49 ! [V_x,V_xs,T_a,V_i] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => 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 ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_list__update__same__conv,axiom,
% 28.45/28.49 ! [V_x_2,V_xs_2,T_b,V_i_2] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2) = V_xs_2
% 28.45/28.49 <=> hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = V_x_2 ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_nth__list__update,axiom,
% 28.45/28.49 ! [V_x,V_j,V_xs,T_a,V_i] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => ( ( V_i = V_j
% 28.45/28.49 => 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 )
% 28.45/28.49 & ( V_i != V_j
% 28.45/28.49 => 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) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_set__update__memI,axiom,
% 28.45/28.49 ! [V_x_2,V_xs_2,T_b,V_n_2] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => 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)))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_butlast__list__update,axiom,
% 28.45/28.49 ! [V_x,V_xs,T_a,V_k] :
% 28.45/28.49 ( ( 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))
% 28.45/28.49 => 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) )
% 28.45/28.49 & ( 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))
% 28.45/28.49 => 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) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listrel1__iff__update,axiom,
% 28.45/28.49 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 <=> ? [B_y,B_n] :
% 28.45/28.49 ( 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))
% 28.45/28.49 & 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)))
% 28.45/28.49 & V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),B_n),B_y) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_distinct__list__update,axiom,
% 28.45/28.49 ! [V_i_2,V_a_2,V_xs_2,T_b] :
% 28.45/28.49 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 28.45/28.49 => ( ~ 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))))))
% 28.45/28.49 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_a_2))) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_distinct__n__lists,axiom,
% 28.45/28.49 ! [V_n,V_xs,T_a] :
% 28.45/28.49 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 28.45/28.49 => hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n,V_xs))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_distinct__zipI1,axiom,
% 28.45/28.49 ! [V_ys,T_b,V_xs,T_a] :
% 28.45/28.49 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 28.45/28.49 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_distinct__zipI2,axiom,
% 28.45/28.49 ! [V_xs,T_b,V_ys,T_a] :
% 28.45/28.49 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys))
% 28.45/28.49 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_distinct__sublistI,axiom,
% 28.45/28.49 ! [V_I_2,V_xs_2,T_b] :
% 28.45/28.49 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 28.45/28.49 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_distinct__product,axiom,
% 28.45/28.49 ! [V_ys,T_b,V_xs,T_a] :
% 28.45/28.49 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 28.45/28.49 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys))
% 28.45/28.49 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs,V_ys))) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_distinct__upto,axiom,
% 28.45/28.49 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_distinct__take,axiom,
% 28.45/28.49 ! [V_i,V_xs,T_a] :
% 28.45/28.49 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 28.45/28.49 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_distinct_Osimps_I2_J,axiom,
% 28.45/28.49 ! [V_xs_2,V_x_2,T_b] :
% 28.45/28.49 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))
% 28.45/28.49 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.45/28.49 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_card__distinct,axiom,
% 28.45/28.49 ! [V_xs_2,T_b] :
% 28.45/28.49 ( 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)
% 28.45/28.49 => hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_distinct__card,axiom,
% 28.45/28.49 ! [V_xs_2,T_b] :
% 28.45/28.49 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 28.45/28.49 => 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) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_nth__eq__iff__index__eq,axiom,
% 28.45/28.49 ! [V_j_2,V_i_2,V_xs_2,T_b] :
% 28.45/28.49 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 28.45/28.49 => ( 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)))
% 28.45/28.49 => ( 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)))
% 28.45/28.49 => ( 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)
% 28.45/28.49 <=> V_i_2 = V_j_2 ) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_distinct__conv__nth,axiom,
% 28.45/28.49 ! [V_xs_2,T_b] :
% 28.45/28.49 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 28.45/28.49 <=> ! [B_i] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => ! [B_j] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => ( B_i != B_j
% 28.45/28.49 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j) ) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_distinct__listsum__conv__Setsum,axiom,
% 28.45/28.49 ! [V_xs_2,T_b] :
% 28.45/28.49 ( class_Groups_Ocomm__monoid__add(T_b)
% 28.45/28.49 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 28.45/28.49 => 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)) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_Nitpick_Ocard_H__def,axiom,
% 28.45/28.49 ! [V_A_2,T_b] :
% 28.45/28.49 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => 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)))) )
% 28.45/28.49 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => c_Nitpick_Ocard_H(T_b,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_set__remove1__eq,axiom,
% 28.45/28.49 ! [V_x_2,V_xs_2,T_b] :
% 28.45/28.49 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 28.45/28.49 => 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)))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_distinct__remove1,axiom,
% 28.45/28.49 ! [V_x,V_xs,T_a] :
% 28.45/28.49 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 28.45/28.49 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_remove1_Osimps_I2_J,axiom,
% 28.45/28.49 ! [V_xs,T_a,V_y,V_x] :
% 28.45/28.49 ( ( V_x = V_y
% 28.45/28.49 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs )
% 28.45/28.49 & ( V_x != V_y
% 28.45/28.49 => 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)) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_remove1__commute,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_remove1__idem,axiom,
% 28.45/28.49 ! [V_xs_2,V_x_2,T_b] :
% 28.45/28.49 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.45/28.49 => c_List_Oremove1(T_b,V_x_2,V_xs_2) = V_xs_2 ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_notin__set__remove1,axiom,
% 28.45/28.49 ! [V_y_2,V_xs_2,V_x_2,T_b] :
% 28.45/28.49 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.45/28.49 => ~ 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)))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_in__set__remove1,axiom,
% 28.45/28.49 ! [V_xs_2,T_b,V_b_2,V_a_2] :
% 28.45/28.49 ( V_a_2 != V_b_2
% 28.45/28.49 => ( 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))))
% 28.45/28.49 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_set__remove1__subset,axiom,
% 28.45/28.49 ! [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))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_length__remove1,axiom,
% 28.45/28.49 ! [V_xs_2,V_x_2,T_b] :
% 28.45/28.49 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.45/28.49 => 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)) )
% 28.45/28.49 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.45/28.49 => 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) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_sorted__list__of__set__remove,axiom,
% 28.45/28.49 ! [V_x_2,V_A_2,T_b] :
% 28.45/28.49 ( class_Orderings_Olinorder(T_b)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => 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)) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_take__Cons__number__of,axiom,
% 28.45/28.49 ! [V_xs,V_x,T_a,V_v] :
% 28.45/28.49 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.45/28.49 => 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) )
% 28.45/28.49 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.45/28.49 => 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)) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_lists_ONil,axiom,
% 28.45/28.49 ! [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))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listrel__Nil2,axiom,
% 28.45/28.49 ! [V_r_2,V_xs_2,T_b] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listrel__Nil1,axiom,
% 28.45/28.49 ! [V_r_2,V_xs_2,T_b] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_distinct_Osimps_I1_J,axiom,
% 28.45/28.49 ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_distinct__butlast,axiom,
% 28.45/28.49 ! [T_a,V_xs] :
% 28.45/28.49 ( V_xs != c_List_Olist_ONil(T_a)
% 28.45/28.49 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 28.45/28.49 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_remove1_Osimps_I1_J,axiom,
% 28.45/28.49 ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_zip__Nil,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_zip_Osimps_I1_J,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_sorted__list__of__set__empty,axiom,
% 28.45/28.49 ! [T_b] :
% 28.45/28.49 ( class_Orderings_Olinorder(T_b)
% 28.45/28.49 => 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) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_sublist__nil,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listrelp_Oequations_I1_J,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listrelp_ONil,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_list_Osize_I1_J,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_upto__empty,axiom,
% 28.45/28.49 ! [V_i,V_j] :
% 28.45/28.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i))
% 28.45/28.49 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_product_Osimps_I1_J,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_list_Osimps_I2_J,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_list_Osimps_I3_J,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_sublists_Osimps_I1_J,axiom,
% 28.45/28.49 ! [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))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_take__0,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_take__eq__Nil,axiom,
% 28.45/28.49 ! [V_xs_2,V_n_2,T_b] :
% 28.45/28.49 ( hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 28.45/28.49 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.45/28.49 | V_xs_2 = c_List_Olist_ONil(T_b) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_take__Nil,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_n__lists__Nil,axiom,
% 28.45/28.49 ! [T_a,V_n] :
% 28.45/28.49 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.45/28.49 => 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))) )
% 28.45/28.49 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.45/28.49 => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_n__lists_Osimps_I1_J,axiom,
% 28.45/28.49 ! [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))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_set__empty,axiom,
% 28.45/28.49 ! [V_xs_2,T_b] :
% 28.45/28.49 ( hAPP(c_List_Oset(T_b),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.45/28.49 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_set__empty2,axiom,
% 28.45/28.49 ! [V_xs_2,T_b] :
% 28.45/28.49 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_List_Oset(T_b),V_xs_2)
% 28.45/28.49 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_List_Oset_Osimps_I1_J,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_butlast_Osimps_I2_J,axiom,
% 28.45/28.49 ! [V_x,T_a,V_xs] :
% 28.45/28.49 ( ( V_xs = c_List_Olist_ONil(T_a)
% 28.45/28.49 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) )
% 28.45/28.49 & ( V_xs != c_List_Olist_ONil(T_a)
% 28.45/28.49 => 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)) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_length__0__conv,axiom,
% 28.45/28.49 ! [V_xs_2,T_b] :
% 28.45/28.49 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.45/28.49 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_list_Osize_I3_J,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_butlast_Osimps_I1_J,axiom,
% 28.45/28.49 ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listsum__simps_I1_J,axiom,
% 28.45/28.49 ! [T_a] :
% 28.45/28.49 ( class_Groups_Omonoid__add(T_a)
% 28.45/28.49 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_list__update__code_I1_J,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_list__update_Osimps_I1_J,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_list__update__nonempty,axiom,
% 28.45/28.49 ! [V_x_2,V_k_2,V_xs_2,T_b] :
% 28.45/28.49 ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_b)
% 28.45/28.49 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_sublist__empty,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_length__greater__0__conv,axiom,
% 28.45/28.49 ! [V_xs_2,T_b] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 <=> V_xs_2 != c_List_Olist_ONil(T_b) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_take__1__Cons,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_not__Nil__listrel1,axiom,
% 28.45/28.49 ! [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))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_not__listrel1__Nil,axiom,
% 28.45/28.49 ! [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))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listrel_ONil,axiom,
% 28.45/28.49 ! [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))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_lexord__Nil__right,axiom,
% 28.45/28.49 ! [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))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_Nil2__notin__lex,axiom,
% 28.45/28.49 ! [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))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_Nil__notin__lex,axiom,
% 28.45/28.49 ! [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))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_take__Cons,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_upto_Osimps,axiom,
% 28.45/28.49 ! [V_j,V_i] :
% 28.45/28.49 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 28.45/28.49 => 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)) )
% 28.45/28.49 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 28.45/28.49 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_sublist__singleton,axiom,
% 28.45/28.49 ! [V_x_2,T_b,V_A_2] :
% 28.45/28.49 ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 28.45/28.49 => 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)) )
% 28.45/28.49 & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 28.45/28.49 => 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) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_lists__empty,axiom,
% 28.45/28.49 ! [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))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_take__Cons_H,axiom,
% 28.45/28.49 ! [V_xs,V_x,T_a,V_n] :
% 28.45/28.49 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.45/28.49 => 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) )
% 28.45/28.49 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.45/28.49 => 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)) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_upto__rec__number__of,axiom,
% 28.45/28.49 ! [V_n,V_m] :
% 28.45/28.49 ( ( 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)))
% 28.45/28.49 => 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))) )
% 28.45/28.49 & ( ~ 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)))
% 28.45/28.49 => 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) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listrel__Nil,axiom,
% 28.45/28.49 ! [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))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_set__Cons__sing__Nil,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_upto_Opsimps,axiom,
% 28.45/28.49 ! [V_j_2,V_i_2] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 28.45/28.49 => 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)) )
% 28.45/28.49 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 28.45/28.49 => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_select,axiom,
% 28.45/28.49 ! [V_s_2,T_b,V_xs_2] :
% 28.45/28.49 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 28.45/28.49 => 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))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listset_Osimps_I1_J,axiom,
% 28.45/28.49 ! [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))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_zip__Cons,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_list_Osimps_I5_J,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_list_Osimps_I4_J,axiom,
% 28.45/28.49 ! [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 ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listset_Osimps_I2_J,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_zip__Cons1,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_upto_Opinduct,axiom,
% 28.45/28.49 ! [V_P_2,V_a1_2,V_a0_2] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => ( ! [B_i,B_j] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j))
% 28.45/28.49 => 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)) )
% 28.45/28.49 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) )
% 28.45/28.49 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_anamorph_Osimps,axiom,
% 28.45/28.49 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
% 28.45/28.49 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 28.45/28.49 => 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) )
% 28.45/28.49 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 28.45/28.49 => 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)) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_sublist__Cons,axiom,
% 28.45/28.49 ! [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)))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_snoc__listrel1__snoc__iff,axiom,
% 28.45/28.49 ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 <=> ( ( 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)))
% 28.45/28.49 & V_x_2 = V_y_2 )
% 28.45/28.49 | ( V_xs_2 = V_ys_2
% 28.45/28.49 & 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)) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_append__eq__Cons__conv,axiom,
% 28.45/28.49 ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_b] :
% 28.45/28.49 ( 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)
% 28.45/28.49 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b)
% 28.45/28.49 & V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) )
% 28.45/28.49 | ? [B_ys_H] :
% 28.45/28.49 ( V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H)
% 28.45/28.49 & hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) = V_xs_2 ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_Cons__eq__append__conv,axiom,
% 28.45/28.49 ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_b] :
% 28.45/28.49 ( 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)
% 28.45/28.49 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b)
% 28.45/28.49 & hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = V_zs_2 )
% 28.45/28.49 | ? [B_ys_H] :
% 28.45/28.49 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) = V_ys_2
% 28.45/28.49 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_append1__eq__conv,axiom,
% 28.45/28.49 ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 <=> ( V_xs_2 = V_ys_2
% 28.45/28.49 & V_x_2 = V_y_2 ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_append__Cons,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_Cons__eq__appendI,axiom,
% 28.45/28.49 ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] :
% 28.45/28.49 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys
% 28.45/28.49 => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs)
% 28.45/28.49 => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_append__in__lists__conv,axiom,
% 28.45/28.49 ! [V_A_2,V_ys_2,V_xs_2,T_b] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
% 28.45/28.49 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),c_List_Olists(T_b,V_A_2))) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_append__eq__appendI,axiom,
% 28.45/28.49 ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] :
% 28.45/28.49 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs
% 28.45/28.49 => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us)
% 28.45/28.49 => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_append__same__eq,axiom,
% 28.45/28.49 ! [V_zs_2,V_xs_2,V_ys_2,T_b] :
% 28.45/28.49 ( 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)
% 28.45/28.49 <=> V_ys_2 = V_zs_2 ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_same__append__eq,axiom,
% 28.45/28.49 ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
% 28.45/28.49 ( 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)
% 28.45/28.49 <=> V_ys_2 = V_zs_2 ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_append__eq__append__conv2,axiom,
% 28.45/28.49 ! [V_tsa_2,V_zs_2,V_ys_2,V_xs_2,T_b] :
% 28.45/28.49 ( 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)
% 28.45/28.49 <=> ? [B_us] :
% 28.45/28.49 ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),B_us)
% 28.45/28.49 & hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ys_2) = V_tsa_2 )
% 28.45/28.49 | ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),B_us) = V_zs_2
% 28.45/28.49 & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),V_tsa_2) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_append__assoc,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_set__append,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_zip__append,axiom,
% 28.45/28.49 ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] :
% 28.45/28.49 ( 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)
% 28.45/28.49 => ( 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)
% 28.45/28.49 => 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)) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_length__append,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listsum__append,axiom,
% 28.45/28.49 ! [V_ys,V_xs,T_a] :
% 28.45/28.49 ( class_Groups_Omonoid__add(T_a)
% 28.45/28.49 => 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)) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_butlast__append,axiom,
% 28.45/28.49 ! [V_xs,T_a,V_ys] :
% 28.45/28.49 ( ( V_ys = c_List_Olist_ONil(T_a)
% 28.45/28.49 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) )
% 28.45/28.49 & ( V_ys != c_List_Olist_ONil(T_a)
% 28.45/28.49 => 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)) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_append__Nil,axiom,
% 28.45/28.49 ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys ).
% 28.45/28.49
% 28.45/28.49 fof(fact_Nil__is__append__conv,axiom,
% 28.45/28.49 ! [V_ys_2,V_xs_2,T_b] :
% 28.45/28.49 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 28.45/28.49 <=> ( V_xs_2 = c_List_Olist_ONil(T_b)
% 28.45/28.49 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_append__Nil2,axiom,
% 28.45/28.49 ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs ).
% 28.45/28.49
% 28.45/28.49 fof(fact_self__append__conv,axiom,
% 28.45/28.49 ! [V_ys_2,T_b,V_xs_2] :
% 28.45/28.49 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 28.45/28.49 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_self__append__conv2,axiom,
% 28.45/28.49 ! [V_xs_2,T_b,V_ys_2] :
% 28.45/28.49 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 28.45/28.49 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_append__is__Nil__conv,axiom,
% 28.45/28.49 ! [V_ys_2,V_xs_2,T_b] :
% 28.45/28.49 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_b)
% 28.45/28.49 <=> ( V_xs_2 = c_List_Olist_ONil(T_b)
% 28.45/28.49 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_append__self__conv,axiom,
% 28.45/28.49 ! [V_ys_2,V_xs_2,T_b] :
% 28.45/28.49 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_xs_2
% 28.45/28.49 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_append__self__conv2,axiom,
% 28.45/28.49 ! [V_ys_2,V_xs_2,T_b] :
% 28.45/28.49 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_ys_2
% 28.45/28.49 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_eq__Nil__appendI,axiom,
% 28.45/28.49 ! [T_a,V_ys,V_xs] :
% 28.45/28.49 ( V_xs = V_ys
% 28.45/28.49 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_nth__append__length,axiom,
% 28.45/28.49 ! [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 ).
% 28.45/28.49
% 28.45/28.49 fof(fact_nth__append__length__plus,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_take__append,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_list__update__append1,axiom,
% 28.45/28.49 ! [V_x,V_ys,V_xs,T_a,V_i] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => 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) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_list__update__length,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_remove1__append,axiom,
% 28.45/28.49 ! [V_ys_2,V_xs_2,V_x_2,T_b] :
% 28.45/28.49 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.45/28.49 => 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) )
% 28.45/28.49 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.45/28.49 => 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)) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_in__set__butlast__appendI,axiom,
% 28.45/28.49 ! [V_ys_2,V_xs_2,V_x_2,T_b] :
% 28.45/28.49 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2))))
% 28.45/28.49 | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_ys_2)))) )
% 28.45/28.49 => 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))))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_butlast__snoc,axiom,
% 28.45/28.49 ! [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 ).
% 28.45/28.49
% 28.45/28.49 fof(fact_append__listrel1I,axiom,
% 28.45/28.49 ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 28.45/28.49 ( ( ( 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)))
% 28.45/28.49 & V_us_2 = V_vs_2 )
% 28.45/28.49 | ( V_xs_2 = V_ys_2
% 28.45/28.49 & 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))) ) )
% 28.45/28.49 => 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))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_lexord__append__leftI,axiom,
% 28.45/28.49 ! [V_x_2,V_r_2,V_v_2,V_u_2,T_b] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => 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))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_distinct__append,axiom,
% 28.45/28.49 ! [V_ys_2,V_xs_2,T_b] :
% 28.45/28.49 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))
% 28.45/28.49 <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 28.45/28.49 & hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
% 28.45/28.49 & 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)) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_nth__append,axiom,
% 28.45/28.49 ! [V_ys,V_xs,T_a,V_n] :
% 28.45/28.49 ( ( 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)))
% 28.45/28.49 => 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) )
% 28.45/28.49 & ( ~ 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)))
% 28.45/28.49 => 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))) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_list__update__append,axiom,
% 28.45/28.49 ! [V_x,V_ys,V_xs,T_a,V_n] :
% 28.45/28.49 ( ( 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)))
% 28.45/28.49 => 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) )
% 28.45/28.49 & ( ~ 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)))
% 28.45/28.49 => 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)) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_sublist__append,axiom,
% 28.45/28.49 ! [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)))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listrel1I,axiom,
% 28.45/28.49 ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 28.45/28.49 ( 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))
% 28.45/28.49 => ( 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))
% 28.45/28.49 => ( 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))
% 28.45/28.49 => 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))) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_lexord__append__left__rightI,axiom,
% 28.45/28.49 ! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_b] :
% 28.45/28.49 ( 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))
% 28.45/28.49 => 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))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_take__Suc__conv__app__nth,axiom,
% 28.45/28.49 ! [V_xs,T_a,V_i] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => 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))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listrel1E,axiom,
% 28.45/28.49 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => ~ ! [B_x,B_y] :
% 28.45/28.49 ( 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))
% 28.45/28.49 => ! [B_us,B_vs] :
% 28.45/28.49 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_vs))
% 28.45/28.49 => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_vs)) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_lexord__append__leftD,axiom,
% 28.45/28.49 ! [V_r_2,V_v_2,V_u_2,V_x_2,T_b] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => ( ! [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))
% 28.45/28.49 => 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))) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_rotate1__def,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_upd__conv__take__nth__drop,axiom,
% 28.45/28.49 ! [V_a,V_xs,T_a,V_i] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => 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))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_append__take__drop__id,axiom,
% 28.45/28.49 ! [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 ).
% 28.45/28.49
% 28.45/28.49 fof(fact_drop__1__Cons,axiom,
% 28.45/28.49 ! [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 ).
% 28.45/28.49
% 28.45/28.49 fof(fact_drop__Suc__Cons,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_nth__via__drop,axiom,
% 28.45/28.49 ! [V_ys,V_y,V_xs,V_n,T_a] :
% 28.45/28.49 ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)
% 28.45/28.49 => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_distinct__drop,axiom,
% 28.45/28.49 ! [V_i,V_xs,T_a] :
% 28.45/28.49 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 28.45/28.49 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_distinct1__rotate,axiom,
% 28.45/28.49 ! [V_xs_2,T_b] :
% 28.45/28.49 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2)))
% 28.45/28.49 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_drop__zip,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_drop__0,axiom,
% 28.45/28.49 ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs ).
% 28.45/28.49
% 28.45/28.49 fof(fact_drop__drop,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_drop__take,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_take__drop,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_in__set__dropD,axiom,
% 28.45/28.49 ! [V_xs_2,V_n_2,V_x_2,T_b] :
% 28.45/28.49 ( 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))))
% 28.45/28.49 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_set__rotate1,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_set__drop__subset,axiom,
% 28.45/28.49 ! [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))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_length__drop,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_length__rotate1,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_butlast__drop,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_drop__butlast,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_drop__Nil,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_rotate1__is__Nil__conv,axiom,
% 28.45/28.49 ! [V_xs_2,T_b] :
% 28.45/28.49 ( hAPP(c_List_Orotate1(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
% 28.45/28.49 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_set__drop__subset__set__drop,axiom,
% 28.45/28.49 ! [V_xs_2,T_b,V_m_2,V_n_2] :
% 28.45/28.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2))
% 28.45/28.49 => 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)))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_drop__eq__Nil,axiom,
% 28.45/28.49 ! [V_xs_2,V_n_2,T_b] :
% 28.45/28.49 ( hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 28.45/28.49 <=> 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)) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_drop__all,axiom,
% 28.45/28.49 ! [V_n,V_xs,T_a] :
% 28.45/28.49 ( 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))
% 28.45/28.49 => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_drop__append,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_append__eq__conv__conj,axiom,
% 28.45/28.49 ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
% 28.45/28.49 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_zs_2
% 28.45/28.49 <=> ( 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)
% 28.45/28.49 & 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) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_drop__Cons,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_drop__Cons_H,axiom,
% 28.45/28.49 ! [V_xs,V_x,T_a,V_n] :
% 28.45/28.49 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.45/28.49 => 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) )
% 28.45/28.49 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.45/28.49 => 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) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_nth__drop,axiom,
% 28.45/28.49 ! [V_xs,T_a,V_i,V_n] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => 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)) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_append__eq__append__conv__if,axiom,
% 28.45/28.49 ! [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] :
% 28.45/28.49 ( 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)
% 28.45/28.49 <=> ( ( 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)))
% 28.45/28.49 => ( 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)
% 28.45/28.49 & 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) ) )
% 28.45/28.49 & ( ~ 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)))
% 28.45/28.49 => ( 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
% 28.45/28.49 & 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 ) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_nth__drop_H,axiom,
% 28.45/28.49 ! [V_xs,T_a,V_i] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => 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) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_rotate__simps,axiom,
% 28.45/28.49 ! [V_xs,V_x,T_b,T_a] :
% 28.45/28.49 ( hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a)
% 28.45/28.49 & 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))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_drop__Cons__number__of,axiom,
% 28.45/28.49 ! [V_xs,V_x,T_a,V_v] :
% 28.45/28.49 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.45/28.49 => 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) )
% 28.45/28.49 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.45/28.49 => 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) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_take__add,axiom,
% 28.45/28.49 ! [V_xs,T_a,V_j,V_i] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => 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))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_rotate1__length01,axiom,
% 28.45/28.49 ! [V_xs,T_a] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_zip__append2,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_zip__append1,axiom,
% 28.45/28.49 ! [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))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_id__take__nth__drop,axiom,
% 28.45/28.49 ! [V_xs,T_a,V_i] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => 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))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_take__hd__drop,axiom,
% 28.45/28.49 ! [V_xs,T_a,V_n] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => 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) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_hd__drop__conv__nth,axiom,
% 28.45/28.49 ! [V_n,T_a,V_xs] :
% 28.45/28.49 ( V_xs != c_List_Olist_ONil(T_a)
% 28.45/28.49 => ( 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)))
% 28.45/28.49 => 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) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_hd_Osimps,axiom,
% 28.45/28.49 ! [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 ).
% 28.45/28.49
% 28.45/28.49 fof(fact_hd__append2,axiom,
% 28.45/28.49 ! [V_ys,T_a,V_xs] :
% 28.45/28.49 ( V_xs != c_List_Olist_ONil(T_a)
% 28.45/28.49 => 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) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_hd__append,axiom,
% 28.45/28.49 ! [V_ys,T_a,V_xs] :
% 28.45/28.49 ( ( V_xs = c_List_Olist_ONil(T_a)
% 28.45/28.49 => 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) )
% 28.45/28.49 & ( V_xs != c_List_Olist_ONil(T_a)
% 28.45/28.49 => 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) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_hd__in__set,axiom,
% 28.45/28.49 ! [T_b,V_xs_2] :
% 28.45/28.49 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 28.45/28.49 => 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))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_hd__conv__nth,axiom,
% 28.45/28.49 ! [T_a,V_xs] :
% 28.45/28.49 ( V_xs != c_List_Olist_ONil(T_a)
% 28.45/28.49 => 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)) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_rotate1__hd__tl,axiom,
% 28.45/28.49 ! [T_a,V_xs] :
% 28.45/28.49 ( V_xs != c_List_Olist_ONil(T_a)
% 28.45/28.49 => 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))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_hd__rotate__conv__nth,axiom,
% 28.45/28.49 ! [V_n,T_a,V_xs] :
% 28.45/28.49 ( V_xs != c_List_Olist_ONil(T_a)
% 28.45/28.49 => 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))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_drop__tl,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_tl__drop,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_tl_Osimps_I2_J,axiom,
% 28.45/28.49 ! [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 ).
% 28.45/28.49
% 28.45/28.49 fof(fact_distinct__tl,axiom,
% 28.45/28.49 ! [V_xs,T_a] :
% 28.45/28.49 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 28.45/28.49 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_distinct__rotate,axiom,
% 28.45/28.49 ! [V_xs_2,V_n_2,T_b] :
% 28.45/28.49 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)))
% 28.45/28.49 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_rotate__add,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_rotate0,axiom,
% 28.45/28.49 ! [T_b] : c_List_Orotate(T_b,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_rotate__rotate,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_set__rotate,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_length__rotate,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_tl_Osimps_I1_J,axiom,
% 28.45/28.49 ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_rotate__is__Nil__conv,axiom,
% 28.45/28.49 ! [V_xs_2,V_n_2,T_b] :
% 28.45/28.49 ( hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 28.45/28.49 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_rotate__def,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_rotate1__rotate__swap,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_tl__append2,axiom,
% 28.45/28.49 ! [V_ys,T_a,V_xs] :
% 28.45/28.49 ( V_xs != c_List_Olist_ONil(T_a)
% 28.45/28.49 => 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) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_take__tl,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_rotate__conv__mod,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_drop__Suc,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_rotate__Suc,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_tl__append,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_rotate__id,axiom,
% 28.45/28.49 ! [V_xs,T_a,V_n] :
% 28.45/28.49 ( 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)
% 28.45/28.49 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_rotate__length01,axiom,
% 28.45/28.49 ! [V_n,V_xs,T_a] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_length__tl,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_tl__take,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_take__Suc,axiom,
% 28.45/28.49 ! [V_n,T_a,V_xs] :
% 28.45/28.49 ( V_xs != c_List_Olist_ONil(T_a)
% 28.45/28.49 => 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))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_rotate__drop__take,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_fold1__set,axiom,
% 28.45/28.49 ! [V_xs_2,T_b] :
% 28.45/28.49 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 28.45/28.49 => ( V_xs_2 != c_List_Olist_ONil(T_b)
% 28.45/28.49 => 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)) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_lexord__append__rightI,axiom,
% 28.45/28.49 ! [V_r_2,V_x_2,T_b,V_y_2] :
% 28.45/28.49 ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_b),B_z)
% 28.45/28.49 => 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))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_foldl__Nil,axiom,
% 28.45/28.49 ! [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 ).
% 28.45/28.49
% 28.45/28.49 fof(fact_start__le__sum,axiom,
% 28.45/28.49 ! [V_ns_2,V_n_2,V_m_2] :
% 28.45/28.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 28.45/28.49 => 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))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_foldl__assoc,axiom,
% 28.45/28.49 ! [V_zs_2,V_y_2,V_x_2,T_b] :
% 28.45/28.49 ( class_Groups_Osemigroup__add(T_b)
% 28.45/28.49 => 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)) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_foldl__absorb0,axiom,
% 28.45/28.49 ! [V_zs_2,V_x_2,T_b] :
% 28.45/28.49 ( class_Groups_Omonoid__add(T_b)
% 28.45/28.49 => 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) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_foldl__Cons,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_foldl__append,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listsum__foldl,axiom,
% 28.45/28.49 ! [T_b] :
% 28.45/28.49 ( class_Groups_Omonoid__add(T_b)
% 28.45/28.49 => 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)) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_sum__eq__0__conv,axiom,
% 28.45/28.49 ! [V_ns_2,V_m_2] :
% 28.45/28.49 ( 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)
% 28.45/28.49 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.45/28.49 & ! [B_x] :
% 28.45/28.49 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 28.45/28.49 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_fun__left__comm__idem_Ofold__set,axiom,
% 28.45/28.49 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
% 28.45/28.49 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 28.45/28.49 => 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) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_Sup__set__fold,axiom,
% 28.45/28.49 ! [V_xs_2,T_b] :
% 28.45/28.49 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.45/28.49 => 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) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_Inf__set__fold,axiom,
% 28.45/28.49 ! [V_xs_2,T_b] :
% 28.45/28.49 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.45/28.49 => 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) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_Sup__fin__set__fold,axiom,
% 28.45/28.49 ! [V_xs_2,V_x_2,T_b] :
% 28.45/28.49 ( class_Lattices_Olattice(T_b)
% 28.45/28.49 => 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) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_Inf__fin__set__fold,axiom,
% 28.45/28.49 ! [V_xs_2,V_x_2,T_b] :
% 28.45/28.49 ( class_Lattices_Olattice(T_b)
% 28.45/28.49 => 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) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_Min__fin__set__fold,axiom,
% 28.45/28.49 ! [V_xs_2,V_x_2,T_b] :
% 28.45/28.49 ( class_Orderings_Olinorder(T_b)
% 28.45/28.49 => 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) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_Max__fin__set__fold,axiom,
% 28.45/28.49 ! [V_xs_2,V_x_2,T_b] :
% 28.45/28.49 ( class_Orderings_Olinorder(T_b)
% 28.45/28.49 => 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) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_min__max_OInf__fin__set__fold,axiom,
% 28.45/28.49 ! [V_xs_2,V_x_2,T_b] :
% 28.45/28.49 ( class_Orderings_Olinorder(T_b)
% 28.45/28.49 => 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) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_min__max_OSup__fin__set__fold,axiom,
% 28.45/28.49 ! [V_xs_2,V_x_2,T_b] :
% 28.45/28.49 ( class_Orderings_Olinorder(T_b)
% 28.45/28.49 => 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) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_SUPR__set__fold,axiom,
% 28.45/28.49 ! [V_f_2,V_xs_2,T_c,T_b] :
% 28.45/28.49 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.45/28.49 => 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) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_INFI__set__fold,axiom,
% 28.45/28.49 ! [V_f_2,V_xs_2,T_c,T_b] :
% 28.45/28.49 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.45/28.49 => 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) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_elem__le__sum,axiom,
% 28.45/28.49 ! [V_ns_2,V_n_2] :
% 28.45/28.49 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 28.45/28.49 => 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))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_sorted__list__of__set__insert,axiom,
% 28.45/28.49 ! [V_x_2,V_A_2,T_b] :
% 28.45/28.49 ( class_Orderings_Olinorder(T_b)
% 28.45/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => 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)))))) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_lexord__Nil__left,axiom,
% 28.45/28.49 ! [V_r_2,V_y_2,T_b] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_x) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_insort__key_Osimps_I1_J,axiom,
% 28.45/28.49 ! [V_x_2,V_f_2,T_b,T_c] :
% 28.45/28.49 ( class_Orderings_Olinorder(T_c)
% 28.45/28.49 => 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)) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_insort__key_Osimps_I2_J,axiom,
% 28.45/28.49 ! [V_ys_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
% 28.45/28.49 ( class_Orderings_Olinorder(T_b)
% 28.45/28.49 => ( ( 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)))
% 28.45/28.49 => 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)) )
% 28.45/28.49 & ( ~ 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)))
% 28.45/28.49 => 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)) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_remove1__insort,axiom,
% 28.45/28.49 ! [V_xs_2,V_x_2,T_b] :
% 28.45/28.49 ( class_Orderings_Olinorder(T_b)
% 28.45/28.49 => 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 ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_insort__left__comm,axiom,
% 28.45/28.49 ! [V_xs_2,V_y_2,V_x_2,T_b] :
% 28.45/28.49 ( class_Orderings_Olinorder(T_b)
% 28.45/28.49 => 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)) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_insort__key__left__comm,axiom,
% 28.45/28.49 ! [V_xs_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
% 28.45/28.49 ( class_Orderings_Olinorder(T_b)
% 28.45/28.49 => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2)
% 28.45/28.49 => 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)) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_fun__left__comm__insort,axiom,
% 28.45/28.49 ! [T_b] :
% 28.45/28.49 ( class_Orderings_Olinorder(T_b)
% 28.45/28.49 => 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))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_set__insort,axiom,
% 28.45/28.49 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 28.45/28.49 ( class_Orderings_Olinorder(T_c)
% 28.45/28.49 => 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)) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_length__insort,axiom,
% 28.45/28.49 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 28.45/28.49 ( class_Orderings_Olinorder(T_c)
% 28.45/28.49 => 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)) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_insort__not__Nil,axiom,
% 28.45/28.49 ! [V_xs_2,V_a_2,V_f_2,T_b,T_c] :
% 28.45/28.49 ( class_Orderings_Olinorder(T_c)
% 28.45/28.49 => 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) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_distinct__insort,axiom,
% 28.45/28.49 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 28.45/28.49 ( class_Orderings_Olinorder(T_c)
% 28.45/28.49 => ( 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)))
% 28.45/28.49 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.45/28.49 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_insort__insert__insort__key,axiom,
% 28.45/28.49 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
% 28.45/28.49 ( class_Orderings_Olinorder(T_b)
% 28.45/28.49 => ( ~ 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))))
% 28.45/28.49 => 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) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_insort__insert__insort,axiom,
% 28.45/28.49 ! [V_xs_2,V_x_2,T_b] :
% 28.45/28.49 ( class_Orderings_Olinorder(T_b)
% 28.45/28.49 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.45/28.49 => 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) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_distinct__insort__insert,axiom,
% 28.45/28.49 ! [V_x_2,V_f_2,V_xs_2,T_b,T_c] :
% 28.45/28.49 ( class_Orderings_Olinorder(T_c)
% 28.45/28.49 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 28.45/28.49 => 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))) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_insort__insert__triv,axiom,
% 28.45/28.49 ! [V_xs_2,V_x_2,T_b] :
% 28.45/28.49 ( class_Orderings_Olinorder(T_b)
% 28.45/28.49 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.45/28.49 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_set__insort__insert,axiom,
% 28.45/28.49 ! [V_xs_2,V_x_2,T_b] :
% 28.45/28.49 ( class_Orderings_Olinorder(T_b)
% 28.45/28.49 => 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)) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_insort__insert__key__triv,axiom,
% 28.45/28.49 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
% 28.45/28.49 ( class_Orderings_Olinorder(T_b)
% 28.45/28.49 => ( 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))))
% 28.45/28.49 => c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_last__list__update,axiom,
% 28.45/28.49 ! [V_x,V_k,T_a,V_xs] :
% 28.45/28.49 ( V_xs != c_List_Olist_ONil(T_a)
% 28.45/28.49 => ( ( 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))
% 28.45/28.49 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x )
% 28.45/28.49 & ( 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))
% 28.45/28.49 => 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) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_last__conv__nth,axiom,
% 28.45/28.49 ! [T_a,V_xs] :
% 28.45/28.49 ( V_xs != c_List_Olist_ONil(T_a)
% 28.45/28.49 => 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))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_last__appendL,axiom,
% 28.45/28.49 ! [V_xs,T_a,V_ys] :
% 28.45/28.49 ( V_ys = c_List_Olist_ONil(T_a)
% 28.45/28.49 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_last__appendR,axiom,
% 28.45/28.49 ! [V_xs,T_a,V_ys] :
% 28.45/28.49 ( V_ys != c_List_Olist_ONil(T_a)
% 28.45/28.49 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_last__append,axiom,
% 28.45/28.49 ! [V_xs,T_a,V_ys] :
% 28.45/28.49 ( ( V_ys = c_List_Olist_ONil(T_a)
% 28.45/28.49 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) )
% 28.45/28.49 & ( V_ys != c_List_Olist_ONil(T_a)
% 28.45/28.49 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_last__ConsL,axiom,
% 28.45/28.49 ! [V_x,T_a,V_xs] :
% 28.45/28.49 ( V_xs = c_List_Olist_ONil(T_a)
% 28.45/28.49 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_last__ConsR,axiom,
% 28.45/28.49 ! [V_x,T_a,V_xs] :
% 28.45/28.49 ( V_xs != c_List_Olist_ONil(T_a)
% 28.45/28.49 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_last_Osimps,axiom,
% 28.45/28.49 ! [V_x,T_a,V_xs] :
% 28.45/28.49 ( ( V_xs = c_List_Olist_ONil(T_a)
% 28.45/28.49 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x )
% 28.45/28.49 & ( V_xs != c_List_Olist_ONil(T_a)
% 28.45/28.49 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_last__in__set,axiom,
% 28.45/28.49 ! [T_b,V_as_2] :
% 28.45/28.49 ( V_as_2 != c_List_Olist_ONil(T_b)
% 28.45/28.49 => hBOOL(hAPP(hAPP(c_member(T_b),c_List_Olast(T_b,V_as_2)),hAPP(c_List_Oset(T_b),V_as_2))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_last__snoc,axiom,
% 28.45/28.49 ! [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 ).
% 28.45/28.49
% 28.45/28.49 fof(fact_last__drop,axiom,
% 28.45/28.49 ! [V_xs,T_a,V_n] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_append__butlast__last__id,axiom,
% 28.45/28.49 ! [T_a,V_xs] :
% 28.45/28.49 ( V_xs != c_List_Olist_ONil(T_a)
% 28.45/28.49 => 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 ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_snoc__eq__iff__butlast,axiom,
% 28.45/28.49 ! [V_ys_2,V_x_2,V_xs_2,T_b] :
% 28.45/28.49 ( 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
% 28.45/28.49 <=> ( V_ys_2 != c_List_Olist_ONil(T_b)
% 28.45/28.49 & c_List_Obutlast(T_b,V_ys_2) = V_xs_2
% 28.45/28.49 & c_List_Olast(T_b,V_ys_2) = V_x_2 ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_lists_Osimps,axiom,
% 28.45/28.49 ! [V_A_2,V_a_2,T_b] :
% 28.45/28.49 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_a_2),c_List_Olists(T_b,V_A_2)))
% 28.45/28.49 <=> ( V_a_2 = c_List_Olist_ONil(T_b)
% 28.45/28.49 | ? [B_a,B_l] :
% 28.45/28.49 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_l)
% 28.45/28.49 & hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 28.45/28.49 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_l),c_List_Olists(T_b,V_A_2))) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_select__weigth__select,axiom,
% 28.45/28.49 ! [T_b,V_xs_2] :
% 28.45/28.49 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 28.45/28.49 => 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) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_inj__mapI,axiom,
% 28.45/28.49 ! [V_f_2,T_c,T_b] :
% 28.45/28.49 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 28.45/28.49 => 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))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_last__map,axiom,
% 28.45/28.49 ! [V_f_2,T_c,T_b,V_xs_2] :
% 28.45/28.49 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 28.45/28.49 => 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)) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_inj__on__map__eq__map,axiom,
% 28.45/28.49 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => ( 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)
% 28.45/28.49 <=> V_xs_2 = V_ys_2 ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_map__inj__on,axiom,
% 28.45/28.49 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 28.45/28.49 ( 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)
% 28.45/28.49 => ( 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)))
% 28.45/28.49 => V_xs_2 = V_ys_2 ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_foldl__map,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_rotate__map,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_map__tl,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_map__is__Nil__conv,axiom,
% 28.45/28.49 ! [V_xs_2,V_f_2,T_b,T_c] :
% 28.45/28.49 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 28.45/28.49 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_map_Osimps_I1_J,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_Nil__is__map__conv,axiom,
% 28.45/28.49 ! [V_xs_2,V_f_2,T_c,T_b] :
% 28.45/28.49 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)
% 28.45/28.49 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_map__update,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listsum__addf,axiom,
% 28.45/28.49 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 28.45/28.49 ( class_Groups_Ocomm__monoid__add(T_b)
% 28.45/28.49 => 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))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listsum__0,axiom,
% 28.45/28.49 ! [V_xs_2,T_c,T_b] :
% 28.45/28.49 ( class_Groups_Omonoid__add(T_b)
% 28.45/28.49 => 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) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listsum__mult__const,axiom,
% 28.45/28.49 ! [V_xs_2,V_c_2,V_f_2,T_c,T_b] :
% 28.45/28.49 ( class_Rings_Osemiring__0(T_b)
% 28.45/28.49 => 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) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listsum__const__mult,axiom,
% 28.45/28.49 ! [V_xs_2,V_f_2,V_c_2,T_c,T_b] :
% 28.45/28.49 ( class_Rings_Osemiring__0(T_b)
% 28.45/28.49 => 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))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listsum__subtractf,axiom,
% 28.45/28.49 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 28.45/28.49 ( class_Groups_Oab__group__add(T_b)
% 28.45/28.49 => 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))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_map__butlast,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_map__eq__imp__length__eq,axiom,
% 28.45/28.49 ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_b,T_c] :
% 28.45/28.49 ( 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)
% 28.45/28.49 => 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) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_length__map,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_map__eq__conv,axiom,
% 28.45/28.49 ! [V_g_2,V_xs_2,V_f_2,T_b,T_c] :
% 28.45/28.49 ( 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)
% 28.45/28.49 <=> ! [B_x] :
% 28.45/28.49 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2)))
% 28.45/28.49 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_take__map,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_map__injective,axiom,
% 28.45/28.49 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 28.45/28.49 ( 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)
% 28.45/28.49 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 28.45/28.49 => V_xs_2 = V_ys_2 ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_inj__map__eq__map,axiom,
% 28.45/28.49 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
% 28.45/28.49 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 28.45/28.49 => ( 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)
% 28.45/28.49 <=> V_xs_2 = V_ys_2 ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_map__ident,axiom,
% 28.45/28.49 ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)),V_xs_2) = V_xs_2 ).
% 28.45/28.49
% 28.45/28.49 fof(fact_set__map,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_map_Osimps_I2_J,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_zip__same__conv__map,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_zip__map__map,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_zip__map1,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_map__zip__map,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_map__zip__map2,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_zip__map2,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_map__append,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_hd__map,axiom,
% 28.45/28.49 ! [V_f_2,T_c,T_b,V_xs_2] :
% 28.45/28.49 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 28.45/28.49 => 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)) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_drop__map,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_list__size__map,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_List_Omap_Ocomp,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_map__comp__map,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_List_Omap_Ocompositionality,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_map__map,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_List_Omap_Oidentity,axiom,
% 28.45/28.49 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_List_Omap_Oid,axiom,
% 28.45/28.49 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_nth__map,axiom,
% 28.45/28.49 ! [V_f_2,T_c,V_xs_2,T_b,V_n_2] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => 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)) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_map__fun__upd,axiom,
% 28.45/28.49 ! [V_v_2,V_f_2,T_c,V_xs_2,V_y_2,T_b] :
% 28.45/28.49 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.45/28.49 => 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) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_distinct__map,axiom,
% 28.45/28.49 ! [V_xs_2,V_f_2,T_c,T_b] :
% 28.45/28.49 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)))
% 28.45/28.49 <=> ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
% 28.45/28.49 & c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(c_List_Oset(T_c),V_xs_2)) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listsum__abs,axiom,
% 28.45/28.49 ! [V_xs_2,T_b] :
% 28.45/28.49 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 28.45/28.49 => 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)))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_uminus__listsum__map,axiom,
% 28.45/28.49 ! [V_xs_2,V_f_2,T_c,T_b] :
% 28.45/28.49 ( class_Groups_Oab__group__add(T_b)
% 28.45/28.49 => 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)) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_inj__map,axiom,
% 28.45/28.49 ! [V_f_2,T_c,T_b] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 <=> c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_inj__mapD,axiom,
% 28.45/28.49 ! [V_f_2,T_c,T_b] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listsum__distinct__conv__setsum__set,axiom,
% 28.45/28.49 ! [V_f_2,V_xs_2,T_b,T_c] :
% 28.45/28.49 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.45/28.49 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 28.45/28.49 => 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)) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listsum__triv,axiom,
% 28.45/28.49 ! [V_xs_2,V_r_2,T_c,T_b] :
% 28.45/28.49 ( class_Rings_Osemiring__1(T_b)
% 28.45/28.49 => 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) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_product_Osimps_I2_J,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listsum__map__remove1,axiom,
% 28.45/28.49 ! [V_f_2,V_xs_2,V_x_2,T_b,T_c] :
% 28.45/28.49 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.45/28.49 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.45/28.49 => 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)))) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_inj__on__mapI,axiom,
% 28.45/28.49 ! [V_A_2,V_f_2,T_c,T_b] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => 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) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_Nitpick_Osetsum_H__def,axiom,
% 28.45/28.49 ! [V_f_2,V_A_2,T_b,T_c] :
% 28.45/28.49 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.45/28.49 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => 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))))) )
% 28.45/28.49 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.45/28.49 => c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_pick__same,axiom,
% 28.45/28.49 ! [V_xs_2,T_b,V_l_2] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => 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) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_sublists_Osimps_I2_J,axiom,
% 28.45/28.49 ! [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))))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_less__code__numeral__code,axiom,
% 28.45/28.49 ! [V_m_2,V_n_2] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_zero__code__numeral__def,axiom,
% 28.45/28.49 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_Code__Numeral_Oof__nat__inject,axiom,
% 28.45/28.49 ! [V_m_2,V_n_2] :
% 28.45/28.49 ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2)
% 28.45/28.49 <=> V_n_2 = V_m_2 ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_Code__Numeral_Oof__nat__code,axiom,
% 28.45/28.49 c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_times__code__numeral__code,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_one__code__numeral__def,axiom,
% 28.45/28.49 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_code__numeral_Oof__nat__inject,axiom,
% 28.45/28.49 ! [V_y_2,V_x_2] :
% 28.45/28.49 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 28.45/28.49 => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 28.45/28.49 => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2)
% 28.45/28.49 <=> V_x_2 = V_y_2 ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_map__fst__zip,axiom,
% 28.45/28.49 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 28.45/28.49 ( 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)
% 28.45/28.49 => 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 ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_map__snd__zip,axiom,
% 28.45/28.49 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 28.45/28.49 ( 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)
% 28.45/28.49 => 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 ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_number__of__code__numeral__def,axiom,
% 28.45/28.49 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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_zip__map__fst__snd,axiom,
% 28.45/28.49 ! [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 ).
% 28.45/28.49
% 28.45/28.49 fof(fact_plus__code__numeral__code,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_less__eq__code__numeral__code,axiom,
% 28.45/28.49 ! [V_m_2,V_n_2] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_distinct__set__sublists,axiom,
% 28.45/28.49 ! [V_xs_2,T_b] :
% 28.45/28.49 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 28.45/28.49 => 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)))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_pick__member,axiom,
% 28.45/28.49 ! [V_xs_2,T_b,V_i_2] :
% 28.45/28.49 ( 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))))
% 28.45/28.49 => 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)))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_zip__eq__conv,axiom,
% 28.45/28.49 ! [V_zs_2,V_ys_2,T_c,V_xs_2,T_b] :
% 28.45/28.49 ( 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)
% 28.45/28.49 => ( hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2) = V_zs_2
% 28.45/28.49 <=> ( 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
% 28.45/28.49 & 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 ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_list__size__conv__listsum,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_code__numeral__not__eq__zero,axiom,
% 28.45/28.49 ! [V_i_2] :
% 28.45/28.49 ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 28.45/28.49 <=> 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)) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_interv__listsum__conv__setsum__set__int,axiom,
% 28.45/28.49 ! [V_l_2,V_k_2,V_f_2,T_b] :
% 28.45/28.49 ( class_Groups_Ocomm__monoid__add(T_b)
% 28.45/28.49 => 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))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_setsum__set__upto__conv__listsum__int,axiom,
% 28.45/28.49 ! [V_j_2,V_i_2,V_f_2,T_b] :
% 28.45/28.49 ( class_Groups_Ocomm__monoid__add(T_b)
% 28.45/28.49 => 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))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_select__weight__member,axiom,
% 28.45/28.49 ! [V_s_2,V_xs_2,T_b] :
% 28.45/28.49 ( 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))))
% 28.45/28.49 => 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)))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_select__weight__def,axiom,
% 28.45/28.49 ! [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))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_select__def,axiom,
% 28.45/28.49 ! [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))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_subtract__code__numeral__code,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_nat__of__inverse,axiom,
% 28.45/28.49 ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x ).
% 28.45/28.49
% 28.45/28.49 fof(fact_of__nat__nat__of,axiom,
% 28.45/28.49 ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k ).
% 28.45/28.49
% 28.45/28.49 fof(fact_nat__of__of__nat,axiom,
% 28.45/28.49 ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n ).
% 28.45/28.49
% 28.45/28.49 fof(fact_times__code__numeral__def,axiom,
% 28.45/28.49 ! [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))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_Code__Numeral_Onat__of__inject,axiom,
% 28.45/28.49 ! [V_l_2,V_k_2] :
% 28.45/28.49 ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2)
% 28.45/28.49 <=> V_k_2 = V_l_2 ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_code__numeral_Onat__of__inject,axiom,
% 28.45/28.49 ! [V_y_2,V_x_2] :
% 28.45/28.49 ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2)
% 28.45/28.49 <=> V_x_2 = V_y_2 ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_type__definition__code__numeral,axiom,
% 28.45/28.49 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))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_less__code__numeral__def,axiom,
% 28.45/28.49 ! [V_m_2,V_n_2] :
% 28.45/28.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 28.45/28.49 <=> 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))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_nat__of,axiom,
% 28.45/28.49 ! [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)))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_nat__of__number,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_int__of__def,axiom,
% 28.45/28.49 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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_less__eq__code__numeral__def,axiom,
% 28.45/28.49 ! [V_m_2,V_n_2] :
% 28.45/28.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 28.45/28.49 <=> 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))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_nat__of__code,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_nat__of__aux__def,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_Suc__code__numeral__def,axiom,
% 28.45/28.49 ! [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))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_minus__code__numeral__def,axiom,
% 28.45/28.49 ! [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))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_of__nat__inverse,axiom,
% 28.45/28.49 ! [V_y_2] :
% 28.45/28.49 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 28.45/28.49 => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_plus__code__numeral__def,axiom,
% 28.45/28.49 ! [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))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_div__code__numeral__def,axiom,
% 28.45/28.49 ! [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))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_subtract__code__numeral__def,axiom,
% 28.45/28.49 c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_minus__code__numeral__code,axiom,
% 28.45/28.49 ! [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) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_mod__code__numeral__def,axiom,
% 28.45/28.49 ! [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))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_code__numeral__decr,axiom,
% 28.45/28.49 ! [V_k] :
% 28.45/28.49 ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 28.45/28.49 => 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))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listsum__mono,axiom,
% 28.45/28.49 ! [V_g_2,V_f_2,V_xs_2,T_b,T_c] :
% 28.45/28.49 ( ( class_Groups_Omonoid__add(T_c)
% 28.45/28.49 & class_Groups_Oordered__ab__semigroup__add(T_c) )
% 28.45/28.49 => ( ! [B_x] :
% 28.45/28.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.45/28.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 28.45/28.49 => 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)))) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_New__DSequence_Opos__not__seq__def,axiom,
% 28.45/28.49 ! [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))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_partition__set,axiom,
% 28.45/28.49 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_b] :
% 28.45/28.49 ( 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)
% 28.45/28.49 => 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) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_lists__IntI,axiom,
% 28.45/28.49 ! [V_B_2,V_A_2,V_l_2,T_b] :
% 28.45/28.49 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_A_2)))
% 28.45/28.49 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_B_2)))
% 28.45/28.49 => 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)) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listsp_ONil,axiom,
% 28.45/28.49 ! [V_A_2,T_b] : hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listsp_Oequations_I1_J,axiom,
% 28.45/28.49 ! [V_A_2,T_b] : hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_in__listsp__conv__set,axiom,
% 28.45/28.49 ! [V_xs_2,V_A_2,T_b] :
% 28.45/28.49 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2))
% 28.45/28.49 <=> ! [B_x] :
% 28.45/28.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.45/28.49 => hBOOL(hAPP(V_A_2,B_x)) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listsp__infI,axiom,
% 28.45/28.49 ! [V_B_2,V_l_2,V_A_2,T_b] :
% 28.45/28.49 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_l_2))
% 28.45/28.49 => ( hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_l_2))
% 28.45/28.49 => 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)) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listsp__inf__eq,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listsp__conj__eq,axiom,
% 28.45/28.49 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 28.45/28.49 ( 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))
% 28.45/28.49 <=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_x_2))
% 28.45/28.49 & hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_x_2)) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listsp_Oequations_I2_J,axiom,
% 28.45/28.49 ! [V_a2_2,V_a1_2,V_A_2,T_b] :
% 28.45/28.49 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a1_2),V_a2_2)))
% 28.45/28.49 <=> ( hBOOL(hAPP(V_A_2,V_a1_2))
% 28.45/28.49 & hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_a2_2)) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_append__in__listsp__conv,axiom,
% 28.45/28.49 ! [V_ys_2,V_xs_2,V_A_2,T_b] :
% 28.45/28.49 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))
% 28.45/28.49 <=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2))
% 28.45/28.49 & hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_ys_2)) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listsp__mono,axiom,
% 28.45/28.49 ! [V_B_2,V_A_2,T_b] :
% 28.45/28.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.45/28.49 => 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))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_partition__P,axiom,
% 28.45/28.49 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_b] :
% 28.45/28.49 ( 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)
% 28.45/28.49 => ( ! [B_x] :
% 28.45/28.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_yes_2)))
% 28.45/28.49 => hBOOL(hAPP(V_P_2,B_x)) )
% 28.45/28.49 & ! [B_x] :
% 28.45/28.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_no_2)))
% 28.45/28.49 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_partition_Osimps_I1_J,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_listsp__lists__eq,axiom,
% 28.45/28.49 ! [V_x_2,V_A_2,T_b] :
% 28.45/28.49 ( 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))
% 28.45/28.49 <=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_x_2),c_List_Olists(T_b,V_A_2))) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_partition_Osimps_I2_J,axiom,
% 28.45/28.49 ! [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)) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_lists__Int__eq,axiom,
% 28.45/28.49 ! [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))) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_list__all2__def,axiom,
% 28.45/28.49 ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 28.45/28.49 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 28.45/28.49 <=> ( 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)
% 28.45/28.49 & ! [B_x] :
% 28.45/28.49 ( 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))))
% 28.45/28.49 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2),B_x)) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_all__nth__imp__all__set,axiom,
% 28.45/28.49 ! [V_x_2,V_P_2,V_xs_2,T_b] :
% 28.45/28.49 ( ! [B_i] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) )
% 28.45/28.49 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.45/28.49 => hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_list__all2__map1,axiom,
% 28.45/28.49 ! [V_bs_2,V_as_2,V_f_2,T_d,V_P_2,T_c,T_b] :
% 28.45/28.49 ( 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)
% 28.45/28.49 <=> 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) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_list__all2__map2,axiom,
% 28.45/28.49 ! [V_bs_2,V_f_2,T_d,V_as_2,V_P_2,T_c,T_b] :
% 28.45/28.49 ( 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))
% 28.45/28.49 <=> 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) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_list__all2__append,axiom,
% 28.45/28.49 ! [V_vs_2,V_us_2,V_P_2,V_ys_2,T_c,V_xs_2,T_b] :
% 28.45/28.49 ( 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)
% 28.45/28.49 => ( 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))
% 28.45/28.49 <=> ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 28.45/28.49 & c_List_Olist__all2(T_b,T_c,V_P_2,V_us_2,V_vs_2) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_list__all2__appendI,axiom,
% 28.45/28.49 ! [V_d_2,V_c_2,V_b_2,V_a_2,V_P_2,T_c,T_b] :
% 28.45/28.49 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_a_2,V_b_2)
% 28.45/28.49 => ( c_List_Olist__all2(T_b,T_c,V_P_2,V_c_2,V_d_2)
% 28.45/28.49 => 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)) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_list__all2__dropI,axiom,
% 28.45/28.49 ! [V_n_2,V_bs_2,V_as_2,V_P_2,T_c,T_b] :
% 28.45/28.49 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_as_2,V_bs_2)
% 28.45/28.49 => 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)) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_list__all2__Cons,axiom,
% 28.45/28.49 ! [V_ys_2,V_y_2,V_xs_2,V_x_2,V_P_2,T_c,T_b] :
% 28.45/28.49 ( 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))
% 28.45/28.49 <=> ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 28.45/28.49 & c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_list__all2__eq,axiom,
% 28.45/28.49 ! [T_b,V_ys_2,V_xs_2] :
% 28.45/28.49 ( V_xs_2 = V_ys_2
% 28.45/28.49 <=> c_List_Olist__all2(T_b,T_b,c_fequal,V_xs_2,V_ys_2) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_list__all2__takeI,axiom,
% 28.45/28.49 ! [V_n_2,V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 28.45/28.49 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 28.45/28.49 => 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)) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_list__all2__lengthD,axiom,
% 28.45/28.49 ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 28.45/28.49 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 28.45/28.49 => 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) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_list__all2__Nil,axiom,
% 28.45/28.49 ! [V_ys_2,V_P_2,T_c,T_b] :
% 28.45/28.49 ( c_List_Olist__all2(T_b,T_c,V_P_2,c_List_Olist_ONil(T_b),V_ys_2)
% 28.45/28.49 <=> V_ys_2 = c_List_Olist_ONil(T_c) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_list__all2__Nil2,axiom,
% 28.45/28.49 ! [V_xs_2,V_P_2,T_c,T_b] :
% 28.45/28.49 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,c_List_Olist_ONil(T_c))
% 28.45/28.49 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_list__all2__nthD2,axiom,
% 28.45/28.49 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 28.45/28.49 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 28.45/28.49 => ( 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)))
% 28.45/28.49 => 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))) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_list__all2__nthD,axiom,
% 28.45/28.49 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 28.45/28.49 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 28.45/28.49 => ( 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)))
% 28.45/28.49 => 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))) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_list__all2__conv__all__nth,axiom,
% 28.45/28.49 ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 28.45/28.49 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 28.45/28.49 <=> ( 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)
% 28.45/28.49 & ! [B_i] :
% 28.45/28.49 ( 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)))
% 28.45/28.49 => 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))) ) ) ) ).
% 28.45/28.49
% 28.45/28.49 fof(fact_list__all2__update__cong2,axiom,
% 28.73/28.49 ! [V_i_2,V_y_2,V_x_2,V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 28.73/28.49 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 28.73/28.49 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 28.73/28.49 => ( 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)))
% 28.73/28.49 => 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)) ) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_list__all2__update__cong,axiom,
% 28.73/28.49 ! [V_y_2,V_x_2,V_ys_2,V_P_2,T_c,V_xs_2,T_b,V_i_2] :
% 28.73/28.49 ( 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)))
% 28.73/28.49 => ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 28.73/28.49 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 28.73/28.49 => 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)) ) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_list__all2I,axiom,
% 28.73/28.49 ! [V_P_2,V_b_2,V_a_2,T_c,T_b] :
% 28.73/28.49 ( ! [B_x] :
% 28.73/28.49 ( 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))))
% 28.73/28.49 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2),B_x)) )
% 28.73/28.49 => ( 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)
% 28.73/28.49 => c_List_Olist__all2(T_b,T_c,V_P_2,V_a_2,V_b_2) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_fun__left__comm_Ofold__set__remdups,axiom,
% 28.73/28.49 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
% 28.73/28.49 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 28.73/28.49 => 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)) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_distinct__remdups,axiom,
% 28.73/28.49 ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_length__remdups__leq,axiom,
% 28.73/28.49 ! [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))) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_remdups__eq__nil__iff,axiom,
% 28.73/28.49 ! [V_x_2,T_b] :
% 28.73/28.49 ( c_List_Oremdups(T_b,V_x_2) = c_List_Olist_ONil(T_b)
% 28.73/28.49 <=> V_x_2 = c_List_Olist_ONil(T_b) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_remdups__eq__nil__right__iff,axiom,
% 28.73/28.49 ! [V_x_2,T_b] :
% 28.73/28.49 ( c_List_Olist_ONil(T_b) = c_List_Oremdups(T_b,V_x_2)
% 28.73/28.49 <=> V_x_2 = c_List_Olist_ONil(T_b) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_remdups_Osimps_I1_J,axiom,
% 28.73/28.49 ! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_length__remdups__eq,axiom,
% 28.73/28.49 ! [V_xs_2,T_b] :
% 28.73/28.49 ( 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)
% 28.73/28.49 <=> c_List_Oremdups(T_b,V_xs_2) = V_xs_2 ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_set__remdups,axiom,
% 28.73/28.49 ! [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) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_remdups__remdups,axiom,
% 28.73/28.49 ! [V_xs,T_a] : c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_distinct__remdups__id,axiom,
% 28.73/28.49 ! [V_xs,T_a] :
% 28.73/28.49 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 28.73/28.49 => c_List_Oremdups(T_a,V_xs) = V_xs ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_remdups__id__iff__distinct,axiom,
% 28.73/28.49 ! [V_xs_2,T_b] :
% 28.73/28.49 ( c_List_Oremdups(T_b,V_xs_2) = V_xs_2
% 28.73/28.49 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_remdups__map__remdups,axiom,
% 28.73/28.49 ! [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)) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_remove1__remdups,axiom,
% 28.73/28.49 ! [V_x,V_xs,T_a] :
% 28.73/28.49 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 28.73/28.49 => 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)) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_remdups_Osimps_I2_J,axiom,
% 28.73/28.49 ! [V_xs_2,V_x_2,T_b] :
% 28.73/28.49 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.73/28.49 => 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) )
% 28.73/28.49 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.73/28.49 => 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)) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_length__remdups__card__conv,axiom,
% 28.73/28.49 ! [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)) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_length__remdups__concat,axiom,
% 28.73/28.49 ! [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))) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_sorted__list__of__set__sort__remdups,axiom,
% 28.73/28.49 ! [V_xs_2,T_b] :
% 28.73/28.49 ( class_Orderings_Olinorder(T_b)
% 28.73/28.49 => 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)) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_concat_Osimps_I1_J,axiom,
% 28.73/28.49 ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_concat__conv__foldl,axiom,
% 28.73/28.49 ! [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) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_foldl__conv__concat,axiom,
% 28.73/28.49 ! [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)) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_distinct__sort,axiom,
% 28.73/28.49 ! [V_xs_2,V_f_2,T_b,T_c] :
% 28.73/28.49 ( class_Orderings_Olinorder(T_c)
% 28.73/28.49 => ( hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)))
% 28.73/28.49 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_set__sort,axiom,
% 28.73/28.49 ! [V_xs_2,V_f_2,T_b,T_c] :
% 28.73/28.49 ( class_Orderings_Olinorder(T_c)
% 28.73/28.49 => 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) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_length__sort,axiom,
% 28.73/28.49 ! [V_xs_2,V_f_2,T_b,T_c] :
% 28.73/28.49 ( class_Orderings_Olinorder(T_c)
% 28.73/28.49 => 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) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_sort__key__simps_I1_J,axiom,
% 28.73/28.49 ! [V_f_2,T_b,T_c] :
% 28.73/28.49 ( class_Orderings_Olinorder(T_c)
% 28.73/28.49 => 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) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_concat_Osimps_I2_J,axiom,
% 28.73/28.49 ! [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)) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_concat__eq__Nil__conv,axiom,
% 28.73/28.49 ! [V_xss_2,T_b] :
% 28.73/28.49 ( c_List_Oconcat(T_b,V_xss_2) = c_List_Olist_ONil(T_b)
% 28.73/28.49 <=> ! [B_x] :
% 28.73/28.49 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
% 28.73/28.49 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_Nil__eq__concat__conv,axiom,
% 28.73/28.49 ! [V_xss_2,T_b] :
% 28.73/28.49 ( c_List_Olist_ONil(T_b) = c_List_Oconcat(T_b,V_xss_2)
% 28.73/28.49 <=> ! [B_x] :
% 28.73/28.49 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
% 28.73/28.49 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_map__concat,axiom,
% 28.73/28.49 ! [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)) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_length__concat,axiom,
% 28.73/28.49 ! [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)) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_set__concat,axiom,
% 28.73/28.49 ! [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)) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_sort__key__simps_I2_J,axiom,
% 28.73/28.49 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 28.73/28.49 ( class_Orderings_Olinorder(T_c)
% 28.73/28.49 => 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)) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_concat__append,axiom,
% 28.73/28.49 ! [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)) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_sort__foldl__insort,axiom,
% 28.73/28.49 ! [V_xs_2,T_b] :
% 28.73/28.49 ( class_Orderings_Olinorder(T_b)
% 28.73/28.49 => 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) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_concat__eq__concat__iff,axiom,
% 28.73/28.49 ! [V_ys_2,V_xs_2,T_b] :
% 28.73/28.49 ( ! [B_x] :
% 28.73/28.49 ( 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))))
% 28.73/28.49 => 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)) )
% 28.73/28.49 => ( 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)
% 28.73/28.49 => ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
% 28.73/28.49 <=> V_xs_2 = V_ys_2 ) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_concat__injective,axiom,
% 28.73/28.49 ! [V_ys_2,V_xs_2,T_b] :
% 28.73/28.49 ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
% 28.73/28.49 => ( 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)
% 28.73/28.49 => ( ! [B_x] :
% 28.73/28.49 ( 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))))
% 28.73/28.49 => 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)) )
% 28.73/28.49 => V_xs_2 = V_ys_2 ) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_concat__map__singleton,axiom,
% 28.73/28.49 ! [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) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_n__lists_Osimps_I2_J,axiom,
% 28.73/28.49 ! [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))) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_transpose_Osimps_I3_J,axiom,
% 28.73/28.49 ! [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))))) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_transpose__aux__filter__head,axiom,
% 28.73/28.49 ! [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)) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_filter__concat,axiom,
% 28.73/28.49 ! [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)) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_filter__sort,axiom,
% 28.73/28.49 ! [V_xs_2,V_f_2,V_P_2,T_b,T_c] :
% 28.73/28.49 ( class_Orderings_Olinorder(T_c)
% 28.73/28.49 => 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)) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_filter__map,axiom,
% 28.73/28.49 ! [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)) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_length__filter__map,axiom,
% 28.73/28.49 ! [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)) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_filter__insort__triv,axiom,
% 28.73/28.49 ! [V_xs_2,V_f_2,T_b,V_x_2,V_P_2,T_c] :
% 28.73/28.49 ( class_Orderings_Olinorder(T_c)
% 28.73/28.49 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 28.73/28.49 => 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) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_filter_Osimps_I1_J,axiom,
% 28.73/28.49 ! [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) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_transpose_Osimps_I1_J,axiom,
% 28.73/28.49 ! [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)) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_filter__empty__conv,axiom,
% 28.73/28.49 ! [V_xs_2,V_P_2,T_b] :
% 28.73/28.49 ( hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 28.73/28.49 <=> ! [B_x] :
% 28.73/28.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.73/28.49 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_length__filter__le,axiom,
% 28.73/28.49 ! [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))) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_sum__length__filter__compl,axiom,
% 28.73/28.49 ! [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) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_filter__is__subset,axiom,
% 28.73/28.49 ! [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))) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_filter__id__conv,axiom,
% 28.73/28.49 ! [V_xs_2,V_P_2,T_b] :
% 28.73/28.49 ( hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) = V_xs_2
% 28.73/28.49 <=> ! [B_x] :
% 28.73/28.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.73/28.49 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_filter__filter,axiom,
% 28.73/28.49 ! [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) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_remove1__filter__not,axiom,
% 28.73/28.49 ! [V_xs_2,T_b,V_x_2,V_P_2] :
% 28.73/28.49 ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 28.73/28.49 => 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) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_filter__remove1,axiom,
% 28.73/28.49 ! [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)) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_filter_Osimps_I2_J,axiom,
% 28.73/28.49 ! [V_xs_2,T_b,V_x_2,V_P_2] :
% 28.73/28.49 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 28.73/28.49 => 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)) )
% 28.73/28.49 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 28.73/28.49 => 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) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_filter__append,axiom,
% 28.73/28.49 ! [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)) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_distinct__filter,axiom,
% 28.73/28.49 ! [V_P_2,V_xs_2,T_b] :
% 28.73/28.49 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 28.73/28.49 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_partition__filter1,axiom,
% 28.73/28.49 ! [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) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_partition__filter__conv,axiom,
% 28.73/28.49 ! [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)) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_partition__filter2,axiom,
% 28.73/28.49 ! [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) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_remdups__filter,axiom,
% 28.73/28.49 ! [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)) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_transpose_Osimps_I2_J,axiom,
% 28.73/28.49 ! [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) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_nth__transpose,axiom,
% 28.73/28.49 ! [V_xs_2,T_b,V_i_2] :
% 28.73/28.49 ( 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))))
% 28.73/28.49 => 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)) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_transpose__map__map,axiom,
% 28.73/28.49 ! [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)) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_set__filter,axiom,
% 28.73/28.49 ! [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)) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_length__filter__less,axiom,
% 28.73/28.49 ! [V_P_2,V_xs_2,V_x_2,T_b] :
% 28.73/28.49 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.73/28.49 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 28.73/28.49 => 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))) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_set__minus__filter__out,axiom,
% 28.73/28.49 ! [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)) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_filter__in__sublist,axiom,
% 28.73/28.49 ! [V_s_2,V_xs_2,T_b] :
% 28.73/28.49 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 28.73/28.49 => 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) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_transpose__empty,axiom,
% 28.73/28.49 ! [V_xs_2,T_b] :
% 28.73/28.49 ( c_List_Otranspose(T_b,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_b))
% 28.73/28.49 <=> ! [B_x] :
% 28.73/28.49 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 28.73/28.49 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_length__filter__conv__card,axiom,
% 28.73/28.49 ! [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))))) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_transpose__aux__filter__tail,axiom,
% 28.73/28.49 ! [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)) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_transpose_Opsimps_I3_J,axiom,
% 28.73/28.49 ! [V_xss_2,V_xs_2,V_x_2,T_b] :
% 28.73/28.49 ( 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)))
% 28.73/28.49 => 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))))) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_transpose_Opsimps_I2_J,axiom,
% 28.73/28.49 ! [V_xss_2,T_b] :
% 28.73/28.49 ( 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)))
% 28.73/28.49 => 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) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_sublist__shift__lemma__Suc,axiom,
% 28.73/28.49 ! [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)))) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_select__weigth__drop__zero,axiom,
% 28.73/28.49 ! [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) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_pick__drop__zero,axiom,
% 28.73/28.49 ! [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) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_transpose_Opsimps_I1_J,axiom,
% 28.73/28.49 ! [T_b] :
% 28.73/28.49 ( 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))))
% 28.73/28.49 => c_List_Otranspose(T_b,c_List_Olist_ONil(tc_List_Olist(T_b))) = c_List_Olist_ONil(tc_List_Olist(T_b)) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_transpose__max__length,axiom,
% 28.73/28.49 ! [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)) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_transpose__aux__max,axiom,
% 28.73/28.49 ! [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)))) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_foldr_Osimps_I1_J,axiom,
% 28.73/28.49 ! [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 ).
% 28.73/28.49
% 28.73/28.49 fof(fact_foldr_Osimps_I2_J,axiom,
% 28.73/28.49 ! [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)) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_foldr__append,axiom,
% 28.73/28.49 ! [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)) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_foldr__conv__foldl,axiom,
% 28.73/28.49 ! [V_a_2,V_xs_2,T_b] :
% 28.73/28.49 ( class_Groups_Oab__semigroup__add(T_b)
% 28.73/28.49 => 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) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_foldr__map,axiom,
% 28.73/28.49 ! [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) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_foldl__foldr1,axiom,
% 28.73/28.49 ! [V_xs_2,T_b] :
% 28.73/28.49 ( class_Groups_Omonoid__add(T_b)
% 28.73/28.49 => 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)) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_foldl__foldr1__lemma,axiom,
% 28.73/28.49 ! [V_xs_2,V_a_2,T_b] :
% 28.73/28.49 ( class_Groups_Omonoid__add(T_b)
% 28.73/28.49 => 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))) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_length__transpose,axiom,
% 28.73/28.49 ! [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)) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_sublist__def,axiom,
% 28.73/28.49 ! [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))))) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_sublist__shift__lemma,axiom,
% 28.73/28.49 ! [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))))) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_atLeastLessThan__upt,axiom,
% 28.73/28.49 ! [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)) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_set__upt,axiom,
% 28.73/28.49 ! [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) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_distinct__upt,axiom,
% 28.73/28.49 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_upt__add__eq__append,axiom,
% 28.73/28.49 ! [V_k,V_j,V_i] :
% 28.73/28.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 28.73/28.49 => 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))) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_upt__Suc,axiom,
% 28.73/28.49 ! [V_j,V_i] :
% 28.73/28.49 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 28.73/28.49 => 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))) )
% 28.73/28.49 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 28.73/28.49 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_upt__Suc__append,axiom,
% 28.73/28.49 ! [V_j,V_i] :
% 28.73/28.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 28.73/28.49 => 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))) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_drop__upt,axiom,
% 28.73/28.49 ! [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) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_hd__upt,axiom,
% 28.73/28.49 ! [V_j,V_i] :
% 28.73/28.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 28.73/28.49 => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_upt__rec,axiom,
% 28.73/28.49 ! [V_j,V_i] :
% 28.73/28.49 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 28.73/28.49 => 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)) )
% 28.73/28.49 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 28.73/28.49 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_upt__conv__Cons,axiom,
% 28.73/28.49 ! [V_j,V_i] :
% 28.73/28.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 28.73/28.49 => 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)) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_take__upt,axiom,
% 28.73/28.49 ! [V_n,V_m,V_i] :
% 28.73/28.49 ( 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))
% 28.73/28.49 => 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)) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_sorted__list__of__set__range,axiom,
% 28.73/28.49 ! [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) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_upt__eq__Nil__conv,axiom,
% 28.73/28.49 ! [V_j_2,V_i_2] :
% 28.73/28.49 ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat)
% 28.73/28.49 <=> ( V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.73/28.49 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_upt__conv__Nil,axiom,
% 28.73/28.49 ! [V_i,V_j] :
% 28.73/28.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 28.73/28.49 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_upt__0,axiom,
% 28.73/28.49 ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_length__upt,axiom,
% 28.73/28.49 ! [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) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_upt__rec__number__of,axiom,
% 28.73/28.49 ! [V_n,V_m] :
% 28.73/28.49 ( ( 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)))
% 28.73/28.49 => 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))) )
% 28.73/28.49 & ( ~ 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)))
% 28.73/28.49 => 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) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_upt__eq__Cons__conv,axiom,
% 28.73/28.49 ! [V_xs_2,V_x_2,V_j_2,V_i_2] :
% 28.73/28.49 ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2)
% 28.73/28.49 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2))
% 28.73/28.49 & V_i_2 = V_x_2
% 28.73/28.49 & 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 ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_last__upt,axiom,
% 28.73/28.49 ! [V_j,V_i] :
% 28.73/28.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 28.73/28.49 => 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)) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_map__Suc__upt,axiom,
% 28.73/28.49 ! [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)) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_atLeastAtMost__upt,axiom,
% 28.73/28.49 ! [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))) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_atLeast__upt,axiom,
% 28.73/28.49 ! [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)) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_nth__upt,axiom,
% 28.73/28.49 ! [V_j,V_k,V_i] :
% 28.73/28.49 ( 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))
% 28.73/28.49 => 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) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_greaterThanAtMost__upt,axiom,
% 28.73/28.49 ! [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))) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_greaterThanLessThan__upt,axiom,
% 28.73/28.49 ! [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)) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_atMost__upto,axiom,
% 28.73/28.49 ! [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))) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_map__nth,axiom,
% 28.73/28.49 ! [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 ).
% 28.73/28.49
% 28.73/28.49 fof(fact_setsum__set__upt__conv__listsum__nat,axiom,
% 28.73/28.49 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 28.73/28.49 ( class_Groups_Ocomm__monoid__add(T_b)
% 28.73/28.49 => 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))) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_interv__listsum__conv__setsum__set__nat,axiom,
% 28.73/28.49 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 28.73/28.49 ( class_Groups_Ocomm__monoid__add(T_b)
% 28.73/28.49 => 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))) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_nth__map__upt,axiom,
% 28.73/28.49 ! [V_f_2,T_b,V_m_2,V_n_2,V_i_2] :
% 28.73/28.49 ( 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)))
% 28.73/28.49 => 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)) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_transpose__rectangle,axiom,
% 28.73/28.49 ! [V_n_2,T_b,V_xs_2] :
% 28.73/28.49 ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
% 28.73/28.49 => V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 28.73/28.49 => ( ! [B_i] :
% 28.73/28.49 ( 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)))
% 28.73/28.49 => 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 )
% 28.73/28.49 => 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)) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_insort__key__remove1,axiom,
% 28.73/28.49 ! [V_f_2,V_xs_2,V_a_2,T_b,T_c] :
% 28.73/28.49 ( class_Orderings_Olinorder(T_c)
% 28.73/28.49 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.73/28.49 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
% 28.73/28.49 => ( 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
% 28.73/28.49 => 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 ) ) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_sorted_ONil,axiom,
% 28.73/28.49 ! [T_a] :
% 28.73/28.49 ( class_Orderings_Olinorder(T_a)
% 28.73/28.49 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_sorted__single,axiom,
% 28.73/28.49 ! [V_x,T_a] :
% 28.73/28.49 ( class_Orderings_Olinorder(T_a)
% 28.73/28.49 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_sorted__upt,axiom,
% 28.73/28.49 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_sorted__sort,axiom,
% 28.73/28.49 ! [V_xs_2,T_b] :
% 28.73/28.49 ( class_Orderings_Olinorder(T_b)
% 28.73/28.49 => c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),V_xs_2)) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_sorted__insort,axiom,
% 28.73/28.49 ! [V_xs_2,V_x_2,T_b] :
% 28.73/28.49 ( class_Orderings_Olinorder(T_b)
% 28.73/28.49 => ( 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))
% 28.73/28.49 <=> c_List_Olinorder__class_Osorted(T_b,V_xs_2) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_sorted__tl,axiom,
% 28.73/28.49 ! [V_xs,T_a] :
% 28.73/28.49 ( class_Orderings_Olinorder(T_a)
% 28.73/28.49 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 28.73/28.49 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_sorted_Oequations_I1_J,axiom,
% 28.73/28.49 ! [T_a] :
% 28.73/28.49 ( class_Orderings_Olinorder(T_a)
% 28.73/28.49 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_sorted__butlast,axiom,
% 28.73/28.49 ! [V_xs,T_a] :
% 28.73/28.49 ( class_Orderings_Olinorder(T_a)
% 28.73/28.49 => ( V_xs != c_List_Olist_ONil(T_a)
% 28.73/28.49 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 28.73/28.49 => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_sorted__take,axiom,
% 28.73/28.49 ! [V_n,V_xs,T_a] :
% 28.73/28.49 ( class_Orderings_Olinorder(T_a)
% 28.73/28.49 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 28.73/28.49 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_sorted__upto,axiom,
% 28.73/28.49 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_sorted__remove1,axiom,
% 28.73/28.49 ! [V_a,V_xs,T_a] :
% 28.73/28.49 ( class_Orderings_Olinorder(T_a)
% 28.73/28.49 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 28.73/28.49 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_sorted__many,axiom,
% 28.73/28.49 ! [V_zs,V_y,V_x,T_a] :
% 28.73/28.49 ( class_Orderings_Olinorder(T_a)
% 28.73/28.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 28.73/28.49 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs))
% 28.73/28.49 => 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))) ) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_sorted__many__eq,axiom,
% 28.73/28.49 ! [V_zs_2,V_y_2,V_x_2,T_b] :
% 28.73/28.49 ( class_Orderings_Olinorder(T_b)
% 28.73/28.49 => ( 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)))
% 28.73/28.49 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 28.73/28.49 & c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2)) ) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_sorted__drop,axiom,
% 28.73/28.49 ! [V_n,V_xs,T_a] :
% 28.73/28.49 ( class_Orderings_Olinorder(T_a)
% 28.73/28.49 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 28.73/28.49 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_sorted__insort__insert,axiom,
% 28.73/28.49 ! [V_x_2,V_xs_2,T_b] :
% 28.73/28.49 ( class_Orderings_Olinorder(T_b)
% 28.73/28.49 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 28.73/28.49 => 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)) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_sorted__remdups,axiom,
% 28.73/28.49 ! [V_l,T_a] :
% 28.73/28.49 ( class_Orderings_Olinorder(T_a)
% 28.73/28.49 => ( c_List_Olinorder__class_Osorted(T_a,V_l)
% 28.73/28.49 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l)) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_sorted__distinct__set__unique,axiom,
% 28.73/28.49 ! [V_ys_2,V_xs_2,T_b] :
% 28.73/28.49 ( class_Orderings_Olinorder(T_b)
% 28.73/28.49 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 28.73/28.49 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 28.73/28.49 => ( c_List_Olinorder__class_Osorted(T_b,V_ys_2)
% 28.73/28.49 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
% 28.73/28.49 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
% 28.73/28.49 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_sorted__sort__key,axiom,
% 28.73/28.49 ! [V_xs_2,V_f_2,T_c,T_b] :
% 28.73/28.49 ( class_Orderings_Olinorder(T_b)
% 28.73/28.49 => 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))) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_sorted__insort__insert__key,axiom,
% 28.73/28.49 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
% 28.73/28.49 ( class_Orderings_Olinorder(T_b)
% 28.73/28.49 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 28.73/28.49 => 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))) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_sorted__map__remove1,axiom,
% 28.73/28.49 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
% 28.73/28.49 ( class_Orderings_Olinorder(T_b)
% 28.73/28.49 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 28.73/28.49 => 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))) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_sorted__insort__key,axiom,
% 28.73/28.49 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
% 28.73/28.49 ( class_Orderings_Olinorder(T_b)
% 28.73/28.49 => ( 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)))
% 28.73/28.49 <=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_sorted__filter,axiom,
% 28.73/28.49 ! [V_P_2,V_xs_2,V_f_2,T_c,T_b] :
% 28.73/28.49 ( class_Orderings_Olinorder(T_b)
% 28.73/28.49 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 28.73/28.49 => 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))) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_sorted__map__same,axiom,
% 28.73/28.49 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 28.73/28.49 ( class_Orderings_Olinorder(T_b)
% 28.73/28.49 => 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))) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_sorted__same,axiom,
% 28.73/28.49 ! [V_xs_2,V_g_2,T_b] :
% 28.73/28.49 ( class_Orderings_Olinorder(T_b)
% 28.73/28.49 => 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)) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_sorted__Cons,axiom,
% 28.73/28.49 ! [V_xs_2,V_x_2,T_b] :
% 28.73/28.49 ( class_Orderings_Olinorder(T_b)
% 28.73/28.49 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 28.73/28.49 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 28.73/28.49 & ! [B_x] :
% 28.73/28.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.73/28.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_sorted__append,axiom,
% 28.73/28.49 ! [V_ys_2,V_xs_2,T_b] :
% 28.73/28.49 ( class_Orderings_Olinorder(T_b)
% 28.73/28.49 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
% 28.73/28.49 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 28.73/28.49 & c_List_Olinorder__class_Osorted(T_b,V_ys_2)
% 28.73/28.49 & ! [B_x] :
% 28.73/28.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.73/28.49 => ! [B_xa] :
% 28.73/28.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),V_ys_2)))
% 28.73/28.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) ) ) ) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_filter__insort,axiom,
% 28.73/28.49 ! [V_x_2,V_P_2,V_xs_2,V_f_2,T_c,T_b] :
% 28.73/28.49 ( class_Orderings_Olinorder(T_b)
% 28.73/28.49 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 28.73/28.49 => ( hBOOL(hAPP(V_P_2,V_x_2))
% 28.73/28.49 => 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)) ) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_sorted_Oequations_I2_J,axiom,
% 28.73/28.49 ! [V_a1_2,V_a2_2,T_b] :
% 28.73/28.49 ( class_Orderings_Olinorder(T_b)
% 28.73/28.49 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a1_2))
% 28.73/28.49 <=> ( ! [B_x] :
% 28.73/28.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_a1_2)))
% 28.73/28.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a2_2),B_x)) )
% 28.73/28.49 & c_List_Olinorder__class_Osorted(T_b,V_a1_2) ) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_sorted__list__of__set,axiom,
% 28.73/28.49 ! [V_A_2,T_b] :
% 28.73/28.49 ( class_Orderings_Olinorder(T_b)
% 28.73/28.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.73/28.49 => ( hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) = V_A_2
% 28.73/28.49 & c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))
% 28.73/28.49 & hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))) ) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_insort__remove1,axiom,
% 28.73/28.49 ! [V_xs_2,V_a_2,T_b] :
% 28.73/28.49 ( class_Orderings_Olinorder(T_b)
% 28.73/28.49 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.73/28.49 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 28.73/28.49 => 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 ) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_sorted__nth__mono,axiom,
% 28.73/28.49 ! [V_j,V_i,V_xs,T_a] :
% 28.73/28.49 ( class_Orderings_Olinorder(T_a)
% 28.73/28.49 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 28.73/28.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 28.73/28.49 => ( 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)))
% 28.73/28.49 => 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))) ) ) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_sorted__equals__nth__mono,axiom,
% 28.73/28.49 ! [V_xs_2,T_b] :
% 28.73/28.49 ( class_Orderings_Olinorder(T_b)
% 28.73/28.49 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 28.73/28.49 <=> ! [B_j] :
% 28.73/28.49 ( 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)))
% 28.73/28.49 => ! [B_i] :
% 28.73/28.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
% 28.73/28.49 => 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))) ) ) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_map__sorted__distinct__set__unique,axiom,
% 28.73/28.49 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 28.73/28.49 ( class_Orderings_Olinorder(T_c)
% 28.73/28.49 => ( 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)))
% 28.73/28.49 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
% 28.73/28.49 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)))
% 28.73/28.49 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2))
% 28.73/28.49 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)))
% 28.73/28.49 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
% 28.73/28.49 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_transpose__column,axiom,
% 28.73/28.49 ! [V_i_2,V_xs_2,T_b] :
% 28.73/28.49 ( 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)))
% 28.73/28.49 => ( 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)))
% 28.73/28.49 => 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) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_nth__nth__transpose__sorted,axiom,
% 28.73/28.49 ! [V_j_2,V_i_2,V_xs_2,T_b] :
% 28.73/28.49 ( 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)))
% 28.73/28.49 => ( 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))))
% 28.73/28.49 => ( 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))))
% 28.73/28.49 => 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) ) ) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_inj__on__rev,axiom,
% 28.73/28.49 ! [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) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_rev__is__Nil__conv,axiom,
% 28.73/28.49 ! [V_xs_2,T_b] :
% 28.73/28.49 ( hAPP(c_List_Orev(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
% 28.73/28.49 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_Nil__is__rev__conv,axiom,
% 28.73/28.49 ! [V_xs_2,T_b] :
% 28.73/28.49 ( c_List_Olist_ONil(T_b) = hAPP(c_List_Orev(T_b),V_xs_2)
% 28.73/28.49 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_rev_Osimps_I1_J,axiom,
% 28.73/28.49 ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_singleton__rev__conv,axiom,
% 28.73/28.49 ! [V_xs_2,V_x_2,T_b] :
% 28.73/28.49 ( 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)
% 28.73/28.49 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_rev__singleton__conv,axiom,
% 28.73/28.49 ! [V_x_2,V_xs_2,T_b] :
% 28.73/28.49 ( 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))
% 28.73/28.49 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_rev__append,axiom,
% 28.73/28.49 ! [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)) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_distinct__rev,axiom,
% 28.73/28.49 ! [V_xs_2,T_b] :
% 28.73/28.49 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orev(T_b),V_xs_2)))
% 28.73/28.49 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_rev__concat,axiom,
% 28.73/28.49 ! [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))) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_rev__map,axiom,
% 28.73/28.49 ! [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)) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_rev__filter,axiom,
% 28.73/28.49 ! [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)) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_zip__rev,axiom,
% 28.73/28.49 ! [V_ys,T_b,V_xs,T_a] :
% 28.73/28.49 ( 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)
% 28.73/28.49 => 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)) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_set__rev,axiom,
% 28.73/28.49 ! [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) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_listsum__rev,axiom,
% 28.73/28.49 ! [V_xs,T_a] :
% 28.73/28.49 ( class_Groups_Ocomm__monoid__add(T_a)
% 28.73/28.49 => 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) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_rev__is__rev__conv,axiom,
% 28.73/28.49 ! [V_ys_2,V_xs_2,T_b] :
% 28.73/28.49 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Orev(T_b),V_ys_2)
% 28.73/28.49 <=> V_xs_2 = V_ys_2 ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_rev__swap,axiom,
% 28.73/28.49 ! [V_ys_2,V_xs_2,T_b] :
% 28.73/28.49 ( hAPP(c_List_Orev(T_b),V_xs_2) = V_ys_2
% 28.73/28.49 <=> V_xs_2 = hAPP(c_List_Orev(T_b),V_ys_2) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_rev__rev__ident,axiom,
% 28.73/28.49 ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs ).
% 28.73/28.49
% 28.73/28.49 fof(fact_length__rev,axiom,
% 28.73/28.49 ! [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) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_list__all2__rev1,axiom,
% 28.73/28.49 ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 28.73/28.49 ( c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(c_List_Orev(T_b),V_xs_2),V_ys_2)
% 28.73/28.49 <=> c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,hAPP(c_List_Orev(T_c),V_ys_2)) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_list__all2__rev,axiom,
% 28.73/28.49 ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 28.73/28.49 ( 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))
% 28.73/28.49 <=> c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_foldl__foldr,axiom,
% 28.73/28.49 ! [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) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_foldr__foldl,axiom,
% 28.73/28.49 ! [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)) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_rev_Osimps_I2_J,axiom,
% 28.73/28.49 ! [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))) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_rev__eq__Cons__iff,axiom,
% 28.73/28.49 ! [V_ys_2,V_y_2,V_xs_2,T_b] :
% 28.73/28.49 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)
% 28.73/28.49 <=> 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))) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_last__rev,axiom,
% 28.73/28.49 ! [T_a,V_xs] :
% 28.73/28.49 ( V_xs != c_List_Olist_ONil(T_a)
% 28.73/28.49 => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_hd__rev,axiom,
% 28.73/28.49 ! [T_a,V_xs] :
% 28.73/28.49 ( V_xs != c_List_Olist_ONil(T_a)
% 28.73/28.49 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_sorted__transpose,axiom,
% 28.73/28.49 ! [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)))) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_rev__foldl__cons,axiom,
% 28.73/28.49 ! [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) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_rev__drop,axiom,
% 28.73/28.49 ! [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)) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_rev__take,axiom,
% 28.73/28.49 ! [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)) ).
% 28.73/28.49
% 28.73/28.49 fof(fact_rotate__rev,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_rev__nth,axiom,
% 28.73/28.50 ! [V_xs,T_a,V_n] :
% 28.73/28.50 ( 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)))
% 28.73/28.50 => 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))) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_rev__update,axiom,
% 28.73/28.50 ! [V_y,V_xs,T_a,V_k] :
% 28.73/28.50 ( 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)))
% 28.73/28.50 => 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) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_sorted__rev__nth__mono,axiom,
% 28.73/28.50 ! [V_j,V_i,V_xs,T_a] :
% 28.73/28.50 ( class_Orderings_Olinorder(T_a)
% 28.73/28.50 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs))
% 28.73/28.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 28.73/28.50 => ( 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)))
% 28.73/28.50 => 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))) ) ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_foldr__max__sorted,axiom,
% 28.73/28.50 ! [V_y_2,V_xs_2,T_b] :
% 28.73/28.50 ( class_Orderings_Olinorder(T_b)
% 28.73/28.50 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),V_xs_2))
% 28.73/28.50 => ( ( V_xs_2 = c_List_Olist_ONil(T_b)
% 28.73/28.50 => c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = V_y_2 )
% 28.73/28.50 & ( V_xs_2 != c_List_Olist_ONil(T_b)
% 28.73/28.50 => 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) ) ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_length__transpose__sorted,axiom,
% 28.73/28.50 ! [V_xs_2,T_b] :
% 28.73/28.50 ( 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)))
% 28.73/28.50 => ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
% 28.73/28.50 => 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) )
% 28.73/28.50 & ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_b))
% 28.73/28.50 => 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))) ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_transpose__column__length,axiom,
% 28.73/28.50 ! [V_i_2,V_xs_2,T_b] :
% 28.73/28.50 ( 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)))
% 28.73/28.50 => ( 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)))
% 28.73/28.50 => 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)) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_transpose__transpose,axiom,
% 28.73/28.50 ! [V_xs_2,T_b] :
% 28.73/28.50 ( 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)))
% 28.73/28.50 => 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) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_transfer__nat__int__list__functions_I2_J,axiom,
% 28.73/28.50 c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_sorted__takeWhile,axiom,
% 28.73/28.50 ! [V_P_2,V_xs_2,T_b] :
% 28.73/28.50 ( class_Orderings_Olinorder(T_b)
% 28.73/28.50 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 28.73/28.50 => c_List_Olinorder__class_Osorted(T_b,c_List_OtakeWhile(T_b,V_P_2,V_xs_2)) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_length__takeWhile__le,axiom,
% 28.73/28.50 ! [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))) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_set__takeWhileD,axiom,
% 28.73/28.50 ! [V_xs_2,V_P_2,V_x_2,T_b] :
% 28.73/28.50 ( 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))))
% 28.73/28.50 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.73/28.50 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_takeWhile__eq__all__conv,axiom,
% 28.73/28.50 ! [V_xs_2,V_P_2,T_b] :
% 28.73/28.50 ( c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = V_xs_2
% 28.73/28.50 <=> ! [B_x] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.73/28.50 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_zip__takeWhile__fst,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_zip__takeWhile__snd,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_takeWhile__map,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_distinct__takeWhile,axiom,
% 28.73/28.50 ! [V_P_2,V_xs_2,T_b] :
% 28.73/28.50 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 28.73/28.50 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_takeWhile__tail,axiom,
% 28.73/28.50 ! [V_l_2,V_xs_2,T_b,V_x_2,V_P_2] :
% 28.73/28.50 ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 28.73/28.50 => 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) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_takeWhile_Osimps_I2_J,axiom,
% 28.73/28.50 ! [V_xs_2,T_b,V_x_2,V_P_2] :
% 28.73/28.50 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 28.73/28.50 => 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)) )
% 28.73/28.50 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 28.73/28.50 => 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) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_takeWhile__eq__take,axiom,
% 28.73/28.50 ! [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) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_takeWhile_Osimps_I1_J,axiom,
% 28.73/28.50 ! [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) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_return__list__def,axiom,
% 28.73/28.50 ! [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) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_takeWhile__append1,axiom,
% 28.73/28.50 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_b] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.73/28.50 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 28.73/28.50 => 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) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_takeWhile__nth,axiom,
% 28.73/28.50 ! [V_xs_2,V_P_2,T_b,V_j_2] :
% 28.73/28.50 ( 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))))
% 28.73/28.50 => 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) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_nth__length__takeWhile,axiom,
% 28.73/28.50 ! [V_xs_2,V_P_2,T_b] :
% 28.73/28.50 ( 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)))
% 28.73/28.50 => ~ 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))))) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_takeWhile__not__last,axiom,
% 28.73/28.50 ! [T_b,V_xs_2] :
% 28.73/28.50 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 28.73/28.50 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 28.73/28.50 => 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) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_filter__equals__takeWhile__sorted__rev,axiom,
% 28.73/28.50 ! [V_t_2,V_xs_2,V_f_2,T_c,T_b] :
% 28.73/28.50 ( class_Orderings_Olinorder(T_b)
% 28.73/28.50 => ( 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)))
% 28.73/28.50 => 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) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_transfer__nat__int__list__return__embed,axiom,
% 28.73/28.50 ! [V_l] :
% 28.73/28.50 ( c_List_Onat__list(V_l)
% 28.73/28.50 => c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_transfer__nat__int__list__functions_I1_J,axiom,
% 28.73/28.50 ! [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))) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_embed__list__def,axiom,
% 28.73/28.50 ! [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) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_takeWhile__neq__rev,axiom,
% 28.73/28.50 ! [V_x_2,V_xs_2,T_b] :
% 28.73/28.50 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 28.73/28.50 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.73/28.50 => 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))) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_dropWhile__neq__rev,axiom,
% 28.73/28.50 ! [V_x_2,V_xs_2,T_b] :
% 28.73/28.50 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 28.73/28.50 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.73/28.50 => 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))) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_takeWhile__dropWhile__id,axiom,
% 28.73/28.50 ! [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 ).
% 28.73/28.50
% 28.73/28.50 fof(fact_sorted__dropWhile,axiom,
% 28.73/28.50 ! [V_P_2,V_xs_2,T_b] :
% 28.73/28.50 ( class_Orderings_Olinorder(T_b)
% 28.73/28.50 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 28.73/28.50 => c_List_Olinorder__class_Osorted(T_b,c_List_OdropWhile(T_b,V_P_2,V_xs_2)) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_hd__dropWhile,axiom,
% 28.73/28.50 ! [V_xs_2,V_P_2,T_b] :
% 28.73/28.50 ( c_List_OdropWhile(T_b,V_P_2,V_xs_2) != c_List_Olist_ONil(T_b)
% 28.73/28.50 => ~ hBOOL(hAPP(V_P_2,hAPP(c_List_Ohd(T_b),c_List_OdropWhile(T_b,V_P_2,V_xs_2)))) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_length__dropWhile__le,axiom,
% 28.73/28.50 ! [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))) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_dropWhile__eq__Nil__conv,axiom,
% 28.73/28.50 ! [V_xs_2,V_P_2,T_b] :
% 28.73/28.50 ( c_List_OdropWhile(T_b,V_P_2,V_xs_2) = c_List_Olist_ONil(T_b)
% 28.73/28.50 <=> ! [B_x] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.73/28.50 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_distinct__dropWhile,axiom,
% 28.73/28.50 ! [V_P_2,V_xs_2,T_b] :
% 28.73/28.50 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 28.73/28.50 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OdropWhile(T_b,V_P_2,V_xs_2))) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_dropWhile_Osimps_I2_J,axiom,
% 28.73/28.50 ! [V_xs_2,T_b,V_x_2,V_P_2] :
% 28.73/28.50 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 28.73/28.50 => 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) )
% 28.73/28.50 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 28.73/28.50 => 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) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_dropWhile_Osimps_I1_J,axiom,
% 28.73/28.50 ! [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) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_dropWhile__map,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_dropWhile__append1,axiom,
% 28.73/28.50 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_b] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.73/28.50 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 28.73/28.50 => 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) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_dropWhile__eq__Cons__conv,axiom,
% 28.73/28.50 ! [V_ys_2,V_y_2,V_xs_2,V_P_2,T_b] :
% 28.73/28.50 ( 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)
% 28.73/28.50 <=> ( 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))
% 28.73/28.50 & ~ hBOOL(hAPP(V_P_2,V_y_2)) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_dropWhile__eq__drop,axiom,
% 28.73/28.50 ! [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) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_dropWhile__nth,axiom,
% 28.73/28.50 ! [V_xs_2,V_P_2,T_b,V_j_2] :
% 28.73/28.50 ( 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))))
% 28.73/28.50 => 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)))) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_listsum__map__filter,axiom,
% 28.73/28.50 ! [V_f_2,V_P_2,V_xs_2,T_b,T_c] :
% 28.73/28.50 ( class_Groups_Omonoid__add(T_c)
% 28.73/28.50 => ( ! [B_x] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.73/28.50 => ( ~ hBOOL(hAPP(V_P_2,B_x))
% 28.73/28.50 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) )
% 28.73/28.50 => 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)) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_sorted__nth__monoI,axiom,
% 28.73/28.50 ! [V_xs,T_a] :
% 28.73/28.50 ( class_Orderings_Olinorder(T_a)
% 28.73/28.50 => ( ! [B_i,B_j] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
% 28.73/28.50 => ( 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)))
% 28.73/28.50 => 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))) ) )
% 28.73/28.50 => c_List_Olinorder__class_Osorted(T_a,V_xs) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_takeWhile__eq__filter,axiom,
% 28.73/28.50 ! [V_xs_2,V_P_2,T_b] :
% 28.73/28.50 ( ! [B_x] :
% 28.73/28.50 ( 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))))
% 28.73/28.50 => ~ hBOOL(hAPP(V_P_2,B_x)) )
% 28.73/28.50 => c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_takeWhile__eq__take__P__nth,axiom,
% 28.73/28.50 ! [V_P_2,V_xs_2,T_b,V_n_2] :
% 28.73/28.50 ( ! [B_i] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 28.73/28.50 => ( 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)))
% 28.73/28.50 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) )
% 28.73/28.50 => ( ( 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)))
% 28.73/28.50 => ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2))) )
% 28.73/28.50 => c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_length__takeWhile__less__P__nth,axiom,
% 28.73/28.50 ! [V_xs_2,T_b,V_P_2,V_j_2] :
% 28.73/28.50 ( ! [B_i] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_j_2))
% 28.73/28.50 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) )
% 28.73/28.50 => ( 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)))
% 28.73/28.50 => 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)))) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_sorted_Osimps,axiom,
% 28.73/28.50 ! [V_a_2,T_b] :
% 28.73/28.50 ( class_Orderings_Olinorder(T_b)
% 28.73/28.50 => ( c_List_Olinorder__class_Osorted(T_b,V_a_2)
% 28.73/28.50 <=> ( V_a_2 = c_List_Olist_ONil(T_b)
% 28.73/28.50 | ? [B_xs,B_x] :
% 28.73/28.50 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs)
% 28.73/28.50 & ! [B_xa] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),B_xs)))
% 28.73/28.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) )
% 28.73/28.50 & c_List_Olinorder__class_Osorted(T_b,B_xs) ) ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_map__removeAll__inj__on,axiom,
% 28.73/28.50 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
% 28.73/28.50 ( 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)))
% 28.73/28.50 => 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)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_not__in__set__insert,axiom,
% 28.73/28.50 ! [V_xs_2,V_x_2,T_b] :
% 28.73/28.50 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.73/28.50 => 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) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_removeAll__append,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_insert__remdups,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_removeAll__filter__not__eq,axiom,
% 28.73/28.50 ! [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))) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_removeAll__filter__not,axiom,
% 28.73/28.50 ! [V_xs_2,T_b,V_x_2,V_P_2] :
% 28.73/28.50 ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 28.73/28.50 => 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) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_distinct__insert,axiom,
% 28.73/28.50 ! [V_x,V_xs,T_a] :
% 28.73/28.50 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 28.73/28.50 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oinsert(T_a,V_x,V_xs))) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_distinct__removeAll,axiom,
% 28.73/28.50 ! [V_x,V_xs,T_a] :
% 28.73/28.50 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 28.73/28.50 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs))) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_removeAll_Osimps_I2_J,axiom,
% 28.73/28.50 ! [V_xs,T_a,V_y,V_x] :
% 28.73/28.50 ( ( V_x = V_y
% 28.73/28.50 => 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) )
% 28.73/28.50 & ( V_x != V_y
% 28.73/28.50 => 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)) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_removeAll_Osimps_I1_J,axiom,
% 28.73/28.50 ! [V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_removeAll__id,axiom,
% 28.73/28.50 ! [V_xs_2,V_x_2,T_b] :
% 28.73/28.50 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.73/28.50 => hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2) = V_xs_2 ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_distinct__remove1__removeAll,axiom,
% 28.73/28.50 ! [V_x,V_xs,T_a] :
% 28.73/28.50 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 28.73/28.50 => c_List_Oremove1(T_a,V_x,V_xs) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_in__set__insert,axiom,
% 28.73/28.50 ! [V_xs_2,V_x_2,T_b] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.73/28.50 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2 ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_List_Oset__insert,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_insert__Nil,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_map__removeAll__inj,axiom,
% 28.73/28.50 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
% 28.73/28.50 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 28.73/28.50 => 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)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_set__removeAll,axiom,
% 28.73/28.50 ! [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)))) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_List_Oinsert__def,axiom,
% 28.73/28.50 ! [V_xs_2,V_x_2,T_b] :
% 28.73/28.50 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.73/28.50 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2 )
% 28.73/28.50 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.73/28.50 => 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) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_maps__def,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_concat__map__maps,axiom,
% 28.73/28.50 ! [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) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_maps__simps_I2_J,axiom,
% 28.73/28.50 ! [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) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_maps__simps_I1_J,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_distinct__concat,axiom,
% 28.73/28.50 ! [V_xs_2,T_b] :
% 28.73/28.50 ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_b)),V_xs_2))
% 28.73/28.50 => ( ! [B_ys] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 28.73/28.50 => hBOOL(hAPP(c_List_Odistinct(T_b),B_ys)) )
% 28.73/28.50 => ( ! [B_ys] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 28.73/28.50 => ! [B_zs] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_zs),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 28.73/28.50 => ( B_ys != B_zs
% 28.73/28.50 => 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)) ) ) )
% 28.73/28.50 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Oconcat(T_b,V_xs_2))) ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_measures__lesseq,axiom,
% 28.73/28.50 ! [V_fs_2,T_b,V_y_2,V_x_2,V_f_2] :
% 28.73/28.50 ( 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)))
% 28.73/28.50 => ( 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)))
% 28.73/28.50 => 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)))) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_wf__measures,axiom,
% 28.73/28.50 ! [V_fs_2,T_b] : c_Wellfounded_Owf(T_b,c_List_Omeasures(T_b,V_fs_2)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_in__measures_I1_J,axiom,
% 28.73/28.50 ! [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))))) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_measures__def,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_in__measures_I2_J,axiom,
% 28.73/28.50 ! [V_fs_2,V_f_2,V_y_2,V_x_2,T_b] :
% 28.73/28.50 ( 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))))
% 28.73/28.50 <=> ( 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)))
% 28.73/28.50 | ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 28.73/28.50 & 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))) ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_measures__less,axiom,
% 28.73/28.50 ! [V_fs_2,T_b,V_y_2,V_x_2,V_f_2] :
% 28.73/28.50 ( 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)))
% 28.73/28.50 => 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)))) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_foldl__apply,axiom,
% 28.73/28.50 ! [V_s_2,V_g_2,V_h_2,V_f_2,T_c,T_d,V_xs_2,T_b] :
% 28.73/28.50 ( ! [B_x] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.73/28.50 => 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)) )
% 28.73/28.50 => 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)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_zip__obtain__same__length,axiom,
% 28.73/28.50 ! [V_P_2,V_ys_2,T_c,V_xs_2,T_b] :
% 28.73/28.50 ( ( 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))
% 28.73/28.50 => 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)))) )
% 28.73/28.50 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_pos__not__random__dseq__def,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_dropWhile__append2,axiom,
% 28.73/28.50 ! [V_ys_2,V_P_2,V_xs_2,T_b] :
% 28.73/28.50 ( ! [B_x] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.73/28.50 => hBOOL(hAPP(V_P_2,B_x)) )
% 28.73/28.50 => 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) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_list__all2__all__nthI,axiom,
% 28.73/28.50 ! [V_P_2,V_b_2,T_c,V_a_2,T_b] :
% 28.73/28.50 ( 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)
% 28.73/28.50 => ( ! [B_n] :
% 28.73/28.50 ( 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)))
% 28.73/28.50 => 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))) )
% 28.73/28.50 => c_List_Olist__all2(T_b,T_c,V_P_2,V_a_2,V_b_2) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_finite__sorted__distinct__unique,axiom,
% 28.73/28.50 ! [V_A_2,T_b] :
% 28.73/28.50 ( class_Orderings_Olinorder(T_b)
% 28.73/28.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.73/28.50 => ? [B_x] :
% 28.73/28.50 ( hAPP(c_List_Oset(T_b),B_x) = V_A_2
% 28.73/28.50 & c_List_Olinorder__class_Osorted(T_b,B_x)
% 28.73/28.50 & hBOOL(hAPP(c_List_Odistinct(T_b),B_x))
% 28.73/28.50 & ! [B_y] :
% 28.73/28.50 ( ( hAPP(c_List_Oset(T_b),B_y) = V_A_2
% 28.73/28.50 & c_List_Olinorder__class_Osorted(T_b,B_y)
% 28.73/28.50 & hBOOL(hAPP(c_List_Odistinct(T_b),B_y)) )
% 28.73/28.50 => B_y = B_x ) ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_takeWhile__append2,axiom,
% 28.73/28.50 ! [V_ys_2,V_P_2,V_xs_2,T_b] :
% 28.73/28.50 ( ! [B_x] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.73/28.50 => hBOOL(hAPP(V_P_2,B_x)) )
% 28.73/28.50 => 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)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_insort__is__Cons,axiom,
% 28.73/28.50 ! [V_a_2,V_f_2,V_xs_2,T_b,T_c] :
% 28.73/28.50 ( class_Orderings_Olinorder(T_c)
% 28.73/28.50 => ( ! [B_x] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.73/28.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_a_2)),hAPP(V_f_2,B_x))) )
% 28.73/28.50 => 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) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_Cons__eq__filter__iff,axiom,
% 28.73/28.50 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_b] :
% 28.73/28.50 ( 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)
% 28.73/28.50 <=> ? [B_us,B_vs] :
% 28.73/28.50 ( 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))
% 28.73/28.50 & ! [B_x] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us)))
% 28.73/28.50 => ~ hBOOL(hAPP(V_P_2,B_x)) )
% 28.73/28.50 & hBOOL(hAPP(V_P_2,V_x_2))
% 28.73/28.50 & V_xs_2 = hAPP(c_List_Ofilter(T_b,V_P_2),B_vs) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_filter__eq__Cons__iff,axiom,
% 28.73/28.50 ! [V_xs_2,V_x_2,V_ys_2,V_P_2,T_b] :
% 28.73/28.50 ( 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)
% 28.73/28.50 <=> ? [B_us,B_vs] :
% 28.73/28.50 ( 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))
% 28.73/28.50 & ! [B_x] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us)))
% 28.73/28.50 => ~ hBOOL(hAPP(V_P_2,B_x)) )
% 28.73/28.50 & hBOOL(hAPP(V_P_2,V_x_2))
% 28.73/28.50 & V_xs_2 = hAPP(c_List_Ofilter(T_b,V_P_2),B_vs) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_list__ball__nth,axiom,
% 28.73/28.50 ! [V_P_2,V_xs_2,T_b,V_n_2] :
% 28.73/28.50 ( 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)))
% 28.73/28.50 => ( ! [B_x] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.73/28.50 => hBOOL(hAPP(V_P_2,B_x)) )
% 28.73/28.50 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2))) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_sorted_OCons,axiom,
% 28.73/28.50 ! [V_x_2,V_xs_2,T_b] :
% 28.73/28.50 ( class_Orderings_Olinorder(T_b)
% 28.73/28.50 => ( ! [B_x] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.73/28.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) )
% 28.73/28.50 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 28.73/28.50 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_list__ex__length,axiom,
% 28.73/28.50 ! [V_xs_2,V_P_2,T_b] :
% 28.73/28.50 ( c_List_Olist__ex(T_b,V_P_2,V_xs_2)
% 28.73/28.50 <=> ? [B_n] :
% 28.73/28.50 ( 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)))
% 28.73/28.50 & hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n))) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_in__set__conv__decomp,axiom,
% 28.73/28.50 ! [V_xs_2,V_x_2,T_b] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.73/28.50 <=> ? [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)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_list__ex__simps_I1_J,axiom,
% 28.73/28.50 ! [V_xs_2,V_x_2,V_P_2,T_b] :
% 28.73/28.50 ( c_List_Olist__ex(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 28.73/28.50 <=> ( hBOOL(hAPP(V_P_2,V_x_2))
% 28.73/28.50 | c_List_Olist__ex(T_b,V_P_2,V_xs_2) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_list__ex__rev,axiom,
% 28.73/28.50 ! [V_xs_2,V_P_2,T_b] :
% 28.73/28.50 ( c_List_Olist__ex(T_b,V_P_2,hAPP(c_List_Orev(T_b),V_xs_2))
% 28.73/28.50 <=> c_List_Olist__ex(T_b,V_P_2,V_xs_2) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_list__ex__iff,axiom,
% 28.73/28.50 ! [V_xs_2,V_P_2,T_b] :
% 28.73/28.50 ( c_List_Olist__ex(T_b,V_P_2,V_xs_2)
% 28.73/28.50 <=> ? [B_x] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.73/28.50 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_list__ex__append,axiom,
% 28.73/28.50 ! [V_ys_2,V_xs_2,V_P_2,T_b] :
% 28.73/28.50 ( c_List_Olist__ex(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
% 28.73/28.50 <=> ( c_List_Olist__ex(T_b,V_P_2,V_xs_2)
% 28.73/28.50 | c_List_Olist__ex(T_b,V_P_2,V_ys_2) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_list__ex__simps_I2_J,axiom,
% 28.73/28.50 ! [V_P_2,T_b] : ~ c_List_Olist__ex(T_b,V_P_2,c_List_Olist_ONil(T_b)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_in__set__conv__decomp__first,axiom,
% 28.73/28.50 ! [V_xs_2,V_x_2,T_b] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.73/28.50 <=> ? [B_ys] :
% 28.73/28.50 ( ? [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))
% 28.73/28.50 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_ys))) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_in__set__conv__decomp__last,axiom,
% 28.73/28.50 ! [V_xs_2,V_x_2,T_b] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.73/28.50 <=> ? [B_ys,B_zs] :
% 28.73/28.50 ( 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))
% 28.73/28.50 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_zs))) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_list__all__length,axiom,
% 28.73/28.50 ! [V_xs_2,V_P_2,T_b] :
% 28.73/28.50 ( c_List_Olist__all(T_b,V_P_2,V_xs_2)
% 28.73/28.50 <=> ! [B_n] :
% 28.73/28.50 ( 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)))
% 28.73/28.50 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n))) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_finite__induct,axiom,
% 28.73/28.50 ! [V_P_2,V_F_2,T_b] :
% 28.73/28.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 28.73/28.50 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 28.73/28.50 => ( ! [B_x,B_F] :
% 28.73/28.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F))
% 28.73/28.50 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_F))
% 28.73/28.50 => ( hBOOL(hAPP(V_P_2,B_F))
% 28.73/28.50 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_x),B_F))) ) ) )
% 28.73/28.50 => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_list__all__simps_I1_J,axiom,
% 28.73/28.50 ! [V_xs_2,V_x_2,V_P_2,T_b] :
% 28.73/28.50 ( c_List_Olist__all(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 28.73/28.50 <=> ( hBOOL(hAPP(V_P_2,V_x_2))
% 28.73/28.50 & c_List_Olist__all(T_b,V_P_2,V_xs_2) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_list__all__rev,axiom,
% 28.73/28.50 ! [V_xs_2,V_P_2,T_b] :
% 28.73/28.50 ( c_List_Olist__all(T_b,V_P_2,hAPP(c_List_Orev(T_b),V_xs_2))
% 28.73/28.50 <=> c_List_Olist__all(T_b,V_P_2,V_xs_2) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_list__all__iff,axiom,
% 28.73/28.50 ! [V_xs_2,V_P_2,T_b] :
% 28.73/28.50 ( c_List_Olist__all(T_b,V_P_2,V_xs_2)
% 28.73/28.50 <=> ! [B_x] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.73/28.50 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_list__all__append,axiom,
% 28.73/28.50 ! [V_ys_2,V_xs_2,V_P_2,T_b] :
% 28.73/28.50 ( c_List_Olist__all(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
% 28.73/28.50 <=> ( c_List_Olist__all(T_b,V_P_2,V_xs_2)
% 28.73/28.50 & c_List_Olist__all(T_b,V_P_2,V_ys_2) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_list__all__simps_I2_J,axiom,
% 28.73/28.50 ! [V_P_2,T_b] : c_List_Olist__all(T_b,V_P_2,c_List_Olist_ONil(T_b)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_Ball__set__list__all,axiom,
% 28.73/28.50 ! [V_P_2,V_xs_2,T_b] :
% 28.73/28.50 ( ! [B_x] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.73/28.50 => hBOOL(hAPP(V_P_2,B_x)) )
% 28.73/28.50 <=> c_List_Olist__all(T_b,V_P_2,V_xs_2) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_list__all__iff__raw,axiom,
% 28.73/28.50 ! [V_xs_2,V_P_2,T_b] :
% 28.73/28.50 ( c_List_Olist__all(T_b,V_P_2,V_xs_2)
% 28.73/28.50 <=> ! [B_x] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.73/28.50 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_list__ex1__simps_I2_J,axiom,
% 28.73/28.50 ! [V_xs_2,V_x_2,V_P_2,T_b] :
% 28.73/28.50 ( c_List_Olist__ex1(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 28.73/28.50 <=> ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 28.73/28.50 => 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) )
% 28.73/28.50 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 28.73/28.50 => c_List_Olist__ex1(T_b,V_P_2,V_xs_2) ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_measure__function__int,axiom,
% 28.73/28.50 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))) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_list__ex1__simps_I1_J,axiom,
% 28.73/28.50 ! [V_P_2,T_b] : ~ c_List_Olist__ex1(T_b,V_P_2,c_List_Olist_ONil(T_b)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_is__measure_Ointros,axiom,
% 28.73/28.50 ! [V_f_2,T_b] : c_FunDef_Ois__measure(T_b,V_f_2) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_is__measure_Oequations,axiom,
% 28.73/28.50 ! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_is__measure_Osimps,axiom,
% 28.73/28.50 ! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_measure__size,axiom,
% 28.73/28.50 ! [T_b] :
% 28.73/28.50 ( class_Nat_Osize(T_b)
% 28.73/28.50 => c_FunDef_Ois__measure(T_b,c_Nat_Osize__class_Osize(T_b)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_measure__snd,axiom,
% 28.73/28.50 ! [T_c,V_f_2,T_b] :
% 28.73/28.50 ( c_FunDef_Ois__measure(T_b,V_f_2)
% 28.73/28.50 => 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))) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_measure__fst,axiom,
% 28.73/28.50 ! [T_c,V_f_2,T_b] :
% 28.73/28.50 ( c_FunDef_Ois__measure(T_b,V_f_2)
% 28.73/28.50 => 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))) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_list__ex1__iff,axiom,
% 28.73/28.50 ! [V_xs_2,V_P_2,T_b] :
% 28.73/28.50 ( c_List_Olist__ex1(T_b,V_P_2,V_xs_2)
% 28.73/28.50 <=> ? [B_x] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.73/28.50 & hBOOL(hAPP(V_P_2,B_x))
% 28.73/28.50 & ! [B_y] :
% 28.73/28.50 ( ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.73/28.50 & hBOOL(hAPP(V_P_2,B_y)) )
% 28.73/28.50 => B_y = B_x ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_transfer__morphism__int__nat,axiom,
% 28.73/28.50 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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_New__DSequence_Oneg__decr__bind__def,axiom,
% 28.73/28.50 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
% 28.73/28.50 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 28.73/28.50 => 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) )
% 28.73/28.50 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 28.73/28.50 => 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)) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_bool_Osize_I4_J,axiom,
% 28.73/28.50 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_bool_Osize_I3_J,axiom,
% 28.73/28.50 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_New__DSequence_Oneg__bind__def,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_neg__bind__def,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_New__DSequence_Opos__decr__bind__def,axiom,
% 28.73/28.50 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
% 28.73/28.50 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 28.73/28.50 => 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) )
% 28.73/28.50 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 28.73/28.50 => 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)) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_New__DSequence_Opos__empty__def,axiom,
% 28.73/28.50 ! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_pos__empty__def,axiom,
% 28.73/28.50 ! [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) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_New__DSequence_Opos__bind__def,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_pos__bind__def,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_neg__map__def,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_neg__single__def,axiom,
% 28.73/28.50 ! [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) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_pos__map__def,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_New__DSequence_Oneg__single__def,axiom,
% 28.73/28.50 ! [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) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_pos__single__def,axiom,
% 28.73/28.50 ! [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) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_New__DSequence_Opos__single__def,axiom,
% 28.73/28.50 ! [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) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_length__splice,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_splice_Osimps_I3_J,axiom,
% 28.73/28.50 ! [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))) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_splice_Osimps_I1_J,axiom,
% 28.73/28.50 ! [V_ys,T_a] : c_List_Osplice(T_a,c_List_Olist_ONil(T_a),V_ys) = V_ys ).
% 28.73/28.50
% 28.73/28.50 fof(fact_splice__Nil2,axiom,
% 28.73/28.50 ! [V_xs,T_a] : c_List_Osplice(T_a,V_xs,c_List_Olist_ONil(T_a)) = V_xs ).
% 28.73/28.50
% 28.73/28.50 fof(fact_splice_Osimps_I2_J,axiom,
% 28.73/28.50 ! [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) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_,axiom,
% 28.73/28.50 ! [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)))) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_bij__image__Collect__eq,axiom,
% 28.73/28.50 ! [V_P_2,V_f_2,T_c,T_b] :
% 28.73/28.50 ( 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)))
% 28.73/28.50 => 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))) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_inv__into__f__eq,axiom,
% 28.73/28.50 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 28.73/28.50 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 28.73/28.50 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.73/28.50 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 28.73/28.50 => hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_inv__into__f__f,axiom,
% 28.73/28.50 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 28.73/28.50 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 28.73/28.50 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.73/28.50 => 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 ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_inv__f__f,axiom,
% 28.73/28.50 ! [V_x_2,V_f_2,T_c,T_b] :
% 28.73/28.50 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 28.73/28.50 => 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 ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_inv__f__eq,axiom,
% 28.73/28.50 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 28.73/28.50 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 28.73/28.50 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 28.73/28.50 => 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 ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_inv__into__def,axiom,
% 28.73/28.50 ! [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))) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_inv__inv__eq,axiom,
% 28.73/28.50 ! [V_f_2,T_c,T_b] :
% 28.73/28.50 ( 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)))
% 28.73/28.50 => 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 ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_bij__imp__bij__inv,axiom,
% 28.73/28.50 ! [V_f_2,T_c,T_b] :
% 28.73/28.50 ( 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)))
% 28.73/28.50 => 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))) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_bij__betw__inv__into,axiom,
% 28.73/28.50 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 28.73/28.50 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 28.73/28.50 => 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) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_inv__into__inv__into__eq,axiom,
% 28.73/28.50 ! [V_a_2,V_A_H_2,V_A_2,V_f_2,T_c,T_b] :
% 28.73/28.50 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 28.73/28.50 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.73/28.50 => 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) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_image__inv__into__cancel,axiom,
% 28.73/28.50 ! [V_B_H_2,V_A_H_2,V_A_2,V_f_2,T_b,T_c] :
% 28.73/28.50 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2
% 28.73/28.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_H_2),V_A_H_2))
% 28.73/28.50 => 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 ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_surj__iff__all,axiom,
% 28.73/28.50 ! [V_f_2,T_b,T_c] :
% 28.73/28.50 ( 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))
% 28.73/28.50 <=> ! [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 ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_surj__f__inv__f,axiom,
% 28.73/28.50 ! [V_y_2,V_f_2,T_b,T_c] :
% 28.73/28.50 ( 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))
% 28.73/28.50 => 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 ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_image__surj__f__inv__f,axiom,
% 28.73/28.50 ! [V_A_2,V_f_2,T_b,T_c] :
% 28.73/28.50 ( 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))
% 28.73/28.50 => 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 ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_inv__into__injective,axiom,
% 28.73/28.50 ! [V_y_2,V_x_2,V_f_2,V_A_2,T_c,T_b] :
% 28.73/28.50 ( 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)
% 28.73/28.50 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 28.73/28.50 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 28.73/28.50 => V_x_2 = V_y_2 ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_inv__into__into,axiom,
% 28.73/28.50 ! [V_A_2,V_f_2,T_c,V_x_2,T_b] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 28.73/28.50 => 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)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_f__inv__into__f,axiom,
% 28.73/28.50 ! [V_A_2,V_f_2,T_c,V_y_2,T_b] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 28.73/28.50 => 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 ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_inv__id,axiom,
% 28.73/28.50 ! [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) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_inv__def,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_inj__on__inv__into,axiom,
% 28.73/28.50 ! [V_A_2,V_f_2,T_c,V_B_2,T_b] :
% 28.73/28.50 ( 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)))
% 28.73/28.50 => 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) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_inv__into__image__cancel,axiom,
% 28.73/28.50 ! [V_S_2,V_A_2,V_f_2,T_c,T_b] :
% 28.73/28.50 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 28.73/28.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_A_2))
% 28.73/28.50 => 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 ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_inj__imp__surj__inv,axiom,
% 28.73/28.50 ! [V_f_2,T_c,T_b] :
% 28.73/28.50 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 28.73/28.50 => 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)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_image__inv__f__f,axiom,
% 28.73/28.50 ! [V_A_2,V_f_2,T_c,T_b] :
% 28.73/28.50 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 28.73/28.50 => 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 ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_inv__image__comp,axiom,
% 28.73/28.50 ! [V_X_2,V_f_2,T_c,T_b] :
% 28.73/28.50 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 28.73/28.50 => 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 ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_surj__imp__inj__inv,axiom,
% 28.73/28.50 ! [V_f_2,T_b,T_c] :
% 28.73/28.50 ( 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))
% 28.73/28.50 => 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))) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_o__inv__o__cancel,axiom,
% 28.73/28.50 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 28.73/28.50 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 28.73/28.50 => 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 ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_o__inv__distrib,axiom,
% 28.73/28.50 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 28.73/28.50 ( 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)))
% 28.73/28.50 => ( 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)))
% 28.73/28.50 => 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)) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_inv__into__comp,axiom,
% 28.73/28.50 ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] :
% 28.73/28.50 ( 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))
% 28.73/28.50 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2)
% 28.73/28.50 => ( 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))))
% 28.73/28.50 => 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) ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_surj__iff,axiom,
% 28.73/28.50 ! [V_f_2,T_b,T_c] :
% 28.73/28.50 ( 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))
% 28.73/28.50 <=> 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) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_inv__o__cancel,axiom,
% 28.73/28.50 ! [V_f_2,T_c,T_b] :
% 28.73/28.50 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 28.73/28.50 => 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) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_inj__iff,axiom,
% 28.73/28.50 ! [V_f_2,T_c,T_b] :
% 28.73/28.50 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 28.73/28.50 <=> 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) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_bij__vimage__eq__inv__image,axiom,
% 28.73/28.50 ! [V_A_2,V_f_2,T_c,T_b] :
% 28.73/28.50 ( 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)))
% 28.73/28.50 => 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) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_inj__transfer,axiom,
% 28.73/28.50 ! [V_x_2,V_P_2,V_f_2,T_c,T_b] :
% 28.73/28.50 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 28.73/28.50 => ( ! [B_y] :
% 28.73/28.50 ( 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)))))
% 28.73/28.50 => 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))) )
% 28.73/28.50 => hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_small__lazy__list_Osimps,axiom,
% 28.73/28.50 ! [V_d_2,T_b] :
% 28.73/28.50 ( class_Lazy__Sequence_Osmall__lazy(T_b)
% 28.73/28.50 => 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)))) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_small__lazy__prod__def,axiom,
% 28.73/28.50 ! [V_d,T_b,T_a] :
% 28.73/28.50 ( ( class_Lazy__Sequence_Osmall__lazy(T_a)
% 28.73/28.50 & class_Lazy__Sequence_Osmall__lazy(T_b) )
% 28.73/28.50 => 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)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_New__DSequence_Opos__union__def,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_acyclicP__converse,axiom,
% 28.73/28.50 ! [V_r_2,T_b] :
% 28.73/28.50 ( 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))))
% 28.73/28.50 <=> 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))) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_converse__meet,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_conversep__eq,axiom,
% 28.73/28.50 ! [T_b] : c_Predicate_Oconversep(T_b,T_b,c_fequal) = c_fequal ).
% 28.73/28.50
% 28.73/28.50 fof(fact_conversep__conversep,axiom,
% 28.73/28.50 ! [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 ).
% 28.73/28.50
% 28.73/28.50 fof(fact_conversep__iff,axiom,
% 28.73/28.50 ! [V_b_2,V_a_2,V_r_2,T_c,T_b] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2))
% 28.73/28.50 <=> hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_conversep_Oequations,axiom,
% 28.73/28.50 ! [V_a1_2,V_a2_2,V_r_2,T_c,T_b] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a2_2),V_a1_2))
% 28.73/28.50 <=> hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_conversep_Ointros,axiom,
% 28.73/28.50 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 28.73/28.50 => hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_b_2),V_a_2)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_conversepD,axiom,
% 28.73/28.50 ! [V_b_2,V_a_2,V_r_2,T_c,T_b] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2))
% 28.73/28.50 => hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_conversep__noteq,axiom,
% 28.73/28.50 ! [V_y_2,V_x_2,T_b] :
% 28.73/28.50 ( 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))
% 28.73/28.50 <=> V_x_2 != V_y_2 ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_converse__pred__comp,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_converse__join,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_conversep__converse__eq,axiom,
% 28.73/28.50 ! [V_y_2,V_x_2,V_r_2,T_c,T_b] :
% 28.73/28.50 ( 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))
% 28.73/28.50 <=> 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))) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_pos__union__def,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_small__lazy_H_Osimps,axiom,
% 28.73/28.50 ! [V_i,V_d] :
% 28.73/28.50 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i))
% 28.73/28.50 => c_Lazy__Sequence_Osmall__lazy_H(V_d,V_i) = c_Lazy__Sequence_Oempty(tc_Int_Oint) )
% 28.73/28.50 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i))
% 28.73/28.50 => 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)))) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_small__lazy__int__def,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_small__lazy_H_Opsimps,axiom,
% 28.73/28.50 ! [V_i_2,V_d_2] :
% 28.73/28.50 ( 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)))
% 28.73/28.50 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 28.73/28.50 => c_Lazy__Sequence_Osmall__lazy_H(V_d_2,V_i_2) = c_Lazy__Sequence_Oempty(tc_Int_Oint) )
% 28.73/28.50 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 28.73/28.50 => 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)))) ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_tl__replicate,axiom,
% 28.73/28.50 ! [V_x,T_a,V_n] :
% 28.73/28.50 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.73/28.50 => 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) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_map__replicate,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_replicate__0,axiom,
% 28.73/28.50 ! [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) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_empty__replicate,axiom,
% 28.73/28.50 ! [V_x_2,V_n_2,T_b] :
% 28.73/28.50 ( c_List_Olist_ONil(T_b) = c_List_Oreplicate(T_b,V_n_2,V_x_2)
% 28.73/28.50 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_replicate__empty,axiom,
% 28.73/28.50 ! [V_x_2,V_n_2,T_b] :
% 28.73/28.50 ( c_List_Oreplicate(T_b,V_n_2,V_x_2) = c_List_Olist_ONil(T_b)
% 28.73/28.50 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_concat__replicate__trivial,axiom,
% 28.73/28.50 ! [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) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_filter__replicate,axiom,
% 28.73/28.50 ! [V_n_2,T_b,V_x_2,V_P_2] :
% 28.73/28.50 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 28.73/28.50 => 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) )
% 28.73/28.50 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 28.73/28.50 => 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) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_append__replicate__commute,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_replicate__add,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_nth__replicate,axiom,
% 28.73/28.50 ! [V_x,T_a,V_n,V_i] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n))
% 28.73/28.50 => hAPP(hAPP(c_List_Onth(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_i) = V_x ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_replicate__eq__replicate,axiom,
% 28.73/28.50 ! [V_y_2,V_n_2,V_x_2,V_m_2,T_b] :
% 28.73/28.50 ( c_List_Oreplicate(T_b,V_m_2,V_x_2) = c_List_Oreplicate(T_b,V_n_2,V_y_2)
% 28.73/28.50 <=> ( V_m_2 = V_n_2
% 28.73/28.50 & ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.73/28.50 => V_x_2 = V_y_2 ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_Bex__set__replicate,axiom,
% 28.73/28.50 ! [V_P_2,V_a_2,V_n_2,T_b] :
% 28.73/28.50 ( ? [B_x] :
% 28.73/28.50 ( 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))))
% 28.73/28.50 & hBOOL(hAPP(V_P_2,B_x)) )
% 28.73/28.50 <=> ( hBOOL(hAPP(V_P_2,V_a_2))
% 28.73/28.50 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_Ball__set__replicate,axiom,
% 28.73/28.50 ! [V_P_2,V_a_2,V_n_2,T_b] :
% 28.73/28.50 ( ! [B_x] :
% 28.73/28.50 ( 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))))
% 28.73/28.50 => hBOOL(hAPP(V_P_2,B_x)) )
% 28.73/28.50 <=> ( hBOOL(hAPP(V_P_2,V_a_2))
% 28.73/28.50 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_zip__replicate,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_drop__replicate,axiom,
% 28.73/28.50 ! [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) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_hd__replicate,axiom,
% 28.73/28.50 ! [V_x,T_a,V_n] :
% 28.73/28.50 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.73/28.50 => hAPP(c_List_Ohd(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_take__replicate,axiom,
% 28.73/28.50 ! [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) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_last__replicate,axiom,
% 28.73/28.50 ! [V_x,T_a,V_n] :
% 28.73/28.50 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.73/28.50 => c_List_Olast(T_a,c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_rev__replicate,axiom,
% 28.73/28.50 ! [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) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_replicate__Suc,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_replicate__app__Cons__same,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_map__replicate__const,axiom,
% 28.73/28.50 ! [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) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_length__replicate,axiom,
% 28.73/28.50 ! [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 ).
% 28.73/28.50
% 28.73/28.50 fof(fact_replicate__length__filter,axiom,
% 28.73/28.50 ! [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) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_in__set__replicate,axiom,
% 28.73/28.50 ! [V_y_2,V_n_2,V_x_2,T_b] :
% 28.73/28.50 ( 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))))
% 28.73/28.50 <=> ( V_x_2 = V_y_2
% 28.73/28.50 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_replicate__append__same,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_map__replicate__trivial,axiom,
% 28.73/28.50 ! [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) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_set__replicate,axiom,
% 28.73/28.50 ! [V_x_2,T_b,V_n_2] :
% 28.73/28.50 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.73/28.50 => 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))) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_set__replicate__conv__if,axiom,
% 28.73/28.50 ! [V_x_2,T_b,V_n_2] :
% 28.73/28.50 ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.73/28.50 => 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)) )
% 28.73/28.50 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.73/28.50 => 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))) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_set__replicate__Suc,axiom,
% 28.73/28.50 ! [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))) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_small__lazy_H_Opinduct,axiom,
% 28.73/28.50 ! [V_P_2,V_a1_2,V_a0_2] :
% 28.73/28.50 ( 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)))
% 28.73/28.50 => ( ! [B_d,B_i] :
% 28.73/28.50 ( 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)))
% 28.73/28.50 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i))
% 28.73/28.50 => 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)))) )
% 28.73/28.50 => hBOOL(hAPP(hAPP(V_P_2,B_d),B_i)) ) )
% 28.73/28.50 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_eq__comp__r,axiom,
% 28.73/28.50 ! [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 ).
% 28.73/28.50
% 28.73/28.50 fof(fact_field__le__epsilon,axiom,
% 28.73/28.50 ! [V_y,V_x,T_a] :
% 28.73/28.50 ( class_Fields_Olinordered__field(T_a)
% 28.73/28.50 => ( ! [B_e] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_e))
% 28.73/28.50 => 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))) )
% 28.73/28.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_lazy__sequence_Osize_I4_J,axiom,
% 28.73/28.50 ! [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))) ).
% 28.73/28.50
% 28.73/28.50 fof(fact__01,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_lazy__sequence_Oinject,axiom,
% 28.73/28.50 ! [V_lazy__sequence_H_2,V_a_H_2,V_lazy__sequence_2,V_a_2,T_b] :
% 28.73/28.50 ( 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)
% 28.73/28.50 <=> ( V_a_2 = V_a_H_2
% 28.73/28.50 & V_lazy__sequence_2 = V_lazy__sequence_H_2 ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_lazy__sequence_Osize_I2_J,axiom,
% 28.73/28.50 ! [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))) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_size__code,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_lazy__sequence__size__code,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_seq__case,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_yieldn__def,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_lazy__sequence_Osimps_I5_J,axiom,
% 28.73/28.50 ! [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) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_refl__on__INTER,axiom,
% 28.73/28.50 ! [V_r_2,V_A_2,T_c,V_S_2,T_b] :
% 28.73/28.50 ( ! [B_x] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 28.73/28.50 => c_Relation_Orefl__on(T_c,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x)) )
% 28.73/28.50 => 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)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_in__set__member,axiom,
% 28.73/28.50 ! [V_xs_2,V_x_2,T_b] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.73/28.50 <=> hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_x_2)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_member__rec_I1_J,axiom,
% 28.73/28.50 ! [V_y_2,V_xs_2,V_x_2,T_b] :
% 28.73/28.50 ( 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))
% 28.73/28.50 <=> ( V_x_2 = V_y_2
% 28.73/28.50 | hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_y_2)) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_member__set,axiom,
% 28.73/28.50 ! [T_b] : c_List_Omember(T_b) = c_List_Oset(T_b) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_member__rec_I2_J,axiom,
% 28.73/28.50 ! [V_y,T_a] : ~ hBOOL(hAPP(hAPP(c_List_Omember(T_a),c_List_Olist_ONil(T_a)),V_y)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_List_Omember__def,axiom,
% 28.73/28.50 ! [V_x_2,V_xs_2,T_b] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_x_2))
% 28.73/28.50 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_pair__box_Osize_I1_J,axiom,
% 28.73/28.50 ! [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))) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_list__ex1__iff__raw,axiom,
% 28.73/28.50 ! [V_xs_2,V_P_2,T_b] :
% 28.73/28.50 ( c_List_Olist__ex1(T_b,V_P_2,V_xs_2)
% 28.73/28.50 <=> ? [B_x] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.73/28.50 & hBOOL(hAPP(V_P_2,B_x))
% 28.73/28.50 & ! [B_y] :
% 28.73/28.50 ( ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.73/28.50 & hBOOL(hAPP(V_P_2,B_y)) )
% 28.73/28.50 => B_y = B_x ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_pair__box_Oinject,axiom,
% 28.73/28.50 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 28.73/28.50 ( 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)
% 28.73/28.50 <=> ( V_a_2 = V_a_H_2
% 28.73/28.50 & V_b_2 = V_b_H_2 ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_pair__box_Osize_I2_J,axiom,
% 28.73/28.50 ! [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) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_pair__box_Orecs,axiom,
% 28.73/28.50 ! [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) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_pair__box_Osimps_I2_J,axiom,
% 28.73/28.50 ! [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) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_THE__default__def,axiom,
% 28.73/28.50 ! [V_d_2,T_b,V_P_2] :
% 28.73/28.50 ( ( ? [B_x] :
% 28.73/28.50 ( hBOOL(hAPP(V_P_2,B_x))
% 28.73/28.50 & ! [B_y] :
% 28.73/28.50 ( hBOOL(hAPP(V_P_2,B_y))
% 28.73/28.50 => B_y = B_x ) )
% 28.73/28.50 => c_FunDef_OTHE__default(T_b,V_d_2,V_P_2) = c_HOL_OThe(T_b,V_P_2) )
% 28.73/28.50 & ( ~ ? [B_x] :
% 28.73/28.50 ( hBOOL(hAPP(V_P_2,B_x))
% 28.73/28.50 & ! [B_y] :
% 28.73/28.50 ( hBOOL(hAPP(V_P_2,B_y))
% 28.73/28.50 => B_y = B_x ) )
% 28.73/28.50 => c_FunDef_OTHE__default(T_b,V_d_2,V_P_2) = V_d_2 ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_setsum__UNION__zero,axiom,
% 28.73/28.50 ! [V_f_2,V_S_2,T_b,T_c] :
% 28.73/28.50 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.73/28.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_S_2))
% 28.73/28.50 => ( ! [B_x] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_S_2))
% 28.73/28.50 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)) )
% 28.73/28.50 => ( ! [B_T1] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_T1),V_S_2))
% 28.73/28.50 => ! [B_T2] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_T2),V_S_2))
% 28.73/28.50 => ( B_T1 != B_T2
% 28.73/28.50 => ! [B_x] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_T1))
% 28.73/28.50 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_T2))
% 28.73/28.50 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) )
% 28.73/28.50 => 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) ) ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_finite__maxlen,axiom,
% 28.73/28.50 ! [V_M_2,T_b] :
% 28.73/28.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),V_M_2))
% 28.73/28.50 => ? [B_n] :
% 28.73/28.50 ! [B_x] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),V_M_2))
% 28.73/28.50 => 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)) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_lazy__sequence_Osize_I3_J,axiom,
% 28.73/28.50 ! [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) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_lazy__sequence_Osimps_I2_J,axiom,
% 28.73/28.50 ! [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) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_lazy__sequence_Osimps_I3_J,axiom,
% 28.73/28.50 ! [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) ).
% 28.73/28.50
% 28.73/28.50 fof(fact__02,axiom,
% 28.73/28.50 ! [V_yq,T_a] : c_Lazy__Sequence_Oappend(T_a,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a),V_yq) = V_yq ).
% 28.73/28.50
% 28.73/28.50 fof(fact_lazy__sequence_Osimps_I4_J,axiom,
% 28.73/28.50 ! [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 ).
% 28.73/28.50
% 28.73/28.50 fof(fact_lazy__sequence_Osize_I1_J,axiom,
% 28.73/28.50 ! [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) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_list__all__iff__all__interval__int,axiom,
% 28.73/28.50 ! [V_j_2,V_i_2,V_P_2] :
% 28.73/28.50 ( c_List_Olist__all(tc_Int_Oint,V_P_2,c_List_Oupto(V_i_2,V_j_2))
% 28.73/28.50 <=> c_List_Oall__interval__int(V_P_2,V_i_2,V_j_2) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_list__ex__iff__not__all__inverval__int,axiom,
% 28.73/28.50 ! [V_j_2,V_i_2,V_P_2] :
% 28.73/28.50 ( c_List_Olist__ex(tc_Int_Oint,V_P_2,c_List_Oupto(V_i_2,V_j_2))
% 28.73/28.50 <=> ~ 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) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_all__interval__int__def,axiom,
% 28.73/28.50 ! [V_j_2,V_i_2,V_P_2] :
% 28.73/28.50 ( c_List_Oall__interval__int(V_P_2,V_i_2,V_j_2)
% 28.73/28.50 <=> ! [B_x] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2)))
% 28.73/28.50 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_code__numeral_Orecs_I2_J,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_Random_Osimps,axiom,
% 28.73/28.50 ! [V_size_2,V_g_2,T_b,V_nrandom_2] :
% 28.73/28.50 ( ( 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)))
% 28.73/28.50 => 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)) )
% 28.73/28.50 & ( ~ 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)))
% 28.73/28.50 => 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))))))) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_code__numeral_Orecs_I1_J,axiom,
% 28.73/28.50 ! [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 ).
% 28.73/28.50
% 28.73/28.50 fof(fact_Random__Sequence_Oempty__def,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_Random__Sequence_Osingle__def,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_Random__Sequence_Omap__def,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_exE__realizer,axiom,
% 28.73/28.50 ! [T_d,V_f_2,V_Q_2,V_p_2,T_b,T_c,V_P_2] :
% 28.73/28.50 ( 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)))
% 28.73/28.50 => ( ! [B_x,B_y] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(V_P_2,B_y),B_x))
% 28.73/28.50 => hBOOL(hAPP(V_Q_2,hAPP(hAPP(V_f_2,B_x),B_y))) )
% 28.73/28.50 => 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))) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_Image__Collect__split,axiom,
% 28.73/28.50 ! [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)))) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_lexord__trans,axiom,
% 28.73/28.50 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] :
% 28.73/28.50 ( 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)))
% 28.73/28.50 => ( 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)))
% 28.73/28.50 => ( c_Relation_Otrans(T_b,V_r_2)
% 28.73/28.50 => 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))) ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_trans__less__than,axiom,
% 28.73/28.50 c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_trans__lex__prod,axiom,
% 28.73/28.50 ! [V_R2_2,T_c,V_R1_2,T_b] :
% 28.73/28.50 ( c_Relation_Otrans(T_b,V_R1_2)
% 28.73/28.50 => ( c_Relation_Otrans(T_c,V_R2_2)
% 28.73/28.50 => c_Relation_Otrans(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_R1_2,V_R2_2)) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_transD,axiom,
% 28.73/28.50 ! [V_c_2,V_b_2,V_a_2,V_r_2,T_b] :
% 28.73/28.50 ( c_Relation_Otrans(T_b,V_r_2)
% 28.73/28.50 => ( 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))
% 28.73/28.50 => ( 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))
% 28.73/28.50 => 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)) ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_trans__def,axiom,
% 28.73/28.50 ! [V_r_2,T_b] :
% 28.73/28.50 ( c_Relation_Otrans(T_b,V_r_2)
% 28.73/28.50 <=> ! [B_x,B_y] :
% 28.73/28.50 ( 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))
% 28.73/28.50 => ! [B_z] :
% 28.73/28.50 ( 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))
% 28.73/28.50 => 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)) ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_UN__eq,axiom,
% 28.73/28.50 ! [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))))) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_Union__eq,axiom,
% 28.73/28.50 ! [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)))) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_trans__inv__image,axiom,
% 28.73/28.50 ! [V_f_2,T_c,V_r_2,T_b] :
% 28.73/28.50 ( c_Relation_Otrans(T_b,V_r_2)
% 28.73/28.50 => c_Relation_Otrans(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_trans__O__subset,axiom,
% 28.73/28.50 ! [V_r_2,T_b] :
% 28.73/28.50 ( c_Relation_Otrans(T_b,V_r_2)
% 28.73/28.50 => 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)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_SUPR__bool__eq,axiom,
% 28.73/28.50 ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_HOL_Obool) = c_Set_OBex(T_b) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_trans__Int,axiom,
% 28.73/28.50 ! [V_s_2,V_r_2,T_b] :
% 28.73/28.50 ( c_Relation_Otrans(T_b,V_r_2)
% 28.73/28.50 => ( c_Relation_Otrans(T_b,V_s_2)
% 28.73/28.50 => 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)) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_bex__UNIV,axiom,
% 28.73/28.50 ! [V_P_2,T_b] :
% 28.73/28.50 ( ? [B_x] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 28.73/28.50 & hBOOL(hAPP(V_P_2,B_x)) )
% 28.73/28.50 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_trans__rtrancl,axiom,
% 28.73/28.50 ! [V_r_2,T_b] : c_Relation_Otrans(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_lexord__transI,axiom,
% 28.73/28.50 ! [V_r_2,T_b] :
% 28.73/28.50 ( c_Relation_Otrans(T_b,V_r_2)
% 28.73/28.50 => c_Relation_Otrans(tc_List_Olist(T_b),c_List_Olexord(T_b,V_r_2)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_trans__finite__psubset,axiom,
% 28.73/28.50 ! [T_b] : c_Relation_Otrans(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_trans__Id__on,axiom,
% 28.73/28.50 ! [V_A_2,T_b] : c_Relation_Otrans(T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_trancl__id,axiom,
% 28.73/28.50 ! [V_r_2,T_b] :
% 28.73/28.50 ( c_Relation_Otrans(T_b,V_r_2)
% 28.73/28.50 => c_Transitive__Closure_Otrancl(T_b,V_r_2) = V_r_2 ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_trans__trancl,axiom,
% 28.73/28.50 ! [V_r_2,T_b] : c_Relation_Otrans(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_trans__Id,axiom,
% 28.73/28.50 ! [T_b] : c_Relation_Otrans(T_b,c_Relation_OId(T_b)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_trans__converse,axiom,
% 28.73/28.50 ! [V_r_2,T_b] :
% 28.73/28.50 ( c_Relation_Otrans(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 28.73/28.50 <=> c_Relation_Otrans(T_b,V_r_2) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_listrel__trans,axiom,
% 28.73/28.50 ! [V_r_2,T_b] :
% 28.73/28.50 ( c_Relation_Otrans(T_b,V_r_2)
% 28.73/28.50 => c_Relation_Otrans(tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_bex__empty,axiom,
% 28.73/28.50 ! [V_P_2,T_b] :
% 28.73/28.50 ~ ? [B_x] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 28.73/28.50 & hBOOL(hAPP(V_P_2,B_x)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_finite__Collect__bex,axiom,
% 28.73/28.50 ! [V_Q_2,T_c,V_A_2,T_b] :
% 28.73/28.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.73/28.50 => ( 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)))))
% 28.73/28.50 <=> ! [B_x] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.73/28.50 => 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)))) ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_trans__reflclI,axiom,
% 28.73/28.50 ! [V_r_2,T_b] :
% 28.73/28.50 ( c_Relation_Otrans(T_b,V_r_2)
% 28.73/28.50 => 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))) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_list__ex__iff__raw,axiom,
% 28.73/28.50 ! [V_xs_2,V_P_2,T_b] :
% 28.73/28.50 ( c_List_Olist__ex(T_b,V_P_2,V_xs_2)
% 28.73/28.50 <=> ? [B_x] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.73/28.50 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_Bex__set__list__ex,axiom,
% 28.73/28.50 ! [V_P_2,V_xs_2,T_b] :
% 28.73/28.50 ( ? [B_x] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.73/28.50 & hBOOL(hAPP(V_P_2,B_x)) )
% 28.73/28.50 <=> c_List_Olist__ex(T_b,V_P_2,V_xs_2) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_INT__eq,axiom,
% 28.73/28.50 ! [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))))) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_Sup__fun__def,axiom,
% 28.73/28.50 ! [V_x_2,V_A_2,T_c,T_b] :
% 28.73/28.50 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.73/28.50 => 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)))))) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_Sup__apply,axiom,
% 28.73/28.50 ! [V_x_2,V_A_2,T_c,T_b] :
% 28.73/28.50 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.73/28.50 => 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)))))) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_Inf__fun__def,axiom,
% 28.73/28.50 ! [V_x_2,V_A_2,T_c,T_b] :
% 28.73/28.50 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.73/28.50 => 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)))))) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_Inf__apply,axiom,
% 28.73/28.50 ! [V_x_2,V_A_2,T_c,T_b] :
% 28.73/28.50 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.73/28.50 => 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)))))) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_max__extp_Ointros,axiom,
% 28.73/28.50 ! [V_R_2,V_Y_2,V_X_2,T_b] :
% 28.73/28.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2))
% 28.73/28.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2))
% 28.73/28.50 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.73/28.50 => ( ! [B_x] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2))
% 28.73/28.50 => ? [B_xa] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2))
% 28.73/28.50 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) )
% 28.73/28.50 => c_Wellfounded_Omax__extp(T_b,V_R_2,V_X_2,V_Y_2) ) ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_transp__def,axiom,
% 28.73/28.50 ! [V_r_2,T_b] :
% 28.73/28.50 ( c_Predicate_Otransp(T_b,V_r_2)
% 28.73/28.50 <=> 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))) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_transpE,axiom,
% 28.73/28.50 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] :
% 28.73/28.50 ( c_Predicate_Otransp(T_b,V_r_2)
% 28.73/28.50 => ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
% 28.73/28.50 => ( hBOOL(hAPP(hAPP(V_r_2,V_y_2),V_z_2))
% 28.73/28.50 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_z_2)) ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_equivpE,axiom,
% 28.73/28.50 ! [V_R_2,T_b] :
% 28.73/28.50 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 28.73/28.50 => ~ ( c_Predicate_Oreflp(T_b,V_R_2)
% 28.73/28.50 => ( c_Predicate_Osymp(T_b,V_R_2)
% 28.73/28.50 => ~ c_Predicate_Otransp(T_b,V_R_2) ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_equivpI,axiom,
% 28.73/28.50 ! [V_R_2,T_b] :
% 28.73/28.50 ( c_Predicate_Oreflp(T_b,V_R_2)
% 28.73/28.50 => ( c_Predicate_Osymp(T_b,V_R_2)
% 28.73/28.50 => ( c_Predicate_Otransp(T_b,V_R_2)
% 28.73/28.50 => c_Equiv__Relations_Oequivp(T_b,V_R_2) ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_sympE,axiom,
% 28.73/28.50 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 28.73/28.50 ( c_Predicate_Osymp(T_b,V_r_2)
% 28.73/28.50 => ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
% 28.73/28.50 => hBOOL(hAPP(hAPP(V_r_2,V_y_2),V_x_2)) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_equivp__reflp__symp__transp,axiom,
% 28.73/28.50 ! [V_R_2,T_b] :
% 28.73/28.50 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 28.73/28.50 <=> ( c_Predicate_Oreflp(T_b,V_R_2)
% 28.73/28.50 & c_Predicate_Osymp(T_b,V_R_2)
% 28.73/28.50 & c_Predicate_Otransp(T_b,V_R_2) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_max__extp_Osimps,axiom,
% 28.73/28.50 ! [V_a2_2,V_a1_2,V_R_2,T_b] :
% 28.73/28.50 ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2)
% 28.73/28.50 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 28.73/28.50 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 28.73/28.50 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.73/28.50 & ! [B_x] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 28.73/28.50 => ? [B_xa] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 28.73/28.50 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_trans__diff__Id,axiom,
% 28.73/28.50 ! [V_r_2,T_b] :
% 28.73/28.50 ( c_Relation_Otrans(T_b,V_r_2)
% 28.73/28.50 => ( c_Relation_Oantisym(T_b,V_r_2)
% 28.73/28.50 => 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))) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_antisym__empty,axiom,
% 28.73/28.50 ! [T_b] : c_Relation_Oantisym(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_antisym__converse,axiom,
% 28.73/28.50 ! [V_r_2,T_b] :
% 28.73/28.50 ( c_Relation_Oantisym(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 28.73/28.50 <=> c_Relation_Oantisym(T_b,V_r_2) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_antisym__Id,axiom,
% 28.73/28.50 ! [T_b] : c_Relation_Oantisym(T_b,c_Relation_OId(T_b)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_antisym__Id__on,axiom,
% 28.73/28.50 ! [V_A_2,T_b] : c_Relation_Oantisym(T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_antisym__subset,axiom,
% 28.73/28.50 ! [V_s_2,V_r_2,T_b] :
% 28.73/28.50 ( 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))
% 28.73/28.50 => ( c_Relation_Oantisym(T_b,V_s_2)
% 28.73/28.50 => c_Relation_Oantisym(T_b,V_r_2) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_antisym__def,axiom,
% 28.73/28.50 ! [V_r_2,T_b] :
% 28.73/28.50 ( c_Relation_Oantisym(T_b,V_r_2)
% 28.73/28.50 <=> ! [B_x,B_y] :
% 28.73/28.50 ( 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))
% 28.73/28.50 => ( 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))
% 28.73/28.50 => B_x = B_y ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_antisymD,axiom,
% 28.73/28.50 ! [V_b_2,V_a_2,V_r_2,T_b] :
% 28.73/28.50 ( c_Relation_Oantisym(T_b,V_r_2)
% 28.73/28.50 => ( 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))
% 28.73/28.50 => ( 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))
% 28.73/28.50 => V_a_2 = V_b_2 ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_antisym__reflcl,axiom,
% 28.73/28.50 ! [V_r_2,T_b] :
% 28.73/28.50 ( 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)))
% 28.73/28.50 <=> c_Relation_Oantisym(T_b,V_r_2) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_acyclic__impl__antisym__rtrancl,axiom,
% 28.73/28.50 ! [V_r_2,T_b] :
% 28.73/28.50 ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 28.73/28.50 => c_Relation_Oantisym(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_fun__lub__def,axiom,
% 28.73/28.50 ! [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)))))) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_sym__trans__comp__subset,axiom,
% 28.73/28.50 ! [V_r_2,T_b] :
% 28.73/28.50 ( c_Relation_Osym(T_b,V_r_2)
% 28.73/28.50 => ( c_Relation_Otrans(T_b,V_r_2)
% 28.73/28.50 => 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)) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_symD,axiom,
% 28.73/28.50 ! [V_b_2,V_a_2,V_r_2,T_b] :
% 28.73/28.50 ( c_Relation_Osym(T_b,V_r_2)
% 28.73/28.50 => ( 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))
% 28.73/28.50 => 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)) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_sym__def,axiom,
% 28.73/28.50 ! [V_r_2,T_b] :
% 28.73/28.50 ( c_Relation_Osym(T_b,V_r_2)
% 28.73/28.50 <=> ! [B_x,B_y] :
% 28.73/28.50 ( 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))
% 28.73/28.50 => 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)) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_sym__inv__image,axiom,
% 28.73/28.50 ! [V_f_2,T_c,V_r_2,T_b] :
% 28.73/28.50 ( c_Relation_Osym(T_b,V_r_2)
% 28.73/28.50 => c_Relation_Osym(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_sym__Int__converse,axiom,
% 28.73/28.50 ! [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))) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_sym__Int,axiom,
% 28.73/28.50 ! [V_s_2,V_r_2,T_b] :
% 28.73/28.50 ( c_Relation_Osym(T_b,V_r_2)
% 28.73/28.50 => ( c_Relation_Osym(T_b,V_s_2)
% 28.73/28.50 => 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)) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_sym__rtrancl,axiom,
% 28.73/28.50 ! [V_r_2,T_b] :
% 28.73/28.50 ( c_Relation_Osym(T_b,V_r_2)
% 28.73/28.50 => c_Relation_Osym(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_sym__Id__on,axiom,
% 28.73/28.50 ! [V_A_2,T_b] : c_Relation_Osym(T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_sym__trancl,axiom,
% 28.73/28.50 ! [V_r_2,T_b] :
% 28.73/28.50 ( c_Relation_Osym(T_b,V_r_2)
% 28.73/28.50 => c_Relation_Osym(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_sym__Un,axiom,
% 28.73/28.50 ! [V_s_2,V_r_2,T_b] :
% 28.73/28.50 ( c_Relation_Osym(T_b,V_r_2)
% 28.73/28.50 => ( c_Relation_Osym(T_b,V_s_2)
% 28.73/28.50 => 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)) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_sym__Id,axiom,
% 28.73/28.50 ! [T_b] : c_Relation_Osym(T_b,c_Relation_OId(T_b)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_sym__conv__converse__eq,axiom,
% 28.73/28.50 ! [V_r_2,T_b] :
% 28.73/28.50 ( c_Relation_Osym(T_b,V_r_2)
% 28.73/28.50 <=> hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2) = V_r_2 ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_sym__converse,axiom,
% 28.73/28.50 ! [V_r_2,T_b] :
% 28.73/28.50 ( c_Relation_Osym(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 28.73/28.50 <=> c_Relation_Osym(T_b,V_r_2) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_listrel__sym,axiom,
% 28.73/28.50 ! [V_r_2,T_b] :
% 28.73/28.50 ( c_Relation_Osym(T_b,V_r_2)
% 28.73/28.50 => c_Relation_Osym(tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_sym__Un__converse,axiom,
% 28.73/28.50 ! [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))) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_equiv__def,axiom,
% 28.73/28.50 ! [V_r_2,V_A_2,T_b] :
% 28.73/28.50 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 28.73/28.50 <=> ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 28.73/28.50 & c_Relation_Osym(T_b,V_r_2)
% 28.73/28.50 & c_Relation_Otrans(T_b,V_r_2) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_equivI,axiom,
% 28.73/28.50 ! [V_r_2,V_A_2,T_b] :
% 28.73/28.50 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 28.73/28.50 => ( c_Relation_Osym(T_b,V_r_2)
% 28.73/28.50 => ( c_Relation_Otrans(T_b,V_r_2)
% 28.73/28.50 => c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_equivE,axiom,
% 28.73/28.50 ! [V_r_2,V_A_2,T_b] :
% 28.73/28.50 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 28.73/28.50 => ~ ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 28.73/28.50 => ( c_Relation_Osym(T_b,V_r_2)
% 28.73/28.50 => ~ c_Relation_Otrans(T_b,V_r_2) ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_symp__def,axiom,
% 28.73/28.50 ! [V_r_2,T_b] :
% 28.73/28.50 ( c_Predicate_Osymp(T_b,V_r_2)
% 28.73/28.50 <=> 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))) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_part__equivpI,axiom,
% 28.73/28.50 ! [T_b,V_R_2] :
% 28.73/28.50 ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 28.73/28.50 => ( c_Predicate_Osymp(T_b,V_R_2)
% 28.73/28.50 => ( c_Predicate_Otransp(T_b,V_R_2)
% 28.73/28.50 => c_Equiv__Relations_Opart__equivp(T_b,V_R_2) ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_part__equivp__refl__symp__transp,axiom,
% 28.73/28.50 ! [V_R_2,T_b] :
% 28.73/28.50 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 28.73/28.50 <=> ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 28.73/28.50 & c_Predicate_Osymp(T_b,V_R_2)
% 28.73/28.50 & c_Predicate_Otransp(T_b,V_R_2) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_part__equivp__transp,axiom,
% 28.73/28.50 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] :
% 28.73/28.50 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 28.73/28.50 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 28.73/28.50 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
% 28.73/28.50 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_part__equivp__symp,axiom,
% 28.73/28.50 ! [V_y_2,V_x_2,V_R_2,T_b] :
% 28.73/28.50 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 28.73/28.50 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 28.73/28.50 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_part__equivp__def,axiom,
% 28.73/28.50 ! [V_R_2,T_b] :
% 28.73/28.50 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 28.73/28.50 <=> ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 28.73/28.50 & ! [B_x,B_y] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
% 28.73/28.50 <=> ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 28.73/28.50 & hBOOL(hAPP(hAPP(V_R_2,B_y),B_y))
% 28.73/28.50 & hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_equivp__implies__part__equivp,axiom,
% 28.73/28.50 ! [V_R_2,T_b] :
% 28.73/28.50 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 28.73/28.50 => c_Equiv__Relations_Opart__equivp(T_b,V_R_2) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_part__equivpE,axiom,
% 28.73/28.50 ! [V_R_2,T_b] :
% 28.73/28.50 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 28.73/28.50 => ~ ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 28.73/28.50 => ( c_Predicate_Osymp(T_b,V_R_2)
% 28.73/28.50 => ~ c_Predicate_Otransp(T_b,V_R_2) ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_part__equivp__typedef,axiom,
% 28.73/28.50 ! [V_R_2,T_b] :
% 28.73/28.50 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 28.73/28.50 => ? [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))))) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_fold__image__UN__disjoint,axiom,
% 28.73/28.50 ! [V_g_2,V_A_2,T_c,V_I_2,T_b,T_d] :
% 28.73/28.50 ( class_Groups_Ocomm__monoid__mult(T_d)
% 28.73/28.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_I_2))
% 28.73/28.50 => ( ! [B_x] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 28.73/28.50 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x))) )
% 28.73/28.50 => ( ! [B_x] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 28.73/28.50 => ! [B_xa] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_I_2))
% 28.73/28.50 => ( B_x != B_xa
% 28.73/28.50 => 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)) ) ) )
% 28.73/28.50 => 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) ) ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_nat__of__cases,axiom,
% 28.73/28.50 ! [V_y_2] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 28.73/28.50 => ~ ! [B_x] : V_y_2 != hAPP(c_Code__Numeral_Onat__of,B_x) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_nat__of__induct,axiom,
% 28.73/28.50 ! [V_P_2,V_y_2] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 28.73/28.50 => ( ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Code__Numeral_Onat__of,B_x)))
% 28.73/28.50 => hBOOL(hAPP(V_P_2,V_y_2)) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_of__nat__cases,axiom,
% 28.73/28.50 ! [V_x_2] :
% 28.73/28.50 ~ ! [B_y] :
% 28.73/28.50 ( V_x_2 = hAPP(c_Code__Numeral_Oof__nat,B_y)
% 28.73/28.50 => ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_y),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_of__nat__induct,axiom,
% 28.73/28.50 ! [V_x_2,V_P_2] :
% 28.73/28.50 ( ! [B_y] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_y),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 28.73/28.50 => hBOOL(hAPP(V_P_2,hAPP(c_Code__Numeral_Oof__nat,B_y))) )
% 28.73/28.50 => hBOOL(hAPP(V_P_2,V_x_2)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_lazy__sequence_Orecs_I1_J,axiom,
% 28.73/28.50 ! [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 ).
% 28.73/28.50
% 28.73/28.50 fof(fact_lazy__sequence_Orecs_I2_J,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_Least__Suc2,axiom,
% 28.73/28.50 ! [V_m_2,V_Q_2,V_n_2,V_P_2] :
% 28.73/28.50 ( hBOOL(hAPP(V_P_2,V_n_2))
% 28.73/28.50 => ( hBOOL(hAPP(V_Q_2,V_m_2))
% 28.73/28.50 => ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 28.73/28.50 => ( ! [B_k] :
% 28.73/28.50 ( hBOOL(hAPP(V_P_2,hAPP(c_Nat_OSuc,B_k)))
% 28.73/28.50 <=> hBOOL(hAPP(V_Q_2,B_k)) )
% 28.73/28.50 => 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)) ) ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_beyond__def,axiom,
% 28.73/28.50 ! [V_l,V_k] :
% 28.73/28.50 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 28.73/28.50 => c_Quickcheck_Obeyond(V_k,V_l) = V_l )
% 28.73/28.50 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 28.73/28.50 => c_Quickcheck_Obeyond(V_k,V_l) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_beyond__zero,axiom,
% 28.73/28.50 ! [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) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_curry__def,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_refl__on__UNION,axiom,
% 28.73/28.50 ! [V_r_2,V_A_2,T_c,V_S_2,T_b] :
% 28.73/28.50 ( ! [B_x] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 28.73/28.50 => c_Relation_Orefl__on(T_c,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x)) )
% 28.73/28.50 => 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)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_curryI,axiom,
% 28.73/28.50 ! [V_b_2,V_a_2,T_c,T_b,V_f_2] :
% 28.73/28.50 ( hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))
% 28.73/28.50 => hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_curry__split,axiom,
% 28.73/28.50 ! [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 ).
% 28.73/28.50
% 28.73/28.50 fof(fact_split__curry,axiom,
% 28.73/28.50 ! [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 ).
% 28.73/28.50
% 28.73/28.50 fof(fact_curry__conv,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_curryD,axiom,
% 28.73/28.50 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2))
% 28.73/28.50 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_curryE,axiom,
% 28.73/28.50 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2))
% 28.73/28.50 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_bex__reg__eqv,axiom,
% 28.73/28.50 ! [V_P_2,V_R_2,T_b] :
% 28.73/28.50 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 28.73/28.50 => ( ? [B_x] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Quotient_ORespects(T_b,V_R_2)))
% 28.73/28.50 & hBOOL(hAPP(V_P_2,B_x)) )
% 28.73/28.50 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_wf__weak__decr__stable,axiom,
% 28.73/28.50 ! [V_r_2,V_f_2,T_b] :
% 28.73/28.50 ( ! [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)))
% 28.73/28.50 => ( c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2))
% 28.73/28.50 => ? [B_i] :
% 28.73/28.50 ! [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) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_in__respects,axiom,
% 28.73/28.50 ! [V_R_2,V_x_2,T_b] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Quotient_ORespects(T_b,V_R_2)))
% 28.73/28.50 <=> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_Respects__def,axiom,
% 28.73/28.50 ! [V_x_2,V_R_2,T_b] :
% 28.73/28.50 ( hBOOL(hAPP(c_Quotient_ORespects(T_b,V_R_2),V_x_2))
% 28.73/28.50 <=> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_bex__reg__right,axiom,
% 28.73/28.50 ! [V_P_2,V_Q_2,V_R_2,T_b] :
% 28.73/28.50 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 28.73/28.50 => ( ! [B_x] :
% 28.73/28.50 ( hBOOL(hAPP(V_Q_2,B_x))
% 28.73/28.50 => hBOOL(hAPP(V_P_2,B_x)) )
% 28.73/28.50 => ( ? [B_x1] : hBOOL(hAPP(V_Q_2,B_x1))
% 28.73/28.50 => ? [B_x] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Quotient_ORespects(T_b,V_R_2)))
% 28.73/28.50 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_babs__reg__eqv,axiom,
% 28.73/28.50 ! [V_P_2,T_c,V_R_2,T_b] :
% 28.73/28.50 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 28.73/28.50 => c_Quotient_OBabs(T_b,T_c,c_Quotient_ORespects(T_b,V_R_2),V_P_2) = V_P_2 ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_Babs__def,axiom,
% 28.73/28.50 ! [V_m_2,T_c,V_p_2,V_x_2,T_b] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_p_2))
% 28.73/28.50 => hAPP(c_Quotient_OBabs(T_b,T_c,V_p_2,V_m_2),V_x_2) = hAPP(V_m_2,V_x_2) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_converse__rtranclE2,axiom,
% 28.73/28.50 ! [V_r_2,V_zb_2,V_za_2,V_xb_2,V_xa_2,T_c,T_b] :
% 28.73/28.50 ( 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)))
% 28.73/28.50 => ( 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)
% 28.73/28.50 => ~ ! [B_a,B_b] :
% 28.73/28.50 ( 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))
% 28.73/28.50 => ~ 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))) ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_converse__rtrancl__induct2,axiom,
% 28.73/28.50 ! [V_P_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_c,T_b] :
% 28.73/28.50 ( 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)))
% 28.73/28.50 => ( hBOOL(hAPP(hAPP(V_P_2,V_bx_2),V_by_2))
% 28.73/28.50 => ( ! [B_a,B_b,B_aa,B_ba] :
% 28.73/28.50 ( 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))
% 28.73/28.50 => ( 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)))
% 28.73/28.50 => ( hBOOL(hAPP(hAPP(V_P_2,B_aa),B_ba))
% 28.73/28.50 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) ) )
% 28.73/28.50 => hBOOL(hAPP(hAPP(V_P_2,V_ax_2),V_ay_2)) ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_rtrancl__induct2,axiom,
% 28.73/28.50 ! [V_P_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_c,T_b] :
% 28.73/28.50 ( 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)))
% 28.73/28.50 => ( hBOOL(hAPP(hAPP(V_P_2,V_ax_2),V_ay_2))
% 28.73/28.50 => ( ! [B_a,B_b] :
% 28.73/28.50 ( 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)))
% 28.73/28.50 => ! [B_aa,B_ba] :
% 28.73/28.50 ( 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))
% 28.73/28.50 => ( hBOOL(hAPP(hAPP(V_P_2,B_a),B_b))
% 28.73/28.50 => hBOOL(hAPP(hAPP(V_P_2,B_aa),B_ba)) ) ) )
% 28.73/28.50 => hBOOL(hAPP(hAPP(V_P_2,V_bx_2),V_by_2)) ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_congruent2I_H,axiom,
% 28.73/28.50 ! [T_d,V_f_2,V_r2_2,T_c,V_r1_2,T_b] :
% 28.73/28.50 ( ! [B_y1,B_z1] :
% 28.73/28.50 ( 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))
% 28.73/28.50 => ! [B_y2,B_z2] :
% 28.73/28.50 ( 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))
% 28.73/28.50 => hAPP(hAPP(V_f_2,B_y1),B_y2) = hAPP(hAPP(V_f_2,B_z1),B_z2) ) )
% 28.73/28.50 => c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_congruentI,axiom,
% 28.73/28.50 ! [T_c,V_f_2,V_r_2,T_b] :
% 28.73/28.50 ( ! [B_y,B_z] :
% 28.73/28.50 ( 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))
% 28.73/28.50 => hAPP(V_f_2,B_y) = hAPP(V_f_2,B_z) )
% 28.73/28.50 => c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact__03,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact__04,axiom,
% 28.73/28.50 ! [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) ).
% 28.73/28.50
% 28.73/28.50 fof(fact__05,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_all__interval__nat__def,axiom,
% 28.73/28.50 ! [V_j_2,V_i_2,V_P_2] :
% 28.73/28.50 ( c_List_Oall__interval__nat(V_P_2,V_i_2,V_j_2)
% 28.73/28.50 <=> ! [B_x] :
% 28.73/28.50 ( 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)))
% 28.73/28.50 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact__06,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact__07,axiom,
% 28.73/28.50 ! [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) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_list__all__iff__all__interval__nat,axiom,
% 28.73/28.50 ! [V_j_2,V_i_2,V_P_2] :
% 28.73/28.50 ( c_List_Olist__all(tc_Nat_Onat,V_P_2,c_List_Oupt(V_i_2,V_j_2))
% 28.73/28.50 <=> c_List_Oall__interval__nat(V_P_2,V_i_2,V_j_2) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_list__ex__iff__not__all__inverval__nat,axiom,
% 28.73/28.50 ! [V_j_2,V_i_2,V_P_2] :
% 28.73/28.50 ( c_List_Olist__ex(tc_Nat_Onat,V_P_2,c_List_Oupt(V_i_2,V_j_2))
% 28.73/28.50 <=> ~ 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) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_New__DSequence_Opos__map__def,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_folding__image_Ocong,axiom,
% 28.73/28.50 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 28.73/28.50 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 28.73/28.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 28.73/28.50 => ( ! [B_x] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 28.73/28.50 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) )
% 28.73/28.50 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(V_F_2,V_h_2),V_A_2) ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_power__dvd__imp__le,axiom,
% 28.73/28.50 ! [V_n,V_m,V_i] :
% 28.73/28.50 ( 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)))
% 28.73/28.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_i))
% 28.73/28.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_finite__nonempty__imp__fold1Set,axiom,
% 28.73/28.50 ! [V_f_2,V_A_2,T_b] :
% 28.73/28.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.73/28.50 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.73/28.50 => ? [B_x1] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2),B_x1)) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_dvd_Oorder__refl,axiom,
% 28.73/28.50 ! [V_x] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_x)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_dvd__0__right,axiom,
% 28.73/28.50 ! [V_a,T_a] :
% 28.73/28.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.73/28.50 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_dvd__1__left,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_unity__coeff__ex,axiom,
% 28.73/28.50 ! [V_l_2,V_P_2,T_b] :
% 28.73/28.50 ( ( class_Rings_Odvd(T_b)
% 28.73/28.50 & class_Rings_Osemiring__0(T_b) )
% 28.73/28.50 => ( ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_l_2),B_x)))
% 28.73/28.50 <=> ? [B_x] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_l_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),c_Groups_Ozero__class_Ozero(T_b))))
% 28.73/28.50 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_dvd__mult__div__cancel,axiom,
% 28.73/28.50 ! [V_b,V_a,T_a] :
% 28.73/28.50 ( class_Divides_Osemiring__div(T_a)
% 28.73/28.50 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 28.73/28.50 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_a)) = V_b ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_div__mult__swap,axiom,
% 28.73/28.50 ! [V_a,V_b,V_c,T_a] :
% 28.73/28.50 ( class_Divides_Osemiring__div(T_a)
% 28.73/28.50 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b))
% 28.73/28.50 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_dvd__div__mult__self,axiom,
% 28.73/28.50 ! [V_b,V_a,T_a] :
% 28.73/28.50 ( class_Divides_Osemiring__div(T_a)
% 28.73/28.50 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 28.73/28.50 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_a)),V_a) = V_b ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_dvd__div__mult,axiom,
% 28.73/28.50 ! [V_c,V_b,V_a,T_a] :
% 28.73/28.50 ( class_Divides_Osemiring__div(T_a)
% 28.73/28.50 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 28.73/28.50 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_a)),V_c) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_a) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_div__mult__div__if__dvd,axiom,
% 28.73/28.50 ! [V_w,V_z,V_x,V_y,T_a] :
% 28.73/28.50 ( class_Divides_Osemiring__div(T_a)
% 28.73/28.50 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 28.73/28.50 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_w))
% 28.73/28.50 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_w),V_z)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)) ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_dvd__mult__cancel__left,axiom,
% 28.73/28.50 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 28.73/28.50 ( class_Rings_Oidom(T_b)
% 28.73/28.50 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
% 28.73/28.50 <=> ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 28.73/28.50 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_dvd__mult__cancel__right,axiom,
% 28.73/28.50 ! [V_b_2,V_c_2,V_a_2,T_b] :
% 28.73/28.50 ( class_Rings_Oidom(T_b)
% 28.73/28.50 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2)))
% 28.73/28.50 <=> ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 28.73/28.50 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_dvd__mult__right,axiom,
% 28.73/28.50 ! [V_c,V_b,V_a,T_a] :
% 28.73/28.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.73/28.50 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c))
% 28.73/28.50 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c)) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_dvd__mult__left,axiom,
% 28.73/28.50 ! [V_c,V_b,V_a,T_a] :
% 28.73/28.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.73/28.50 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c))
% 28.73/28.50 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_dvdI,axiom,
% 28.73/28.50 ! [V_k,V_b,V_a,T_a] :
% 28.73/28.50 ( class_Rings_Odvd(T_a)
% 28.73/28.50 => ( V_a = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_k)
% 28.73/28.50 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_a)) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_mult__dvd__mono,axiom,
% 28.73/28.50 ! [V_d,V_c,V_b,V_a,T_a] :
% 28.73/28.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.73/28.50 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 28.73/28.50 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_d))
% 28.73/28.50 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_dvd__mult,axiom,
% 28.73/28.50 ! [V_b,V_c,V_a,T_a] :
% 28.73/28.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.73/28.50 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))
% 28.73/28.50 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_dvd__mult2,axiom,
% 28.73/28.50 ! [V_c,V_b,V_a,T_a] :
% 28.73/28.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.73/28.50 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 28.73/28.50 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_dvd__triv__right,axiom,
% 28.73/28.50 ! [V_b,V_a,T_a] :
% 28.73/28.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.73/28.50 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_dvd__triv__left,axiom,
% 28.73/28.50 ! [V_b,V_a,T_a] :
% 28.73/28.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.73/28.50 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_nat__mult__dvd__cancel__disj,axiom,
% 28.73/28.50 ! [V_n_2,V_m_2,V_k_2] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
% 28.73/28.50 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.73/28.50 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_inf__period_I3_J,axiom,
% 28.73/28.50 ! [V_t_2,V_D_2,V_d_2,T_b] :
% 28.73/28.50 ( ( class_Rings_Ocomm__ring(T_b)
% 28.73/28.50 & class_Rings_Odvd(T_b) )
% 28.73/28.50 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))
% 28.73/28.50 => ! [B_x,B_k] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2)))
% 28.73/28.50 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2))),V_t_2))) ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_inf__period_I4_J,axiom,
% 28.73/28.50 ! [V_t_2,V_D_2,V_d_2,T_b] :
% 28.73/28.50 ( ( class_Rings_Ocomm__ring(T_b)
% 28.73/28.50 & class_Rings_Odvd(T_b) )
% 28.73/28.50 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))
% 28.73/28.50 => ! [B_x,B_k] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2)))
% 28.73/28.50 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2))),V_t_2))) ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_dvd__div__div__eq__mult,axiom,
% 28.73/28.50 ! [V_d_2,V_b_2,V_c_2,V_a_2,T_b] :
% 28.73/28.50 ( class_Divides_Osemiring__div(T_b)
% 28.73/28.50 => ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
% 28.73/28.50 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 28.73/28.50 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 28.73/28.50 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_c_2),V_d_2))
% 28.73/28.50 => ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_d_2),V_c_2)
% 28.73/28.50 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2) ) ) ) ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_dvd__div__eq__mult,axiom,
% 28.73/28.50 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 28.73/28.50 ( class_Divides_Osemiring__div(T_b)
% 28.73/28.50 => ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
% 28.73/28.50 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 28.73/28.50 => ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2) = V_c_2
% 28.73/28.50 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2) ) ) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_dvd_OatLeastAtMost__singleton__iff,axiom,
% 28.73/28.50 ! [V_c_2,V_b_2,V_a_2] :
% 28.73/28.50 ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
% 28.73/28.50 <=> ( V_a_2 = V_b_2
% 28.73/28.50 & V_b_2 = V_c_2 ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_dvd_OatLeastAtMost__singleton,axiom,
% 28.73/28.50 ! [V_a_2] : c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_a_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_dvd_OatLeastAtMost__singleton_H,axiom,
% 28.73/28.50 ! [V_b_2,V_a_2] :
% 28.73/28.50 ( V_a_2 = V_b_2
% 28.73/28.50 => c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_dvd_OgreaterThanAtMost__empty,axiom,
% 28.73/28.50 ! [V_k_2,V_l_2] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
% 28.73/28.50 => c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_dvd_OatLeastLessThan__empty,axiom,
% 28.73/28.50 ! [V_a_2,V_b_2] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2))
% 28.73/28.50 => c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_dvd_OgreaterThanLessThan__empty,axiom,
% 28.73/28.50 ! [V_k_2,V_l_2] :
% 28.73/28.50 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
% 28.73/28.50 => c_SetInterval_Oord_OgreaterThanLessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_dvd_OgreaterThanAtMost__empty__iff,axiom,
% 28.73/28.50 ! [V_l_2,V_k_2] :
% 28.73/28.50 ( c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
% 28.73/28.50 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2))
% 28.73/28.50 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_dvd_OatLeastLessThan__empty__iff,axiom,
% 28.73/28.50 ! [V_b_2,V_a_2] :
% 28.73/28.50 ( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
% 28.73/28.50 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
% 28.73/28.50 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2)) ) ) ).
% 28.73/28.50
% 28.73/28.50 fof(fact_dvd_OgreaterThanAtMost__empty__iff2,axiom,
% 28.73/28.50 ! [V_l_2,V_k_2] :
% 28.73/28.50 ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2)
% 28.73/28.50 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2))
% 28.73/28.50 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) ) ) ).
% 28.73/28.50
% 28.73/28.50 %----Arity declarations (220)
% 28.73/28.50 fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom,
% 28.73/28.50 class_Lattices_Obounded__lattice(tc_HOL_Obool) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_fun__Lattices_Obounded__lattice,axiom,
% 28.73/28.50 ! [T_2,T_1] :
% 28.73/28.50 ( class_Lattices_Obounded__lattice(T_1)
% 28.73/28.50 => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom,
% 28.73/28.50 ! [T_2,T_1] :
% 28.73/28.50 ( class_Complete__Lattice_Ocomplete__lattice(T_1)
% 28.73/28.50 => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_fun__Lattices_Obounded__lattice__top,axiom,
% 28.73/28.50 ! [T_2,T_1] :
% 28.73/28.50 ( class_Lattices_Obounded__lattice(T_1)
% 28.73/28.50 => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_fun__Lattices_Obounded__lattice__bot,axiom,
% 28.73/28.50 ! [T_2,T_1] :
% 28.73/28.50 ( class_Lattices_Obounded__lattice(T_1)
% 28.73/28.50 => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_fun__Lattices_Osemilattice__sup,axiom,
% 28.73/28.50 ! [T_2,T_1] :
% 28.73/28.50 ( class_Lattices_Olattice(T_1)
% 28.73/28.50 => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_fun__Lattices_Osemilattice__inf,axiom,
% 28.73/28.50 ! [T_2,T_1] :
% 28.73/28.50 ( class_Lattices_Olattice(T_1)
% 28.73/28.50 => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_fun__Lattices_Odistrib__lattice,axiom,
% 28.73/28.50 ! [T_2,T_1] :
% 28.73/28.50 ( class_Lattices_Odistrib__lattice(T_1)
% 28.73/28.50 => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_fun__Lattices_Oboolean__algebra,axiom,
% 28.73/28.50 ! [T_2,T_1] :
% 28.73/28.50 ( class_Lattices_Oboolean__algebra(T_1)
% 28.73/28.50 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_fun__Orderings_Opreorder,axiom,
% 28.73/28.50 ! [T_2,T_1] :
% 28.73/28.50 ( class_Orderings_Opreorder(T_1)
% 28.73/28.50 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_fun__Finite__Set_Ofinite,axiom,
% 28.73/28.50 ! [T_1,T_2] :
% 28.73/28.50 ( ( class_Finite__Set_Ofinite(T_2)
% 28.73/28.50 & class_Finite__Set_Ofinite(T_1) )
% 28.73/28.50 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_fun__Lattices_Olattice,axiom,
% 28.73/28.50 ! [T_2,T_1] :
% 28.73/28.50 ( class_Lattices_Olattice(T_1)
% 28.73/28.50 => class_Lattices_Olattice(tc_fun(T_2,T_1)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_fun__Orderings_Oorder,axiom,
% 28.73/28.50 ! [T_2,T_1] :
% 28.73/28.50 ( class_Orderings_Oorder(T_1)
% 28.73/28.50 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_fun__Orderings_Otop,axiom,
% 28.73/28.50 ! [T_2,T_1] :
% 28.73/28.50 ( class_Orderings_Otop(T_1)
% 28.73/28.50 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_fun__Orderings_Oord,axiom,
% 28.73/28.50 ! [T_2,T_1] :
% 28.73/28.50 ( class_Orderings_Oord(T_1)
% 28.73/28.50 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_fun__Orderings_Obot,axiom,
% 28.73/28.50 ! [T_2,T_1] :
% 28.73/28.50 ( class_Orderings_Obot(T_1)
% 28.73/28.50 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_fun__Groups_Ouminus,axiom,
% 28.73/28.50 ! [T_2,T_1] :
% 28.73/28.50 ( class_Groups_Ouminus(T_1)
% 28.73/28.50 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_fun__Groups_Ominus,axiom,
% 28.73/28.50 ! [T_2,T_1] :
% 28.73/28.50 ( class_Groups_Ominus(T_1)
% 28.73/28.50 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_fun__Enum_Oenum,axiom,
% 28.73/28.50 ! [T_1,T_2] :
% 28.73/28.50 ( ( class_Enum_Oenum(T_2)
% 28.73/28.50 & class_Enum_Oenum(T_1) )
% 28.73/28.50 => class_Enum_Oenum(tc_fun(T_2,T_1)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 28.73/28.50 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 28.73/28.50 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 28.73/28.50 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
% 28.73/28.50 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
% 28.73/28.50 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom,
% 28.73/28.50 class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
% 28.73/28.50 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
% 28.73/28.50 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
% 28.73/28.50 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
% 28.73/28.50 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
% 28.73/28.50 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
% 28.73/28.50 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
% 28.73/28.50 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
% 28.73/28.50 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
% 28.73/28.50 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
% 28.73/28.50 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
% 28.73/28.50 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
% 28.73/28.50 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
% 28.73/28.50 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
% 28.73/28.50 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
% 28.73/28.50 class_Rings_Olinordered__semiring(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
% 28.73/28.50 class_Rings_Olinordered__semidom(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Lazy__Sequence_Osmall__lazy,axiom,
% 28.73/28.50 class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom,
% 28.73/28.50 class_Lattices_Osemilattice__sup(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom,
% 28.73/28.50 class_Lattices_Osemilattice__inf(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom,
% 28.73/28.50 class_Lattices_Odistrib__lattice(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
% 28.73/28.50 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
% 28.73/28.50 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
% 28.73/28.50 class_Groups_Oab__semigroup__add(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
% 28.73/28.50 class_Rings_Oordered__semiring(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
% 28.73/28.50 class_Rings_Oordered__ring__abs(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
% 28.73/28.50 class_Rings_Ono__zero__divisors(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
% 28.73/28.50 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
% 28.73/28.50 class_Rings_Olinordered__ring(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
% 28.73/28.50 class_Rings_Olinordered__idom(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
% 28.73/28.50 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Groups_Osemigroup__add,axiom,
% 28.73/28.50 class_Groups_Osemigroup__add(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
% 28.73/28.50 class_Divides_Osemiring__div(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
% 28.73/28.50 class_Rings_Ocomm__semiring(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom,
% 28.73/28.50 class_Nat_Osemiring__char__0(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
% 28.73/28.50 class_Groups_Oab__group__add(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
% 28.73/28.50 class_Rings_Ozero__neq__one(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
% 28.73/28.50 class_Rings_Oordered__ring(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Orderings_Opreorder,axiom,
% 28.73/28.50 class_Orderings_Opreorder(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Orderings_Olinorder,axiom,
% 28.73/28.50 class_Orderings_Olinorder(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
% 28.73/28.50 class_Groups_Omonoid__mult(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
% 28.73/28.50 class_Rings_Ocomm__ring__1(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
% 28.73/28.50 class_Groups_Omonoid__add(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Rings_Osemiring__1,axiom,
% 28.73/28.50 class_Rings_Osemiring__1(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
% 28.73/28.50 class_Rings_Osemiring__0(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Lattices_Olattice,axiom,
% 28.73/28.50 class_Lattices_Olattice(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
% 28.73/28.50 class_Groups_Ogroup__add(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Divides_Oring__div,axiom,
% 28.73/28.50 class_Divides_Oring__div(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Rings_Omult__zero,axiom,
% 28.73/28.50 class_Rings_Omult__zero(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Rings_Ocomm__ring,axiom,
% 28.73/28.50 class_Rings_Ocomm__ring(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Orderings_Oorder,axiom,
% 28.73/28.50 class_Orderings_Oorder(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Int_Oring__char__0,axiom,
% 28.73/28.50 class_Int_Oring__char__0(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Int_Onumber__ring,axiom,
% 28.73/28.50 class_Int_Onumber__ring(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Rings_Osemiring,axiom,
% 28.73/28.50 class_Rings_Osemiring(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Orderings_Oord,axiom,
% 28.73/28.50 class_Orderings_Oord(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Groups_Ouminus,axiom,
% 28.73/28.50 class_Groups_Ouminus(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Groups_Osgn__if,axiom,
% 28.73/28.50 class_Groups_Osgn__if(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Groups_Oabs__if,axiom,
% 28.73/28.50 class_Groups_Oabs__if(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Rings_Oring__1,axiom,
% 28.73/28.50 class_Rings_Oring__1(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Groups_Ominus,axiom,
% 28.73/28.50 class_Groups_Ominus(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Power_Opower,axiom,
% 28.73/28.50 class_Power_Opower(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Groups_Ozero,axiom,
% 28.73/28.50 class_Groups_Ozero(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Rings_Oring,axiom,
% 28.73/28.50 class_Rings_Oring(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Rings_Oidom,axiom,
% 28.73/28.50 class_Rings_Oidom(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Int_Onumber,axiom,
% 28.73/28.50 class_Int_Onumber(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Groups_Oone,axiom,
% 28.73/28.50 class_Groups_Oone(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Int__Oint__Rings_Odvd,axiom,
% 28.73/28.50 class_Rings_Odvd(tc_Int_Oint) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 28.73/28.50 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 28.73/28.50 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 28.73/28.50 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
% 28.73/28.50 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom,
% 28.73/28.50 class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
% 28.73/28.50 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
% 28.73/28.50 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
% 28.73/28.50 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
% 28.73/28.50 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
% 28.73/28.50 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
% 28.73/28.50 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
% 28.73/28.50 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
% 28.73/28.50 class_Rings_Olinordered__semiring(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
% 28.73/28.50 class_Rings_Olinordered__semidom(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom,
% 28.73/28.50 class_Lattices_Osemilattice__sup(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom,
% 28.73/28.50 class_Lattices_Osemilattice__inf(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom,
% 28.73/28.50 class_Lattices_Odistrib__lattice(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
% 28.73/28.50 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
% 28.73/28.50 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
% 28.73/28.50 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
% 28.73/28.50 class_Rings_Oordered__semiring(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
% 28.73/28.50 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
% 28.73/28.50 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
% 28.73/28.50 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom,
% 28.73/28.50 class_Groups_Osemigroup__add(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
% 28.73/28.50 class_Divides_Osemiring__div(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
% 28.73/28.50 class_Rings_Ocomm__semiring(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Orderings_Owellorder,axiom,
% 28.73/28.50 class_Orderings_Owellorder(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom,
% 28.73/28.50 class_Nat_Osemiring__char__0(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
% 28.73/28.50 class_Rings_Ozero__neq__one(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
% 28.73/28.50 class_Orderings_Opreorder(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
% 28.73/28.50 class_Orderings_Olinorder(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
% 28.73/28.50 class_Groups_Omonoid__mult(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
% 28.73/28.50 class_Groups_Omonoid__add(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom,
% 28.73/28.50 class_Rings_Osemiring__1(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
% 28.73/28.50 class_Rings_Osemiring__0(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Lattices_Olattice,axiom,
% 28.73/28.50 class_Lattices_Olattice(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
% 28.73/28.50 class_Rings_Omult__zero(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Orderings_Oorder,axiom,
% 28.73/28.50 class_Orderings_Oorder(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Rings_Osemiring,axiom,
% 28.73/28.50 class_Rings_Osemiring(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Orderings_Oord,axiom,
% 28.73/28.50 class_Orderings_Oord(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Orderings_Obot,axiom,
% 28.73/28.50 class_Orderings_Obot(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Groups_Ominus,axiom,
% 28.73/28.50 class_Groups_Ominus(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Power_Opower,axiom,
% 28.73/28.50 class_Power_Opower(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Groups_Ozero,axiom,
% 28.73/28.50 class_Groups_Ozero(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Int_Onumber,axiom,
% 28.73/28.50 class_Int_Onumber(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Groups_Oone,axiom,
% 28.73/28.50 class_Groups_Oone(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Rings_Odvd,axiom,
% 28.73/28.50 class_Rings_Odvd(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nat__Onat__Nat_Osize,axiom,
% 28.73/28.50 class_Nat_Osize(tc_Nat_Onat) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom,
% 28.73/28.50 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom,
% 28.73/28.50 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom,
% 28.73/28.50 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom,
% 28.73/28.50 class_Lattices_Osemilattice__sup(tc_HOL_Obool) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom,
% 28.73/28.50 class_Lattices_Osemilattice__inf(tc_HOL_Obool) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom,
% 28.73/28.50 class_Lattices_Odistrib__lattice(tc_HOL_Obool) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
% 28.73/28.50 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
% 28.73/28.50 class_Orderings_Opreorder(tc_HOL_Obool) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom,
% 28.73/28.50 class_Finite__Set_Ofinite(tc_HOL_Obool) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_HOL__Obool__Lattices_Olattice,axiom,
% 28.73/28.50 class_Lattices_Olattice(tc_HOL_Obool) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_HOL__Obool__Orderings_Oorder,axiom,
% 28.73/28.50 class_Orderings_Oorder(tc_HOL_Obool) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_HOL__Obool__Orderings_Otop,axiom,
% 28.73/28.50 class_Orderings_Otop(tc_HOL_Obool) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_HOL__Obool__Orderings_Oord,axiom,
% 28.73/28.50 class_Orderings_Oord(tc_HOL_Obool) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_HOL__Obool__Orderings_Obot,axiom,
% 28.73/28.50 class_Orderings_Obot(tc_HOL_Obool) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_HOL__Obool__Groups_Ouminus,axiom,
% 28.73/28.50 class_Groups_Ouminus(tc_HOL_Obool) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_HOL__Obool__Groups_Ominus,axiom,
% 28.73/28.50 class_Groups_Ominus(tc_HOL_Obool) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_HOL__Obool__Enum_Oenum,axiom,
% 28.73/28.50 class_Enum_Oenum(tc_HOL_Obool) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_HOL__Obool__Nat_Osize,axiom,
% 28.73/28.50 class_Nat_Osize(tc_HOL_Obool) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_List__Olist__Lazy__Sequence_Osmall__lazy,axiom,
% 28.73/28.50 ! [T_1] :
% 28.73/28.50 ( class_Lazy__Sequence_Osmall__lazy(T_1)
% 28.73/28.50 => class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(T_1)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_List__Olist__Nat_Osize,axiom,
% 28.73/28.50 ! [T_1] : class_Nat_Osize(tc_List_Olist(T_1)) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_sum__Finite__Set_Ofinite,axiom,
% 28.73/28.50 ! [T_1,T_2] :
% 28.73/28.50 ( ( class_Finite__Set_Ofinite(T_2)
% 28.73/28.50 & class_Finite__Set_Ofinite(T_1) )
% 28.73/28.50 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_sum__Enum_Oenum,axiom,
% 28.73/28.50 ! [T_1,T_2] :
% 28.73/28.50 ( ( class_Enum_Oenum(T_2)
% 28.73/28.50 & class_Enum_Oenum(T_1) )
% 28.73/28.50 => class_Enum_Oenum(tc_sum(T_2,T_1)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_sum__Nat_Osize,axiom,
% 28.73/28.50 ! [T_1,T_2] : class_Nat_Osize(tc_sum(T_2,T_1)) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom,
% 28.73/28.50 ! [T_1] :
% 28.73/28.50 ( class_Finite__Set_Ofinite(T_1)
% 28.73/28.50 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Option__Ooption__Enum_Oenum,axiom,
% 28.73/28.50 ! [T_1] :
% 28.73/28.50 ( class_Enum_Oenum(T_1)
% 28.73/28.50 => class_Enum_Oenum(tc_Option_Ooption(T_1)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Option__Ooption__Nat_Osize,axiom,
% 28.73/28.50 ! [T_1] : class_Nat_Osize(tc_Option_Ooption(T_1)) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Nitpick__Opair____box__Nat_Osize,axiom,
% 28.73/28.50 ! [T_1,T_2] : class_Nat_Osize(tc_Nitpick_Opair__box(T_2,T_1)) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_prod__Lazy__Sequence_Osmall__lazy,axiom,
% 28.73/28.50 ! [T_1,T_2] :
% 28.73/28.50 ( ( class_Lazy__Sequence_Osmall__lazy(T_2)
% 28.73/28.50 & class_Lazy__Sequence_Osmall__lazy(T_1) )
% 28.73/28.50 => class_Lazy__Sequence_Osmall__lazy(tc_prod(T_2,T_1)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_prod__Finite__Set_Ofinite,axiom,
% 28.73/28.50 ! [T_1,T_2] :
% 28.73/28.50 ( ( class_Finite__Set_Ofinite(T_2)
% 28.73/28.50 & class_Finite__Set_Ofinite(T_1) )
% 28.73/28.50 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_prod__Enum_Oenum,axiom,
% 28.73/28.50 ! [T_1,T_2] :
% 28.73/28.50 ( ( class_Enum_Oenum(T_2)
% 28.73/28.50 & class_Enum_Oenum(T_1) )
% 28.73/28.50 => class_Enum_Oenum(tc_prod(T_2,T_1)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_prod__Nat_Osize,axiom,
% 28.73/28.50 ! [T_1,T_2] : class_Nat_Osize(tc_prod(T_2,T_1)) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy,axiom,
% 28.73/28.50 class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom,
% 28.73/28.50 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Product____Type__Ounit__Enum_Oenum,axiom,
% 28.73/28.50 class_Enum_Oenum(tc_Product__Type_Ounit) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Product____Type__Ounit__Nat_Osize,axiom,
% 28.73/28.50 class_Nat_Osize(tc_Product__Type_Ounit) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Code____Evaluation__Oterm__Nat_Osize,axiom,
% 28.73/28.50 class_Nat_Osize(tc_Code__Evaluation_Oterm) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Hoare____Mirabelle__Otriple__Nat_Osize,axiom,
% 28.73/28.50 ! [T_1] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(T_1)) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 28.73/28.50 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 28.73/28.50 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom,
% 28.73/28.50 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom,
% 28.73/28.50 class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom,
% 28.73/28.50 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom,
% 28.73/28.50 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom,
% 28.73/28.50 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom,
% 28.73/28.50 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom,
% 28.73/28.50 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom,
% 28.73/28.50 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom,
% 28.73/28.50 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom,
% 28.73/28.50 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom,
% 28.73/28.50 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom,
% 28.73/28.50 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom,
% 28.73/28.50 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom,
% 28.73/28.50 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom,
% 28.73/28.50 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom,
% 28.73/28.50 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom,
% 28.73/28.50 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom,
% 28.73/28.50 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom,
% 28.73/28.50 class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom,
% 28.73/28.50 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom,
% 28.73/28.50 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom,
% 28.73/28.50 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom,
% 28.73/28.50 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom,
% 28.73/28.50 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom,
% 28.73/28.50 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom,
% 28.73/28.50 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom,
% 28.73/28.50 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom,
% 28.73/28.50 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom,
% 28.73/28.50 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom,
% 28.73/28.50 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom,
% 28.73/28.50 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom,
% 28.73/28.50 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom,
% 28.73/28.50 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom,
% 28.73/28.50 class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom,
% 28.73/28.50 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom,
% 28.73/28.50 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom,
% 28.73/28.50 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom,
% 28.73/28.50 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Code____Numeral__Ocode____numeral__Rings_Odvd,axiom,
% 28.73/28.50 class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osize,axiom,
% 28.73/28.50 class_Nat_Osize(tc_Code__Numeral_Ocode__numeral) ).
% 28.73/28.50
% 28.73/28.50 fof(arity_Lazy____Sequence__Olazy____sequence__Nat_Osize,axiom,
% 28.73/28.50 ! [T_1] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(T_1)) ).
% 28.73/28.50
% 28.73/28.50 %----Helper facts (20)
% 28.73/28.50 fof(help_c__COMBI__1,axiom,
% 28.73/28.50 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ).
% 28.73/28.50
% 28.73/28.50 fof(help_c__COMBK__1,axiom,
% 28.73/28.50 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ).
% 28.73/28.50
% 28.73/28.50 fof(help_c__COMBB__1,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(help_c__COMBC__1,axiom,
% 28.73/28.50 ! [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) ).
% 28.73/28.50
% 28.73/28.50 fof(help_c__COMBS__1,axiom,
% 28.73/28.50 ! [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)) ).
% 28.73/28.50
% 28.73/28.50 fof(help_c__fequal__1,axiom,
% 28.73/28.50 ! [V_y_2,V_x_2] :
% 28.73/28.50 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2))
% 28.73/28.50 | V_x_2 = V_y_2 ) ).
% 28.73/28.50
% 28.73/28.50 fof(help_c__fequal__2,axiom,
% 28.73/28.50 ! [V_y_2,V_x_2] :
% 28.73/28.50 ( V_x_2 != V_y_2
% 28.73/28.50 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(help_c__fFalse__1,axiom,
% 28.73/28.50 ~ hBOOL(c_fFalse) ).
% 28.73/28.50
% 28.73/28.50 fof(help_c__fTrue__1,axiom,
% 28.73/28.50 hBOOL(c_fTrue) ).
% 28.73/28.50
% 28.73/28.50 fof(help_c__fNot__1,axiom,
% 28.73/28.50 ! [V_P_2] :
% 28.73/28.50 ( ~ hBOOL(hAPP(c_fNot,V_P_2))
% 28.73/28.50 | ~ hBOOL(V_P_2) ) ).
% 28.73/28.50
% 28.73/28.50 fof(help_c__fNot__2,axiom,
% 28.73/28.50 ! [V_P_2] :
% 28.73/28.50 ( ~ ~ hBOOL(V_P_2)
% 28.73/28.50 | hBOOL(hAPP(c_fNot,V_P_2)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(help_c__fconj__1,axiom,
% 28.73/28.50 ! [V_Q_2,V_P_2] :
% 28.73/28.50 ( ~ hBOOL(V_P_2)
% 28.73/28.50 | ~ hBOOL(V_Q_2)
% 28.73/28.50 | hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(help_c__fconj__2,axiom,
% 28.73/28.50 ! [V_Q_2,V_P_2] :
% 28.73/28.50 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))
% 28.73/28.50 | hBOOL(V_P_2) ) ).
% 28.73/28.50
% 28.73/28.50 fof(help_c__fconj__3,axiom,
% 28.73/28.50 ! [V_Q_2,V_P_2] :
% 28.73/28.50 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))
% 28.73/28.50 | hBOOL(V_Q_2) ) ).
% 28.73/28.50
% 28.73/28.50 fof(help_c__fdisj__1,axiom,
% 28.73/28.50 ! [V_Q_2,V_P_2] :
% 28.73/28.50 ( ~ hBOOL(V_P_2)
% 28.73/28.50 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(help_c__fdisj__2,axiom,
% 28.73/28.50 ! [V_P_2,V_Q_2] :
% 28.73/28.50 ( ~ hBOOL(V_Q_2)
% 28.73/28.50 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(help_c__fdisj__3,axiom,
% 28.73/28.50 ! [V_Q_2,V_P_2] :
% 28.73/28.50 ( ~ hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2))
% 28.73/28.50 | hBOOL(V_P_2)
% 28.73/28.50 | hBOOL(V_Q_2) ) ).
% 28.73/28.50
% 28.73/28.50 fof(help_c__fimplies__1,axiom,
% 28.73/28.50 ! [V_Q_2,V_P_2] :
% 28.73/28.50 ( hBOOL(V_P_2)
% 28.73/28.50 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(help_c__fimplies__2,axiom,
% 28.73/28.50 ! [V_P_2,V_Q_2] :
% 28.73/28.50 ( ~ hBOOL(V_Q_2)
% 28.73/28.50 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ).
% 28.73/28.50
% 28.73/28.50 fof(help_c__fimplies__3,axiom,
% 28.73/28.50 ! [V_Q_2,V_P_2] :
% 28.73/28.50 ( ~ hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2))
% 28.73/28.50 | ~ hBOOL(V_P_2)
% 28.73/28.50 | hBOOL(V_Q_2) ) ).
% 28.73/28.50
% 28.73/28.50 %----Conjectures (5)
% 28.73/28.50 fof(conj_0,hypothesis,
% 28.73/28.50 c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,v_ts_H) ).
% 28.73/28.50
% 28.73/28.50 fof(conj_1,hypothesis,
% 28.73/28.50 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_ts),v_ts_H)) ).
% 28.73/28.50
% 28.73/28.50 fof(conj_2,hypothesis,
% 28.73/28.50 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),v_Ga)) ).
% 28.73/28.50
% 28.73/28.50 fof(conj_3,hypothesis,
% 28.73/28.50 c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts_H) ).
% 28.73/28.50
% 28.73/28.50 fof(conj_4,conjecture,
% 28.73/28.50 c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts) ).
% 28.73/28.50
% 28.73/28.50 %------------------------------------------------------------------------------
% 28.73/28.50 %-------------------------------------------
% 28.73/28.50 % Proof found
% 28.73/28.50 % SZS status Theorem for theBenchmark
% 28.73/28.50 % SZS output start Proof
% 28.73/28.51 %ClaNum:10535(EqnAxiom:3176)
% 28.73/28.51 %VarNum:81154(SingletonVarNum:23754)
% 28.73/28.51 %MaxLitNum:8
% 28.73/28.51 %MaxfuncDepth:13
% 28.73/28.51 %SharedTerms:998
% 28.73/28.51 %goalClause: 4730
% 28.73/28.51 %singleGoalClaCount:1
% 28.73/28.51 [3180]P1(a179)
% 28.73/28.51 [3181]P2(a923)
% 28.73/28.51 [3182]P2(a925)
% 28.73/28.51 [3183]P2(a1)
% 28.73/28.51 [3184]P2(a91)
% 28.73/28.51 [3185]P3(a923)
% 28.73/28.51 [3186]P3(a925)
% 28.73/28.51 [3187]P3(a1)
% 28.73/28.51 [3188]P3(a91)
% 28.73/28.51 [3189]P4(a925)
% 28.73/28.51 [3190]P4(a1)
% 28.73/28.51 [3191]P4(a91)
% 28.73/28.51 [3192]P113(a923)
% 28.73/28.51 [3193]P113(a925)
% 28.73/28.51 [3194]P113(a1)
% 28.73/28.51 [3195]P113(a91)
% 28.73/28.51 [3196]P5(a923)
% 28.73/28.51 [3197]P5(a928)
% 28.73/28.51 [3198]P114(a925)
% 28.73/28.51 [3199]P6(a923)
% 28.73/28.51 [3200]P67(a923)
% 28.73/28.51 [3201]P67(a1)
% 28.73/28.51 [3202]P96(a923)
% 28.73/28.51 [3203]P68(a1)
% 28.73/28.51 [3204]P69(a1)
% 28.73/28.51 [3205]P102(a923)
% 28.73/28.51 [3206]P102(a925)
% 28.73/28.51 [3207]P102(a1)
% 28.73/28.51 [3208]P107(a923)
% 28.73/28.51 [3209]P107(a925)
% 28.73/28.51 [3210]P107(a1)
% 28.73/28.51 [3211]P108(a923)
% 28.73/28.51 [3212]P108(a925)
% 28.73/28.51 [3213]P108(a1)
% 28.73/28.51 [3214]P103(a923)
% 28.73/28.51 [3215]P115(a923)
% 28.73/28.51 [3216]P106(a923)
% 28.73/28.51 [3217]P106(a925)
% 28.73/28.51 [3218]P106(a1)
% 28.73/28.51 [3219]P109(a923)
% 28.73/28.51 [3220]P109(a925)
% 28.73/28.51 [3221]P104(a923)
% 28.73/28.51 [3222]P70(a1)
% 28.73/28.51 [3223]P83(a923)
% 28.73/28.51 [3224]P83(a925)
% 28.73/28.51 [3225]P83(a1)
% 28.73/28.51 [3226]P83(a91)
% 28.73/28.51 [3227]P76(a925)
% 28.73/28.51 [3228]P76(a1)
% 28.73/28.51 [3229]P76(a91)
% 28.73/28.51 [3230]P116(a1)
% 28.73/28.51 [3231]P117(a1)
% 28.73/28.51 [3232]P71(a923)
% 28.73/28.51 [3233]P71(a928)
% 28.73/28.51 [3234]P126(a1)
% 28.73/28.51 [3235]P78(a925)
% 28.73/28.51 [3236]P78(a1)
% 28.73/28.51 [3237]P78(a91)
% 28.73/28.51 [3238]P86(a925)
% 28.73/28.51 [3239]P86(a1)
% 28.73/28.51 [3240]P86(a91)
% 28.73/28.51 [3241]P79(a925)
% 28.73/28.51 [3242]P79(a1)
% 28.73/28.51 [3243]P79(a91)
% 28.73/28.51 [3244]P87(a925)
% 28.73/28.51 [3245]P87(a1)
% 28.73/28.51 [3246]P87(a91)
% 28.73/28.51 [3247]P143(a925)
% 28.73/28.51 [3248]P143(a1)
% 28.73/28.51 [3249]P143(a91)
% 28.73/28.51 [3250]P129(a925)
% 28.73/28.51 [3251]P129(a1)
% 28.73/28.51 [3252]P129(a91)
% 28.73/28.51 [3253]P144(a1)
% 28.73/28.51 [3254]P118(a1)
% 28.73/28.51 [3255]P121(a925)
% 28.73/28.51 [3256]P121(a1)
% 28.73/28.51 [3257]P121(a91)
% 28.73/28.51 [3258]P89(a925)
% 28.73/28.51 [3259]P89(a1)
% 28.73/28.51 [3260]P89(a91)
% 28.73/28.51 [3261]P148(a925)
% 28.73/28.51 [3262]P148(a1)
% 28.73/28.51 [3263]P80(a925)
% 28.73/28.51 [3264]P80(a1)
% 28.73/28.51 [3265]P80(a91)
% 28.73/28.51 [3266]P81(a925)
% 28.73/28.51 [3267]P81(a1)
% 28.73/28.51 [3268]P81(a91)
% 28.73/28.51 [3269]P77(a925)
% 28.73/28.51 [3270]P77(a1)
% 28.73/28.51 [3271]P77(a91)
% 28.73/28.51 [3272]P90(a925)
% 28.73/28.51 [3273]P90(a1)
% 28.73/28.51 [3274]P90(a91)
% 28.73/28.51 [3275]P91(a925)
% 28.73/28.51 [3276]P91(a1)
% 28.73/28.51 [3277]P91(a91)
% 28.73/28.51 [3278]P146(a925)
% 28.73/28.51 [3279]P146(a1)
% 28.73/28.51 [3280]P146(a91)
% 28.73/28.51 [3281]P122(a925)
% 28.73/28.51 [3282]P122(a1)
% 28.73/28.51 [3283]P122(a91)
% 28.73/28.51 [3284]P132(a1)
% 28.73/28.51 [3285]P149(a925)
% 28.73/28.51 [3286]P149(a1)
% 28.73/28.51 [3287]P149(a91)
% 28.73/28.51 [3288]P110(a925)
% 28.73/28.51 [3289]P110(a1)
% 28.73/28.51 [3290]P110(a91)
% 28.73/28.51 [3291]P97(a925)
% 28.73/28.51 [3292]P97(a1)
% 28.73/28.51 [3293]P97(a91)
% 28.73/28.51 [3294]P88(a925)
% 28.73/28.51 [3295]P88(a1)
% 28.73/28.51 [3296]P88(a91)
% 28.73/28.51 [3297]P84(a1)
% 28.73/28.51 [3298]P133(a925)
% 28.73/28.51 [3299]P133(a1)
% 28.73/28.51 [3300]P133(a91)
% 28.73/28.51 [3301]P147(a1)
% 28.73/28.51 [3302]P138(a925)
% 28.73/28.51 [3303]P138(a1)
% 28.73/28.51 [3304]P138(a91)
% 28.73/28.51 [3305]P150(a925)
% 28.73/28.51 [3306]P150(a1)
% 28.73/28.51 [3307]P150(a91)
% 28.73/28.51 [3308]P93(a925)
% 28.73/28.51 [3309]P93(a1)
% 28.73/28.51 [3310]P93(a91)
% 28.73/28.51 [3311]P139(a925)
% 28.73/28.51 [3312]P139(a1)
% 28.73/28.51 [3313]P139(a91)
% 28.73/28.51 [3314]P141(a925)
% 28.73/28.51 [3315]P141(a1)
% 28.73/28.51 [3316]P141(a91)
% 28.73/28.51 [3317]P140(a925)
% 28.73/28.51 [3318]P140(a1)
% 28.73/28.51 [3319]P140(a91)
% 28.73/28.51 [3320]P130(a1)
% 28.73/28.51 [3321]P131(a1)
% 28.73/28.51 [3322]P127(a925)
% 28.73/28.51 [3323]P127(a1)
% 28.73/28.51 [3324]P127(a91)
% 28.73/28.51 [3325]P134(a925)
% 28.73/28.51 [3326]P134(a1)
% 28.73/28.51 [3327]P134(a91)
% 28.73/28.51 [3328]P135(a925)
% 28.73/28.51 [3329]P135(a1)
% 28.73/28.51 [3330]P135(a91)
% 28.73/28.51 [3331]P145(a1)
% 28.73/28.51 [3332]P136(a1)
% 28.73/28.51 [3333]P137(a1)
% 28.73/28.51 [3334]P98(a1)
% 28.73/28.51 [3335]P94(a1)
% 28.73/28.51 [3336]P92(a1)
% 28.73/28.51 [3337]P142(a1)
% 28.73/28.51 [3338]P82(a1)
% 28.73/28.51 [3339]P85(a925)
% 28.73/28.51 [3340]P85(a1)
% 28.73/28.51 [3341]P85(a91)
% 28.73/28.51 [3342]P119(a925)
% 28.73/28.51 [3343]P119(a1)
% 28.73/28.51 [3344]P119(a91)
% 28.73/28.51 [3345]P65(a925)
% 28.73/28.51 [3346]P65(a1)
% 28.73/28.51 [3347]P65(a91)
% 28.73/28.51 [3348]P66(a1)
% 28.73/28.51 [3349]P99(a1)
% 28.73/28.51 [3350]P100(a925)
% 28.73/28.51 [3351]P100(a1)
% 28.73/28.51 [3352]P100(a91)
% 28.73/28.51 [3353]P95(a925)
% 28.73/28.51 [3354]P95(a1)
% 28.73/28.51 [3355]P95(a91)
% 28.73/28.51 [3356]P112(a923)
% 28.73/28.51 [3357]P112(a925)
% 28.73/28.51 [3358]P112(a928)
% 28.73/28.51 [3359]P112(a91)
% 28.73/28.51 [3360]P112(a315)
% 28.73/28.51 [3361]P111(a1)
% 28.73/28.51 [3362]P111(a928)
% 28.73/28.51 [3363]P123(a925)
% 28.73/28.51 [3364]P123(a1)
% 28.73/28.51 [3365]P123(a91)
% 28.73/28.51 [3366]P120(a1)
% 28.73/28.51 [3367]P105(a923)
% 28.73/28.51 [3382]P38(a925,a232)
% 28.73/28.51 [3383]P38(a925,a309)
% 28.73/28.51 [3384]P39(a925,a232)
% 28.73/28.51 [3464]P15(a922,a934,a935)
% 28.73/28.51 [3465]P15(a922,a936,a935)
% 28.73/28.51 [3466]P41(a925,a925,a104)
% 28.73/28.51 [4713]~E(a89,a77)
% 28.73/28.51 [4714]~E(a89,a77)
% 28.73/28.51 [4715]~P1(a231)
% 28.73/28.51 [4730]~P15(a922,a936,a937)
% 28.73/28.51 [3177]E(f2(a1),a77)
% 28.73/28.51 [3178]E(f92(a91),a3)
% 28.73/28.51 [3179]E(f23(a91),a24)
% 28.73/28.51 [3368]E(f180(a925),f2(a925))
% 28.73/28.51 [3369]E(f93(a925),f224(a925))
% 28.73/28.51 [3370]E(f102(a925),f225(a925))
% 28.73/28.51 [3371]E(f94(a1),f25(a1))
% 28.73/28.51 [3372]E(f78(a231),f2(a925))
% 28.73/28.51 [3373]E(f78(a179),f2(a925))
% 28.73/28.51 [3374]P7(f72(a1))
% 28.73/28.51 [3375]P7(f2(a1))
% 28.73/28.51 [3430]P38(f931(a925,a925),a26)
% 28.73/28.51 [3775]E(f312(a925,a925,a232,a232),a26)
% 28.73/28.51 [4716]~E(f72(a1),f2(a1))
% 28.73/28.51 [3376]E(f4(f2(a91)),f2(a925))
% 28.73/28.51 [3377]E(f103(f2(a925)),f2(a925))
% 28.73/28.51 [3386]E(f319(f73(a1),a77),a77)
% 28.73/28.51 [3389]E(f319(a104,f2(a925)),f72(a925))
% 28.73/28.51 [3390]E(f319(a96,f72(a1)),f72(a925))
% 28.73/28.51 [3391]E(f319(a3,f72(a925)),f72(a91))
% 28.73/28.51 [3392]E(f319(a96,f2(a1)),f2(a925))
% 28.73/28.51 [3393]E(f319(a3,f2(a925)),f2(a91))
% 28.73/28.51 [3394]E(f319(f95(a925),a77),f2(a925))
% 28.73/28.51 [3395]E(f319(f95(a1),a77),f2(a1))
% 28.73/28.51 [3396]E(f319(f95(a91),a77),f2(a91))
% 28.73/28.51 [3397]E(f319(a96,f2(a1)),f2(a925))
% 28.73/28.51 [3398]E(f319(f95(a925),a77),f2(a925))
% 28.73/28.51 [3399]E(f319(f181(a923),a231),f2(a925))
% 28.73/28.51 [3400]E(f319(f181(a923),a179),f2(a925))
% 28.73/28.51 [3406]E(f319(f73(a1),f72(a1)),a89)
% 28.73/28.51 [3411]E(f319(f92(a1),f72(a925)),f72(a1))
% 28.73/28.51 [3412]E(f319(f92(a1),f2(a925)),f2(a1))
% 28.73/28.51 [3413]E(f319(f73(a1),f2(a1)),f2(a1))
% 28.73/28.51 [3414]E(f319(f92(a1),f72(a925)),f72(a1))
% 28.73/28.51 [3415]E(f319(f92(a1),f2(a925)),f2(a1))
% 28.73/28.51 [3416]E(f319(f181(a925),f2(a925)),f2(a925))
% 28.73/28.51 [3417]E(f319(f181(a91),f2(a91)),f2(a925))
% 28.73/28.51 [3427]E(f319(a96,f72(a1)),f319(a104,f2(a925)))
% 28.73/28.51 [3428]E(f310(f931(a925,a925),a26),a27)
% 28.73/28.51 [3429]E(f311(f931(a925,a925),a26),a28)
% 28.73/28.51 [3456]E(f319(f274(a925),f2(a925)),f180(f932(a925,a923)))
% 28.73/28.51 [3457]E(f319(f275(a925),f2(a925)),f234(f932(a925,a923)))
% 28.73/28.51 [3468]P42(f180(f932(a1,a923)))
% 28.73/28.51 [3502]E(f319(f319(f23(a91),f2(a91)),f72(a91)),f2(a91))
% 28.73/28.51 [3546]E(f319(f319(f146(a1,a925),a96),f105(a1)),f105(a925))
% 28.73/28.51 [3577]P1(f319(f319(f227(a1),a89),f2(a1)))
% 28.73/28.51 [3601]P1(f319(f319(f226(a1),f2(a1)),f72(a1)))
% 28.73/28.51 [3602]P1(f319(f319(f226(a1),f2(a1)),f2(a1)))
% 28.73/28.51 [3603]P1(f319(f319(f227(a1),f2(a1)),f72(a1)))
% 28.73/28.51 [3806]E(f319(f319(f281(a925,a925,a925),a309),f299(a925,a309)),a232)
% 28.73/28.51 [3843]P43(a1,a925,a96,f319(f226(a1),f2(a1)))
% 28.73/28.51 [3847]E(f319(f319(f33(a925,f932(a925,a923)),f234(f932(a925,a923))),f274(a925)),f234(f932(a925,a923)))
% 28.73/28.51 [3848]E(f319(f319(f33(a925,f932(a925,a923)),f234(f932(a925,a923))),f275(a925)),f234(f932(a925,a923)))
% 28.73/28.51 [3849]E(f319(f319(f33(a925,f932(a925,a923)),f234(f932(a925,a923))),f293(a925)),f234(f932(a925,a923)))
% 28.73/28.51 [3850]E(f319(f319(f34(a925,f932(a925,a923)),f234(f932(a925,a923))),f296(a925)),f180(f932(a925,a923)))
% 28.73/28.51 [3865]P26(a925,a1,f92(a1),f234(f932(a925,a923)))
% 28.73/28.51 [3879]P43(a925,a1,f92(a1),f319(f16(a923,a925),a179))
% 28.73/28.51 [4016]E(f319(f66(a925,a91,a1,a3),a96),f95(a91))
% 28.73/28.51 [4235]P61(a91,a925,a20,a3,f234(f932(a925,a923)))
% 28.73/28.51 [4240]P61(a1,f932(f931(a925,a925),a923),a99,a83,a90)
% 28.73/28.51 [4494]E(f250(a1,a1,a1,a1,f25(a1),f73(a1)),a45)
% 28.73/28.51 [4725]~E(f319(f95(a1),a89),f319(f95(a1),a77))
% 28.73/28.51 [4726]~P1(f319(a185,f72(a1)))
% 28.73/28.51 [4727]~P1(f319(a185,f2(a1)))
% 28.73/28.51 [4753]~P1(f319(f319(f227(a1),a77),f2(a1)))
% 28.73/28.51 [3448]E(f319(f319(f23(a1),a89),a89),a77)
% 28.73/28.51 [3449]E(f319(f319(f74(a1),a77),a77),a77)
% 28.73/28.51 [3450]E(f319(f319(f74(a1),a77),a89),a89)
% 28.73/28.51 [3463]E(f319(f92(a1),f319(a104,f2(a925))),f72(a1))
% 28.73/28.51 [3531]E(f319(f29(a928),f234(f932(a928,a923))),f72(a925))
% 28.73/28.51 [3551]P1(f319(a185,f319(f95(a1),a89)))
% 28.73/28.51 [3552]P1(f319(f319(f226(a1),a77),a77))
% 28.73/28.51 [3553]P1(f319(f319(f226(a1),a89),a77))
% 28.73/28.51 [3554]P1(f319(f319(f226(a1),a89),a89))
% 28.73/28.51 [3555]P1(f319(f319(f227(a1),a89),a77))
% 28.73/28.51 [3611]E(f319(f319(f301(a925),f2(a925)),f180(f932(a925,a923))),f319(f293(a925),f2(a925)))
% 28.73/28.51 [3666]P1(f319(f319(f226(a1),f2(a1)),f319(f95(a1),a77)))
% 28.73/28.51 [3678]E(f319(f302(a925,a925,a104),f234(f932(a925,a923))),f319(f296(a925),f2(a925)))
% 28.73/28.51 [3684]E(f319(f302(a1,a925,a96),f180(f932(a1,a923))),f180(f932(a925,a923)))
% 28.73/28.51 [3692]E(f319(f302(a925,a1,f92(a1)),f180(f932(a925,a923))),f180(f932(a1,a923)))
% 28.73/28.51 [3713]P9(f931(a925,a925),f234(f932(f931(a925,a925),a923)),a100)
% 28.73/28.51 [4023]E(f319(f66(a925,a1,a91,f92(a1)),a20),a22)
% 28.73/28.51 [4082]P38(a925,f319(f254(f931(a925,a925)),f319(f249(a925,a925,a923),f227(a925))))
% 28.73/28.51 [4744]~P1(f319(a185,f319(f95(a1),a77)))
% 28.73/28.51 [4745]~P1(f319(f319(f226(a1),a77),a89))
% 28.73/28.51 [4746]~P1(f319(f319(f227(a1),a77),a77))
% 28.73/28.51 [4747]~P1(f319(f319(f227(a1),a77),a89))
% 28.73/28.51 [4748]~P1(f319(f319(f227(a1),a89),a89))
% 28.73/28.51 [4757]~P1(f319(f55(a925),f234(f932(a925,a923))))
% 28.73/28.51 [4758]~P1(f319(f55(a1),f234(f932(a1,a923))))
% 28.73/28.51 [4660]E(f319(f249(a1,a1,a923),f319(f319(f8(f932(a1,a923),f932(a1,a923),a1),f319(f18(a1,a923,a923),f319(f319(f8(a923,f932(a923,a923),a1),a317),f319(f227(a1),f2(a1))))),f319(f319(f7(a1,a1,f932(a1,a923)),f319(f319(f8(f932(a1,f932(a1,a923)),f932(a1,f932(a1,a923)),a1),f7(a1,a1,a923)),f319(f319(f8(f932(a1,a1),f932(a1,f932(a1,a923)),a1),f319(f8(a1,f932(a1,a923),a1),a316)),a209))),f72(a1)))),a205)
% 28.73/28.51 [3716]E(f319(f319(f23(a1),f319(f319(f74(a1),a89),a89)),a89),a89)
% 28.73/28.51 [3750]E(f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89),f319(f73(a1),a89))
% 28.73/28.51 [3788]E(f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89),f319(f319(f23(a1),a77),a89))
% 28.73/28.51 [3897]P1(f319(f319(f226(f932(f924(a922),a923)),a934),a936))
% 28.73/28.51 [3898]P1(f319(f319(f226(f932(f924(a922),a923)),a937),a935))
% 28.73/28.51 [3950]E(f319(f319(f54(f931(a925,a925)),f234(f932(f931(a925,a925),a923))),a100),a90)
% 28.73/28.51 [3978]E(f319(f95(a925),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f72(a925))
% 28.73/28.51 [3979]E(f319(f95(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f72(a1))
% 28.73/28.51 [3980]E(f319(f95(a91),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f72(a91))
% 28.73/28.51 [3981]E(f319(f95(a925),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f72(a925))
% 28.73/28.51 [3984]E(f319(f95(a925),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(a104,f2(a925)))
% 28.73/28.51 [4362]E(f319(f319(f102(f932(f931(f931(a925,a925),f931(a925,a925)),a923)),a26),f299(f931(a925,a925),f180(f932(f931(f931(a925,a925),f931(a925,a925)),a923)))),a64)
% 28.73/28.51 [4428]E(f319(a83,f319(f277(f931(a925,a925),f931(a925,a925),a100),f319(f319(f301(f931(a925,a925)),f319(f319(f244(a925,a925),f72(a925)),f2(a925))),f180(f932(f931(a925,a925),a923))))),f72(a1))
% 28.73/28.51 [4429]E(f319(a83,f319(f277(f931(a925,a925),f931(a925,a925),a100),f319(f319(f301(f931(a925,a925)),f319(f319(f244(a925,a925),f2(a925)),f2(a925))),f180(f932(f931(a925,a925),a923))))),f2(a1))
% 28.73/28.51 [4442]E(f319(f254(f931(a925,a925)),f319(f249(a925,a925,a923),f319(f319(f8(a925,f932(a925,a923),a925),f319(f7(a925,a925,a923),a316)),a104))),a309)
% 28.73/28.51 [4413]E(f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))),f319(a104,f319(a104,f2(a925))))
% 28.73/28.51 [4414]E(f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))),f319(a104,f319(a104,f2(a925))))
% 28.73/28.51 [4417]E(f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))),f319(f319(f74(a925),f72(a925)),f72(a925)))
% 28.73/28.51 [4418]E(f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))),f319(f29(a923),f234(f932(a923,a923))))
% 28.73/28.51 [4481]P7(f319(f95(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))))
% 28.73/28.51 [4550]P28(f932(f931(a925,a925),a923),f319(f319(f244(f932(f931(f932(f931(a925,a925),a923),f932(f931(a925,a925),a923)),a923),f932(f931(f932(f931(a925,a925),a923),f932(f931(a925,a925),a923)),a923)),a27),a65))
% 28.73/28.51 [4551]P28(f932(f931(a925,a925),a923),f319(f319(f244(f932(f931(f932(f931(a925,a925),a923),f932(f931(a925,a925),a923)),a923),f932(f931(f932(f931(a925,a925),a923),f932(f931(a925,a925),a923)),a923)),a28),a63))
% 28.73/28.51 [4591]E(f319(f319(f102(f932(f931(f932(f931(a925,a925),a923),f932(f931(a925,a925),a923)),a923)),f311(f931(a925,a925),a64)),f319(f319(f301(f931(f932(f931(a925,a925),a923),f932(f931(a925,a925),a923))),f319(f319(f244(f932(f931(a925,a925),a923),f932(f931(a925,a925),a923)),f180(f932(f931(a925,a925),a923))),f180(f932(f931(a925,a925),a923)))),f180(f932(f931(f932(f931(a925,a925),a923),f932(f931(a925,a925),a923)),a923)))),a63)
% 28.73/28.51 [4592]E(f319(f319(f102(f932(f931(f932(f931(a925,a925),a923),f932(f931(a925,a925),a923)),a923)),f310(f931(a925,a925),a64)),f319(f319(f301(f931(f932(f931(a925,a925),a923),f932(f931(a925,a925),a923))),f319(f319(f244(f932(f931(a925,a925),a923),f932(f931(a925,a925),a923)),f180(f932(f931(a925,a925),a923))),f180(f932(f931(a925,a925),a923)))),f180(f932(f931(f932(f931(a925,a925),a923),f932(f931(a925,a925),a923)),a923)))),a65)
% 28.73/28.51 [4483]E(f319(a96,f319(f95(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),f319(a104,f319(a104,f2(a925))))
% 28.73/28.51 [4527]E(f319(a96,f319(f95(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))))
% 28.73/28.51 [4528]E(f319(f92(a1),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),f319(f95(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))))
% 28.73/28.51 [4561]P1(f319(f319(f226(a1),f2(a1)),f319(f95(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))))
% 28.73/28.51 [4562]E(f319(f95(a925),f319(f319(f23(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))),a89)),f319(a104,f319(a104,f319(a104,f2(a925)))))
% 28.73/28.51 [4606]P7(f319(f95(a1),f319(f319(f23(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))),a89)))
% 28.73/28.51 [4631]E(f319(a96,f319(f95(a1),f319(f319(f23(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))),a89))),f319(f95(a925),f319(f319(f23(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))),a89)))
% 28.73/28.51 [4632]E(f319(f92(a1),f319(f95(a925),f319(f319(f23(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))),a89))),f319(f95(a1),f319(f319(f23(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))),a89)))
% 28.73/28.51 [4645]P1(f319(f319(f226(a1),f2(a1)),f319(f95(a1),f319(f319(f23(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))),a89))))
% 28.73/28.51 [3385]P8(x33851,a316)
% 28.73/28.51 [3776]P26(a925,a925,a104,x37761)
% 28.73/28.51 [3378]P112(f924(x33781))
% 28.73/28.51 [3379]P112(f929(x33791))
% 28.73/28.51 [3380]P112(f926(x33801))
% 28.73/28.51 [3381]P112(f927(x33811))
% 28.73/28.51 [3401]P38(a1,f97(x34011))
% 28.73/28.51 [3402]P38(a1,f98(x34021))
% 28.73/28.51 [3452]P38(f932(x34521,a923),f306(x34521))
% 28.73/28.51 [3453]P39(f932(x34531,a923),f306(x34531))
% 28.73/28.51 [3480]E(f235(x34801,x34801,a316),a316)
% 28.73/28.51 [3495]E(f39(a1,x34951,x34951),f2(a1))
% 28.73/28.51 [3548]P16(x35481,f932(x35481,a923),f301(x35481))
% 28.73/28.51 [4717]~E(f319(a104,x47171),x47171)
% 28.73/28.51 [4718]~E(f319(a104,x47181),x47181)
% 28.73/28.51 [4719]~E(f319(a104,x47191),f2(a925))
% 28.73/28.51 [4720]~E(f319(a104,x47201),f2(a925))
% 28.73/28.51 [4721]~E(f319(a104,x47211),f2(a925))
% 28.73/28.51 [4722]~E(f319(a104,x47221),f2(a925))
% 28.73/28.51 [4723]~E(f319(a104,x47231),f2(a925))
% 28.73/28.51 [4724]~E(f319(a104,x47241),f2(a925))
% 28.73/28.51 [3387]E(f319(f95(a1),x33871),x33871)
% 28.73/28.51 [3388]E(f319(f181(a925),x33881),x33881)
% 28.73/28.51 [3403]E(f319(a83,f320(x34031)),x34031)
% 28.73/28.51 [3404]E(f319(a3,f595(x34041)),x34041)
% 28.73/28.51 [3405]E(f233(x34051,f2(a91)),f2(a91))
% 28.73/28.51 [3418]E(f106(x34181,f105(x34181)),f105(x34181))
% 28.73/28.51 [3419]E(f144(x34191,f105(x34191)),f105(x34191))
% 28.73/28.51 [3424]E(f319(f159(x34241),f105(x34241)),f105(x34241))
% 28.73/28.51 [3425]E(f319(f163(x34251),f105(x34251)),f105(x34251))
% 28.73/28.51 [3426]E(f319(f160(x34261),f105(x34261)),f105(x34261))
% 28.73/28.51 [3431]E(f319(f95(a1),x34311),f319(f94(a1),x34311))
% 28.73/28.51 [3432]E(f319(a83,f319(a99,x34321)),x34321)
% 28.73/28.51 [3433]E(f319(a3,f319(a20,x34331)),x34331)
% 28.73/28.51 [3434]E(f319(a3,f319(a20,x34341)),x34341)
% 28.73/28.51 [3435]E(f319(a20,f319(a3,x34351)),x34351)
% 28.73/28.51 [3437]P7(f319(f92(a1),x34371))
% 28.73/28.51 [3446]E(f319(f181(f926(x34461)),f105(x34461)),f2(a925))
% 28.73/28.51 [3447]E(f319(f181(f927(x34471)),f111(x34471)),f2(a925))
% 28.73/28.51 [3471]E(f319(f319(f23(a925),x34711),f2(a925)),x34711)
% 28.73/28.51 [3472]E(f319(f319(f75(a925),x34721),f72(a925)),x34721)
% 28.73/28.51 [3473]E(f319(f319(f75(a1),x34731),f72(a1)),x34731)
% 28.73/28.51 [3474]E(f319(f319(f74(a925),x34741),f2(a925)),x34741)
% 28.73/28.51 [3475]E(f319(f319(f74(a1),x34751),f2(a1)),x34751)
% 28.73/28.51 [3476]E(f319(f319(f225(a925),x34761),f2(a925)),x34761)
% 28.73/28.51 [3477]E(f319(f319(f75(a925),x34771),f2(a925)),f2(a925))
% 28.73/28.51 [3478]E(f319(f319(f224(a925),x34781),f2(a925)),f2(a925))
% 28.73/28.51 [3479]E(f319(f319(f30(a1),x34791),f2(a1)),f2(a1))
% 28.73/28.51 [3486]E(f319(f164(x34861),f105(x34861)),f180(f932(x34861,a923)))
% 28.73/28.51 [3490]P1(f319(f129(x34901),f105(x34901)))
% 28.73/28.51 [3496]E(f319(f146(x34961,x34961),f5(x34961)),f25(f926(x34961)))
% 28.73/28.51 [3497]E(f319(f146(x34971,x34971),f25(x34971)),f25(f926(x34971)))
% 28.73/28.51 [3498]E(f39(a1,x34981,f2(a1)),x34981)
% 28.73/28.51 [3499]E(f319(f226(a925),f319(a104,x34991)),f319(f227(a925),x34991))
% 28.73/28.51 [3500]E(f319(f274(a925),f319(a104,x35001)),f319(f293(a925),x35001))
% 28.73/28.51 [3501]E(f319(f275(a925),f319(a104,x35011)),f319(f296(a925),x35011))
% 28.73/28.51 [3503]E(f39(a1,f2(a1),x35031),f2(a1))
% 28.73/28.51 [3516]E(f319(f319(f74(a925),x35161),f72(a925)),f319(a104,x35161))
% 28.73/28.51 [3525]E(f319(f294(a925,x35251),f2(a925)),f180(f932(a925,a923)))
% 28.73/28.51 [3537]E(f295(a925,f2(a925),x35371),f319(f293(a925),x35371))
% 28.73/28.51 [3580]E(f319(f319(f23(a925),f319(a104,x35801)),f72(a925)),x35801)
% 28.73/28.51 [3592]E(f41(f2(a1),x35921),f319(f319(f244(a1,a1),f2(a1)),f2(a1)))
% 28.73/28.51 [3596]E(f319(f319(f74(a925),f319(a20,x35961)),f2(a925)),f319(a20,x35961))
% 28.73/28.51 [3641]P1(f319(f319(f227(a925),x36411),f319(a104,x36411)))
% 28.73/28.51 [3653]P1(f319(f319(f227(a925),f2(a925)),f319(a104,x36531)))
% 28.73/28.51 [3664]E(f319(f319(f175(f926(x36641),f926(x36641)),f2(a925)),f159(x36641)),f25(f926(x36641)))
% 28.73/28.51 [3878]E(f85(x38781,x38781,f234(f932(x38781,a923)),f25(x38781)),f25(x38781))
% 28.73/28.51 [3937]E(f319(f319(f23(a91),f319(a3,f319(a104,f319(a20,x39371)))),f72(a91)),x39371)
% 28.73/28.51 [4007]P1(f319(f319(f226(a1),f319(f73(a1),f319(f92(a1),x40071))),f2(a1)))
% 28.73/28.51 [4150]P1(f319(f319(f227(a1),f319(f73(a1),f319(f92(a1),f319(a104,x41501)))),f2(a1)))
% 28.73/28.51 [4248]P27(x42481,x42481,f25(x42481),f234(f932(x42481,a923)),f234(f932(x42481,a923)))
% 28.73/28.51 [4733]~E(f234(f932(x47331,a923)),f180(f932(x47331,a923)))
% 28.73/28.51 [4754]~P1(f319(f319(f227(a925),x47541),f2(a925)))
% 28.73/28.51 [4755]~P1(f319(f319(f227(a925),x47551),f2(a925)))
% 28.73/28.51 [4756]~P1(f319(f319(f227(a925),x47561),f2(a925)))
% 28.73/28.51 [4767]~P1(f319(f319(f227(a1),f319(f92(a1),x47671)),f2(a1)))
% 28.73/28.51 [3436]E(f112(x34361,f111(f927(x34361))),f111(x34361))
% 28.73/28.51 [3451]E(f171(x34511,f105(f926(x34511))),f105(f926(x34511)))
% 28.73/28.51 [3454]E(f319(f319(f75(a1),a77),x34541),a77)
% 28.73/28.51 [3455]E(f319(f319(f74(a1),a77),x34551),x34551)
% 28.73/28.51 [3458]E(f319(a96,f319(f92(a1),x34581)),x34581)
% 28.73/28.51 [3459]E(f319(f319(f23(a1),x34591),a77),x34591)
% 28.73/28.51 [3460]E(f319(f319(f74(a1),x34601),a77),x34601)
% 28.73/28.51 [3462]E(f319(f319(f23(a925),x34621),x34621),f2(a925))
% 28.73/28.51 [3469]E(f319(f73(a1),f319(f73(a1),x34691)),x34691)
% 28.73/28.51 [3470]E(f319(f29(a925),f319(f274(a925),x34701)),x34701)
% 28.73/28.51 [3481]E(f319(f319(f75(a925),f72(a925)),x34811),x34811)
% 28.73/28.51 [3482]E(f319(f319(f75(a1),f72(a1)),x34821),x34821)
% 28.73/28.51 [3483]E(f319(f319(f74(a925),f2(a925)),x34831),x34831)
% 28.73/28.51 [3484]E(f319(f319(f74(a1),f2(a1)),x34841),x34841)
% 28.73/28.51 [3485]E(f319(f319(f225(a925),f2(a925)),x34851),x34851)
% 28.73/28.51 [3491]E(f319(f319(f23(a925),f2(a925)),x34911),f2(a925))
% 28.73/28.51 [3492]E(f319(f319(f75(a925),f2(a925)),x34921),f2(a925))
% 28.73/28.51 [3493]E(f319(f319(f224(a925),f2(a925)),x34931),f2(a925))
% 28.73/28.51 [3494]E(f319(f319(f30(a1),f2(a1)),x34941),f2(a1))
% 28.73/28.51 [3504]E(f120(x35041,f319(f73(a1),x35041)),f124(a1,x35041))
% 28.73/28.51 [3509]E(f319(f294(a925,f2(a925)),x35091),f319(f274(a925),x35091))
% 28.73/28.51 [3510]E(f319(f319(f75(a1),a89),x35101),f319(f73(a1),x35101))
% 28.73/28.51 [3517]E(f319(a96,f319(f95(a1),x35171)),f319(f95(a925),x35171))
% 28.73/28.51 [3518]E(f319(a96,f319(f95(a1),x35181)),f319(f95(a925),x35181))
% 28.73/28.51 [3519]E(f319(a20,f319(f95(a91),x35191)),f319(f95(a925),x35191))
% 28.73/28.51 [3520]E(f319(f29(a925),f319(f293(a925),x35201)),f319(a104,x35201))
% 28.73/28.51 [3529]E(f319(f319(f74(a925),f72(a925)),x35291),f319(a104,x35291))
% 28.73/28.51 [3533]E(f319(f94(a1),f319(f92(a1),x35331)),f319(f92(a1),x35331))
% 28.73/28.51 [3534]E(f319(f69(a1),f319(f92(a1),x35341)),f319(f92(a1),x35341))
% 28.73/28.51 [3538]E(f319(f29(x35381),f180(f932(x35381,a923))),f2(a925))
% 28.73/28.51 [3540]E(f319(f319(f30(a925),x35401),f319(a104,f2(a925))),x35401)
% 28.73/28.51 [3549]E(f39(a925,x35491,f319(a104,f2(a925))),f2(a925))
% 28.73/28.51 [3550]E(f39(a1,x35501,f319(f95(a1),a89)),f2(a1))
% 28.73/28.51 [3557]E(f319(f319(f74(a1),a89),x35571),f319(f319(f74(a1),x35571),a89))
% 28.73/28.51 [3564]E(f319(f319(f30(a1),x35641),f319(f95(a1),a89)),f319(f73(a1),x35641))
% 28.73/28.51 [3568]E(f131(a925,f319(f294(a925,x35681),f2(a925))),f105(a925))
% 28.73/28.51 [3569]E(f319(f319(f74(a1),x35691),f72(a1)),f319(f319(f23(a1),x35691),a89))
% 28.73/28.51 [3570]E(f319(f319(f23(a1),x35701),f72(a1)),f319(f319(f74(a1),x35701),a89))
% 28.73/28.51 [3574]P1(f319(f319(f226(a925),x35741),x35741))
% 28.73/28.51 [3575]P1(f319(f319(f226(a1),x35751),x35751))
% 28.73/28.51 [3576]P1(f319(f319(f279(a925),x35761),x35761))
% 28.73/28.51 [3581]E(f319(f73(a1),f319(f95(a1),x35811)),f319(f95(a1),f319(f73(a1),x35811)))
% 28.73/28.51 [3582]P1(f319(f55(a925),f319(f274(a925),x35821)))
% 28.73/28.51 [3583]P1(f319(f55(a925),f319(f293(a925),x35831)))
% 28.73/28.51 [3590]E(f153(x35901,f234(f932(x35901,a923))),f234(f932(f926(x35901),a923)))
% 28.73/28.51 [3594]P1(f319(f319(f226(a925),f2(a925)),x35941))
% 28.73/28.51 [3595]P1(f319(f319(f226(a925),f2(a925)),x35951))
% 28.73/28.51 [3605]E(f319(f319(f74(a925),f103(x36051)),f319(a104,f2(a925))),f103(f319(a104,x36051)))
% 28.73/28.51 [3606]E(f319(f254(x36061),f319(f16(a923,x36061),a179)),f234(f932(x36061,a923)))
% 28.73/28.51 [3607]E(f319(f254(x36071),f319(f16(a923,x36071),a231)),f180(f932(x36071,a923)))
% 28.73/28.51 [3610]E(f319(f319(f301(a925),x36101),f319(f274(a925),x36101)),f319(f274(a925),f319(a104,x36101)))
% 28.73/28.51 [3622]E(f319(f319(f74(a1),f72(a1)),f319(f92(a1),x36221)),f319(f92(a1),f319(a104,x36221)))
% 28.73/28.51 [3624]E(f319(f319(f143(f926(x36241)),f105(x36241)),f105(f926(x36241))),f48(x36241,f105(x36241)))
% 28.73/28.51 [3644]E(f180(f932(f931(x36441,x36441),a923)),f255(x36441,f180(f932(x36441,a923))))
% 28.73/28.51 [3645]E(f319(f300(x36451),f234(f932(x36451,a923))),f234(f932(f932(x36451,a923),a923)))
% 28.73/28.51 [3646]E(f319(f73(f932(x36461,a923)),f234(f932(x36461,a923))),f180(f932(x36461,a923)))
% 28.73/28.51 [3647]E(f319(f73(f932(x36471,a923)),f180(f932(x36471,a923))),f234(f932(x36471,a923)))
% 28.73/28.51 [3648]P1(f319(f55(x36481),f180(f932(x36481,a923))))
% 28.73/28.51 [3649]P1(f319(f55(x36491),f180(f932(x36491,a923))))
% 28.73/28.51 [3651]E(f319(f294(a925,x36511),f319(a104,x36511)),f319(f319(f301(a925),x36511),f180(f932(a925,a923))))
% 28.73/28.51 [3652]E(f79(f931(a925,a925),f42(x36521,f2(a925))),f319(f319(f244(a925,a925),f2(a925)),x36521))
% 28.73/28.51 [3665]E(f319(f319(f301(a925),f319(a104,x36651)),f319(f293(a925),x36651)),f319(f293(a925),f319(a104,x36651)))
% 28.73/28.51 [3669]P38(x36691,f180(f932(f931(x36691,x36691),a923)))
% 28.73/28.51 [3670]P40(x36701,f180(f932(f931(x36701,x36701),a923)))
% 28.73/28.51 [3672]P1(f319(f319(f226(a1),f2(a1)),f319(f92(a1),x36721)))
% 28.73/28.51 [3673]P1(f319(f319(f226(a1),f2(a1)),f319(f92(a1),x36731)))
% 28.73/28.51 [3680]E(f319(f319(f74(a925),f319(f181(a925),x36801)),f319(a104,f2(a925))),f319(f181(a925),f319(a104,x36801)))
% 28.73/28.51 [3726]P1(f319(f319(f321(a925),f595(x37261)),f234(f932(a925,a923))))
% 28.73/28.51 [3728]E(f319(f302(x37281,x37281,f25(x37281)),f234(f932(x37281,a923))),f234(f932(x37281,a923)))
% 28.73/28.51 [3783]P42(f319(f302(a925,a1,f92(a1)),x37831))
% 28.73/28.51 [3821]P57(x38211,f180(f932(x38211,a923)),f180(f932(f931(x38211,x38211),a923)))
% 28.73/28.51 [3839]E(f319(f319(f244(a1,a1),f319(f95(a1),a89)),f319(f319(f23(a1),x38391),f72(a1))),f44(f319(f95(a1),a89),x38391))
% 28.73/28.51 [3840]P1(f319(f319(f321(a925),f319(a20,x38401)),f234(f932(a925,a923))))
% 28.73/28.51 [3891]P64(x38911,f319(f16(f932(x38911,a923),x38911),f319(f16(a923,x38911),a231)))
% 28.73/28.51 [3905]E(f282(a925,f279(a925),x39051,x39051),f319(f319(f301(a925),x39051),f180(f932(a925,a923))))
% 28.73/28.51 [4076]E(f319(f134(f926(x40761),f926(x40761),f126(x40761),f105(x40761)),f105(f926(x40761))),f105(x40761))
% 28.73/28.51 [4094]P1(f319(f319(f321(f932(f931(a925,a925),a923)),f320(x40941)),a90))
% 28.73/28.51 [4119]P1(f319(f319(f321(f932(f931(a925,a925),a923)),f319(a99,x41191)),a90))
% 28.73/28.51 [4249]P26(x42491,f932(x42491,a923),f319(f319(f7(x42491,f932(x42491,a923),f932(x42491,a923)),f301(x42491)),f180(f932(x42491,a923))),f234(f932(x42491,a923)))
% 28.73/28.51 [4728]~E(f319(f319(f74(a1),x47281),x47281),a89)
% 28.73/28.51 [4729]~E(f319(f319(f74(a1),x47291),x47291),a89)
% 28.73/28.51 [4742]~E(f319(a3,f319(a104,f319(a20,x47421))),f2(a91))
% 28.73/28.51 [4743]~E(f319(a3,f319(a104,f319(a20,x47431))),f2(a91))
% 28.73/28.51 [4749]~P1(f319(a185,f319(f92(a1),x47491)))
% 28.73/28.51 [4751]~P1(f319(f319(f227(a925),x47511),x47511))
% 28.73/28.51 [4752]~P1(f319(f319(f227(a925),x47521),x47521))
% 28.73/28.51 [4760]~P1(f319(f319(f226(a925),f319(a104,x47601)),x47601))
% 28.73/28.51 [3597]E(f319(a96,f319(f73(a1),f319(f92(a1),x35971))),f2(a925))
% 28.73/28.51 [3600]E(f319(f319(f74(a1),f319(f73(a1),x36001)),x36001),f2(a1))
% 28.73/28.51 [3604]E(f319(f29(a1),f319(f294(a1,f2(a1)),x36041)),f319(a96,x36041))
% 28.73/28.51 [3615]E(f319(f319(f236(a925),f319(a104,f2(a925))),x36151),f319(a104,f2(a925)))
% 28.73/28.51 [3710]E(f319(f273(x37101),f180(f932(f931(x37101,x37101),a923))),f180(f932(x37101,a923)))
% 28.73/28.51 [3712]P1(f319(f55(a1),f319(f294(a1,f2(a1)),x37121)))
% 28.73/28.51 [3718]E(f32(f932(x37181,a923),f234(f932(f932(x37181,a923),a923))),f180(f932(x37181,a923)))
% 28.73/28.51 [3719]E(f32(f932(x37191,a923),f180(f932(f932(x37191,a923),a923))),f234(f932(x37191,a923)))
% 28.73/28.51 [3720]E(f31(f932(x37201,a923),f234(f932(f932(x37201,a923),a923))),f234(f932(x37201,a923)))
% 28.73/28.51 [3721]E(f31(f932(x37211,a923),f180(f932(f932(x37211,a923),a923))),f180(f932(x37211,a923)))
% 28.73/28.51 [3725]P1(f319(f319(f279(a925),f319(a104,f2(a925))),x37251))
% 28.73/28.51 [3766]E(f319(f319(f301(f926(x37661)),f105(x37661)),f180(f932(f926(x37661),a923))),f153(x37661,f180(f932(x37661,a923))))
% 28.73/28.51 [3767]E(f319(f319(f301(f926(x37671)),f105(x37671)),f180(f932(f926(x37671),a923))),f154(x37671,f105(f932(x37671,a923))))
% 28.73/28.51 [3792]E(f319(f319(f74(a1),f319(f73(a1),x37921)),f319(f73(a1),x37921)),f319(f73(a1),f319(f319(f74(a1),x37921),x37921)))
% 28.73/28.51 [3805]E(f319(f319(f74(a925),f4(x38051)),f319(a104,f2(a925))),f4(f319(a3,f319(a104,f319(a20,x38051)))))
% 28.73/28.51 [3830]E(f319(f29(a1),f319(f302(a925,a1,f92(a1)),x38301)),f319(f29(a925),x38301))
% 28.73/28.51 [3831]P1(f319(f319(f226(a925),x38311),f319(f319(f75(a925),x38311),x38311)))
% 28.73/28.51 [3869]E(f319(f302(a1,a925,a96),f295(a1,f2(a1),f319(f92(a1),x38691))),f319(f293(a925),x38691))
% 28.73/28.51 [3886]E(f319(f319(f30(a925),f319(a104,f2(a925))),f319(f95(a925),x38861)),f319(a96,f319(f319(f30(a1),f72(a1)),f319(f95(a1),x38861))))
% 28.73/28.51 [3888]E(f319(f164(a925),f131(a925,f319(f294(a925,f2(a925)),f319(a104,x38881)))),f319(f293(a925),x38881))
% 28.73/28.51 [3889]E(f319(f319(f74(a925),f319(f181(a91),x38891)),f319(a104,f2(a925))),f319(f181(a91),f319(a3,f319(a104,f319(a20,x38891)))))
% 28.73/28.51 [3910]P39(x39101,f299(x39101,f180(f932(f931(x39101,x39101),a923))))
% 28.73/28.51 [3911]P40(x39111,f299(x39111,f180(f932(f931(x39111,x39111),a923))))
% 28.73/28.51 [3912]P56(x39121,f299(x39121,f180(f932(f931(x39121,x39121),a923))))
% 28.73/28.51 [3913]E(f319(f302(a1,a925,a96),f319(f302(a925,a1,f92(a1)),x39131)),x39131)
% 28.73/28.51 [3943]E(f319(f319(f301(a925),f2(a925)),f319(f302(a925,a925,a104),f319(f274(a925),x39431))),f319(f274(a925),f319(a104,x39431)))
% 28.73/28.51 [3949]P59(x39491,x39491,f299(x39491,f180(f932(f931(x39491,x39491),a923))))
% 28.73/28.51 [3955]P1(f319(a185,f319(f73(a1),f319(f92(a1),f319(a104,x39551)))))
% 28.73/28.51 [3965]E(f319(f319(f23(f932(a925,a923)),f319(f275(a925),x39651)),f319(f319(f301(a925),x39651),f180(f932(a925,a923)))),f319(f275(a925),f319(a104,x39651)))
% 28.73/28.51 [3982]E(f319(f319(f74(a1),f319(f319(f23(a1),a77),x39821)),f319(f319(f23(a1),a77),x39821)),f319(f319(f23(a1),a77),f319(f319(f74(a1),x39821),x39821)))
% 28.73/28.51 [3985]P57(x39851,f234(f932(x39851,a923)),f299(x39851,f180(f932(f931(x39851,x39851),a923))))
% 28.73/28.51 [3996]E(f319(f319(f301(f932(x39961,a923)),f180(f932(x39961,a923))),f180(f932(f932(x39961,a923),a923))),f319(f300(x39961),f180(f932(x39961,a923))))
% 28.73/28.51 [4024]E(f319(f319(f23(f932(a925,a923)),f319(f296(a925),x40241)),f319(f319(f301(a925),f319(a104,x40241)),f180(f932(a925,a923)))),f319(f296(a925),f319(a104,x40241)))
% 28.73/28.51 [4131]E(f319(f95(a925),f319(f319(f74(a1),x41311),x41311)),f319(f319(f80(a925,a925),f319(f95(a925),x41311)),f319(f319(f18(a925,a925,a925),f74(a925)),f5(a925))))
% 28.73/28.51 [4503]P16(x45031,f932(x45031,a923),f319(f319(f8(f932(x45031,a923),f932(f932(x45031,a923),f932(x45031,a923)),x45031),f319(f7(f932(x45031,a923),f932(x45031,a923),f932(x45031,a923)),f23(f932(x45031,a923)))),f319(f319(f7(x45031,f932(x45031,a923),f932(x45031,a923)),f301(x45031)),f180(f932(x45031,a923)))))
% 28.73/28.51 [4590]E(f319(f254(f931(a1,a1)),f319(f249(a1,a1,a923),f319(f319(f8(f932(a1,a923),f932(a1,a923),a1),f319(f18(a1,a923,a923),f319(f319(f8(a923,f932(a923,a923),a1),a317),f319(f226(a1),x45901)))),f227(a1)))),f97(x45901))
% 28.73/28.51 [4623]E(f319(f254(f931(a1,a1)),f319(f249(a1,a1,a923),f319(f319(f18(a1,f932(a1,a923),f932(a1,a923)),f319(f319(f8(f932(a923,a923),f932(f932(a1,a923),f932(a1,a923)),a1),f8(a923,a923,a1)),f319(f319(f8(a923,f932(a923,a923),a1),a317),f319(f226(a1),x46231)))),f227(a1)))),f98(x46231))
% 28.73/28.51 [4676]E(f319(f254(f931(f932(x46761,a923),f932(x46761,a923))),f319(f249(f932(x46761,a923),f932(x46761,a923),a923),f319(f319(f7(f932(x46761,a923),f932(f932(x46761,a923),a923),f932(f932(x46761,a923),a923)),f319(f319(f8(f932(f932(x46761,a923),f932(a923,a923)),f932(f932(f932(x46761,a923),a923),f932(f932(x46761,a923),a923)),f932(x46761,a923)),f18(f932(x46761,a923),a923,a923)),f319(f319(f8(f932(f932(x46761,a923),a923),f932(f932(x46761,a923),f932(a923,a923)),f932(x46761,a923)),f319(f8(a923,f932(a923,a923),f932(x46761,a923)),a317)),f227(f932(x46761,a923))))),f55(x46761)))),f306(x46761))
% 28.73/28.51 [4764]~P1(f319(f55(f926(x47641)),f234(f932(f926(x47641),a923))))
% 28.73/28.51 [4776]~P1(f319(f319(f226(a1),f2(a1)),f319(f73(a1),f319(f92(a1),f319(a104,x47761)))))
% 28.73/28.51 [3745]E(f319(f319(f23(a1),f319(f319(f74(a1),x37451),a89)),a89),x37451)
% 28.73/28.51 [3759]E(f319(f164(a925),f131(a925,f319(f294(a925,f2(a925)),x37591))),f319(f274(a925),x37591))
% 28.73/28.51 [3956]E(f319(f276(x39561,x39561),f299(x39561,f180(f932(f931(x39561,x39561),a923)))),f234(f932(x39561,a923)))
% 28.73/28.51 [3957]E(f319(f256(x39571,x39571),f299(x39571,f180(f932(f931(x39571,x39571),a923)))),f234(f932(x39571,a923)))
% 28.73/28.51 [4003]E(f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x40031)),x40031),f319(f319(f23(a1),f319(f319(f74(a1),x40031),x40031)),a89))
% 28.73/28.51 [4051]E(f319(f278(x40511,x40511),f299(x40511,f180(f932(f931(x40511,x40511),a923)))),f299(x40511,f180(f932(f931(x40511,x40511),a923))))
% 28.73/28.51 [4097]P1(f319(f319(f226(a925),x40971),f319(f319(f75(a925),x40971),f319(f319(f75(a925),x40971),x40971))))
% 28.73/28.51 [4185]E(f319(f319(f281(x41851,x41851,x41851),f180(f932(f931(x41851,x41851),a923))),f299(x41851,f180(f932(f931(x41851,x41851),a923)))),f180(f932(f931(x41851,x41851),a923)))
% 28.73/28.51 [4366]P1(f319(f55(a925),f319(f254(a925),f319(f319(f7(a925,a925,a923),f226(a925)),x43661))))
% 28.73/28.51 [4367]P1(f319(f55(a925),f319(f254(a925),f319(f319(f7(a925,a925,a923),f227(a925)),x43671))))
% 28.73/28.51 [4639]E(f319(f254(f931(x46391,x46391)),f319(f319(f8(f932(x46391,a923),a923,f931(x46391,x46391)),f81(x46391)),f319(f319(f7(f931(x46391,x46391),f932(x46391,f931(x46391,x46391)),f932(x46391,a923)),f319(f319(f8(f932(f931(x46391,x46391),a923),f932(f932(x46391,f931(x46391,x46391)),f932(x46391,a923)),f931(x46391,x46391)),f8(f931(x46391,x46391),a923,x46391)),a316)),f319(f319(f18(x46391,x46391,f931(x46391,x46391)),f244(x46391,x46391)),f5(x46391))))),f299(x46391,f180(f932(f931(x46391,x46391),a923))))
% 28.73/28.51 [4765]~E(f319(f319(f23(a1),f319(f319(f74(a1),x47651),x47651)),a89),a77)
% 28.73/28.51 [4766]~E(f319(f319(f23(a1),f319(f319(f74(a1),x47661),x47661)),a89),a77)
% 28.73/28.51 [4768]~E(f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x47681)),x47681),f2(a1))
% 28.73/28.51 [4141]E(f319(f319(f74(a1),f319(f319(f23(a1),a89),x41411)),f319(f319(f23(a1),a89),x41411)),f319(f319(f23(a1),a89),f319(f319(f23(a1),f319(f319(f74(a1),x41411),x41411)),a89)))
% 28.73/28.51 [4257]E(f319(f319(f23(a1),f319(f319(f74(a1),f319(f319(f23(a1),a89),x42571)),f319(f319(f23(a1),a89),x42571))),a89),f319(f319(f23(a1),a89),f319(f319(f74(a1),x42571),x42571)))
% 28.73/28.51 [4289]E(f319(f319(f23(a1),f319(f319(f74(a1),f319(f319(f74(a1),x42891),a89)),f319(f319(f74(a1),x42891),a89))),a89),f319(f319(f74(a1),f319(f319(f74(a1),x42891),x42891)),a89))
% 28.73/28.51 [4327]E(f319(f319(f23(a1),f319(f319(f74(a1),f319(f319(f23(a1),a89),x43271)),f319(f319(f23(a1),a89),x43271))),a89),f319(f319(f23(a1),a77),f319(f319(f23(a1),f319(f319(f74(a1),x43271),x43271)),a89)))
% 28.73/28.51 [4424]E(f319(a83,f319(f277(f931(a925,a925),f931(a925,a925),a100),f319(f319(f301(f931(a925,a925)),f319(f319(f244(a925,a925),x44241),f2(a925))),f180(f932(f931(a925,a925),a923))))),f319(f92(a1),x44241))
% 28.73/28.51 [4434]E(f319(a83,f319(f277(f931(a925,a925),f931(a925,a925),a100),f319(f319(f301(f931(a925,a925)),f319(f319(f244(a925,a925),f324(x44341)),f558(x44341))),f180(f932(f931(a925,a925),a923))))),x44341)
% 28.73/28.51 [4467]E(f319(f254(a1),f319(f319(f18(a1,a923,a923),f319(f319(f8(a923,f932(a923,a923),a1),a317),f319(f226(a1),f2(a1)))),x44671)),f319(f302(a925,a1,f92(a1)),f319(f254(a925),f319(f319(f8(a1,a923,a925),x44671),f92(a1)))))
% 28.73/28.51 [4511]P42(f319(f254(a1),f319(f319(f18(a1,a923,a923),f319(f319(f8(a923,f932(a923,a923),a1),a317),f319(f226(a1),f2(a1)))),x45111)))
% 28.73/28.51 [4531]P1(f319(f319(f321(f931(f932(f931(a925,a925),a923),f932(f931(a925,a925),a923))),f319(f319(f244(f932(f931(a925,a925),a923),f932(f931(a925,a925),a923)),x45311),f180(f932(f931(a925,a925),a923)))),a65))
% 28.73/28.51 [4536]E(f319(f302(a1,a925,a96),f319(f254(a1),f319(f319(f18(a1,a923,a923),f319(f319(f8(a923,f932(a923,a923),a1),a317),f319(f226(a1),f2(a1)))),f319(f319(f8(a925,a923,a1),x45361),a96)))),f319(f254(a925),x45361))
% 28.73/28.51 [4691]E(f304(a925,f319(f319(f33(f931(a925,a925),f932(a925,a923)),f319(a99,x46911)),f319(f249(a925,a925,f932(a925,a923)),f319(f319(f7(a925,f932(a925,a923),f932(a925,f932(a925,a923))),f319(f319(f8(f932(a925,f932(f932(a925,a923),f932(a925,a923))),f932(f932(a925,a923),f932(a925,f932(a925,a923))),a925),f7(a925,f932(a925,a923),f932(a925,a923))),f319(f319(f8(f932(a925,a925),f932(a925,f932(f932(a925,a923),f932(a925,a923))),a925),f319(f8(a925,f932(f932(a925,a923),f932(a925,a923)),a925),f301(a925))),f23(a925)))),f180(f932(a925,a923)))))),f319(a96,x46911))
% 28.73/28.51 [4186]E(f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),x41861),x41861)),a89)),a89),f319(f319(f74(a1),x41861),x41861))
% 28.73/28.51 [4236]E(f319(f319(f23(a1),f319(f319(f23(a1),f319(f319(f74(a1),x42361),x42361)),a89)),a89),f319(f319(f74(a1),f319(f319(f23(a1),x42361),a89)),f319(f319(f23(a1),x42361),a89)))
% 28.73/28.51 [4440]E(f319(f319(f23(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f73(a1),x44401)),a89)),f319(f319(f74(a1),f319(f73(a1),x44401)),a89))),a89),f319(f73(a1),f319(f319(f23(a1),f319(f319(f74(a1),x44401),x44401)),a89)))
% 28.73/28.51 [4484]E(f319(f319(f74(a925),x44841),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),f319(a104,f319(a104,x44841)))
% 28.73/28.51 [4485]E(f319(f319(f75(a925),x44851),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),f319(f319(f74(a925),x44851),x44851))
% 28.73/28.51 [4486]E(f319(f319(f30(a925),f319(f319(f74(a925),x44861),x44861)),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),x44861)
% 28.73/28.51 [4564]E(f39(a925,f319(a104,f319(a104,x45641)),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),f39(a925,x45641,f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))))
% 28.73/28.51 [4705]E(f319(a83,f319(f319(f33(f931(a925,a925),f932(f931(a925,a925),a923)),f319(a99,x47051)),f319(f249(a925,a925,f932(f931(a925,a925),a923)),f319(f319(f8(f932(a925,f932(f931(a925,a925),a923)),f932(a925,f932(f931(a925,a925),a923)),a925),f319(f8(f932(f931(a925,a925),a923),f932(f931(a925,a925),a923),a925),f277(f931(a925,a925),f931(a925,a925),a100))),f319(f319(f7(a925,f932(f931(a925,a925),a923),f932(a925,f932(f931(a925,a925),a923))),f319(f319(f8(f932(a925,f932(f932(f931(a925,a925),a923),f932(f931(a925,a925),a923))),f932(f932(f931(a925,a925),a923),f932(a925,f932(f931(a925,a925),a923))),a925),f7(a925,f932(f931(a925,a925),a923),f932(f931(a925,a925),a923))),f319(f319(f8(f932(a925,f931(a925,a925)),f932(a925,f932(f932(f931(a925,a925),a923),f932(f931(a925,a925),a923))),a925),f319(f8(f931(a925,a925),f932(f932(f931(a925,a925),a923),f932(f931(a925,a925),a923)),a925),f301(f931(a925,a925)))),f319(f7(a925,a925,f931(a925,a925)),f244(a925,a925))))),f180(f932(f931(a925,a925),a923))))))),f319(f73(a1),x47051))
% 28.73/28.51 [4559]E(f319(f319(f74(a925),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),x45591),f319(a104,f319(a104,x45591)))
% 28.73/28.51 [4560]E(f319(f319(f75(a925),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),x45601),f319(f319(f74(a925),x45601),x45601))
% 28.73/28.51 [4596]E(f319(f319(f30(a925),f319(a104,f319(a104,x45961))),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),f319(a104,f319(f319(f30(a925),x45961),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))))))
% 28.73/28.51 [4646]E(f319(f319(f74(a925),f319(f95(a925),f319(f319(f23(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))),a89))),x46461),f319(a104,f319(a104,f319(a104,x46461))))
% 28.73/28.51 [4712]E(f319(f249(a1,a1,f931(a1,a1)),f319(f319(f18(a1,f932(a1,f931(a1,a1)),f932(a1,f931(a1,a1))),f319(f319(f8(f932(a1,f932(f931(a1,a1),f931(a1,a1))),f932(f932(a1,f931(a1,a1)),f932(a1,f931(a1,a1))),a1),f18(a1,f931(a1,a1),f931(a1,a1))),f319(f319(f8(f932(a1,f931(a1,a1)),f932(a1,f932(f931(a1,a1),f931(a1,a1))),a1),f319(f18(a1,f931(a1,a1),f932(f931(a1,a1),f931(a1,a1))),f319(f319(f8(a923,f932(f931(a1,a1),f932(f931(a1,a1),f931(a1,a1))),a1),f86(f931(a1,a1))),f319(f319(f8(a1,a923,a1),f319(f226(a1),f2(a1))),f319(f319(f7(a1,a1,a1),f23(a1)),x47121))))),f319(f319(f7(a1,f932(a1,a1),f932(a1,f931(a1,a1))),f319(f319(f8(f932(a1,f931(a1,a1)),f932(f932(a1,a1),f932(a1,f931(a1,a1))),a1),f8(a1,f931(a1,a1),a1)),f319(f319(f8(a1,f932(a1,f931(a1,a1)),a1),f244(a1,a1)),f319(f319(f7(a1,a1,a1),f319(f319(f8(a1,f932(a1,a1),a1),f74(a1)),f319(f75(a1),f319(f95(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))))),f72(a1))))),f319(f319(f7(a1,a1,a1),f23(a1)),x47121))))),f319(f319(f8(a1,f932(a1,f931(a1,a1)),a1),f244(a1,a1)),f319(f75(a1),f319(f95(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))))))),f37(x47121))
% 28.73/28.51 [3421]P112(f931(x34211,x34212))
% 28.73/28.51 [3422]P112(f933(x34221,x34222))
% 28.73/28.51 [3423]P112(f930(x34231,x34232))
% 28.73/28.51 [3440]P14(a1,f170(x34401,x34402))
% 28.73/28.51 [3441]P38(x34411,f145(x34411,x34412))
% 28.73/28.51 [3442]P39(x34421,f255(x34421,x34422))
% 28.73/28.51 [3443]P39(x34431,f299(x34431,x34432))
% 28.73/28.51 [3444]P40(x34441,f255(x34441,x34442))
% 28.73/28.51 [3445]P56(x34451,f255(x34451,x34452))
% 28.73/28.51 [3511]P32(x35111,x35112,f105(x35111))
% 28.73/28.51 [3544]P57(x35441,x35442,f255(x35441,x35442))
% 28.73/28.51 [3545]P59(x35451,x35451,f255(x35451,x35452))
% 28.73/28.51 [3808]P26(x38081,x38081,f5(x38081),x38082)
% 28.73/28.51 [3809]P26(x38091,x38091,f25(x38091),x38092)
% 28.73/28.51 [3816]P33(x38161,x38162,f105(x38161),f105(x38161))
% 28.73/28.51 [3817]P33(x38171,x38172,f105(x38171),f105(x38171))
% 28.73/28.51 [3824]P26(f926(x38241),f926(x38241),f160(x38241),x38242)
% 28.73/28.51 [4226]P27(x42261,x42261,f25(x42261),x42262,x42262)
% 28.73/28.51 [4738]~P34(x47381,x47382,f105(x47381))
% 28.73/28.51 [4739]~P36(x47391,x47392,f105(x47391))
% 28.73/28.51 [3407]E(f319(f5(x34071),x34072),x34072)
% 28.73/28.51 [3408]E(f319(f254(x34081),x34082),x34082)
% 28.73/28.51 [3409]E(f319(f25(x34091),x34092),x34092)
% 28.73/28.51 [3410]E(f319(f25(x34101),x34102),x34102)
% 28.73/28.51 [3420]E(f319(f183(x34201),x34202),f107(x34201))
% 28.73/28.51 [3438]E(f79(x34381,f319(a316,x34382)),x34382)
% 28.73/28.51 [3439]E(f84(x34391,f319(a316,x34392)),x34392)
% 28.73/28.51 [3461]E(f319(f117(x34611,x34612),f111(x34611)),f2(a925))
% 28.73/28.51 [3467]E(f319(f128(x34671,x34672),f105(x34671)),f105(x34671))
% 28.73/28.51 [3487]E(f299(x34871,f299(x34871,x34872)),f299(x34871,x34872))
% 28.73/28.51 [3488]E(f144(x34881,f144(x34881,x34882)),f144(x34881,x34882))
% 28.73/28.51 [3506]E(f319(f319(f126(x35061),x35062),f105(x35061)),x35062)
% 28.73/28.51 [3512]E(f165(x35121,x35122,f105(x35121)),x35122)
% 28.73/28.51 [3513]E(f165(x35131,f105(x35131),x35132),x35132)
% 28.73/28.51 [3514]E(f108(x35141,f111(x35141),x35142),x35142)
% 28.73/28.51 [3515]E(f161(x35151,f2(a925),x35152),f105(x35151))
% 28.73/28.51 [3521]E(f319(f319(f167(x35211),x35212),f105(x35211)),f105(x35211))
% 28.73/28.51 [3522]E(f319(f319(f130(x35221),x35222),f105(x35221)),f105(x35221))
% 28.73/28.51 [3524]E(f147(x35241,x35242,f105(x35241)),f2(a925))
% 28.73/28.51 [3526]E(f162(x35261,x35262,f105(x35261)),f105(x35261))
% 28.73/28.51 [3527]E(f169(x35271,x35272,f105(x35271)),f105(x35271))
% 28.73/28.51 [3528]E(f168(x35281,f105(x35281),x35282),f105(x35281))
% 28.73/28.51 [3532]E(f319(f164(x35321),f144(x35321,x35322)),f319(f164(x35321),x35322))
% 28.73/28.51 [3535]E(f319(f276(x35351,x35351),f255(x35351,x35352)),x35352)
% 28.73/28.51 [3536]E(f319(f256(x35361,x35361),f255(x35361,x35362)),x35362)
% 28.73/28.51 [3543]E(f319(f278(x35431,x35431),f255(x35431,x35432)),f255(x35431,x35432))
% 28.73/28.51 [3556]E(f299(f926(x35561),f149(x35561,x35562)),f150(x35561,f299(x35561,x35562)))
% 28.73/28.51 [3558]P1(f319(f129(a1),f170(x35581,x35582)))
% 28.73/28.51 [3566]E(f319(f276(x35661,x35661),f299(x35661,x35662)),f234(f932(x35661,a923)))
% 28.73/28.51 [3567]E(f319(f256(x35671,x35671),f299(x35671,x35672)),f234(f932(x35671,a923)))
% 28.73/28.51 [3571]P1(f319(f129(x35711),f144(x35711,x35712)))
% 28.73/28.51 [3572]P1(f319(f152(x35721,x35722),f105(x35721)))
% 28.73/28.51 [3573]P1(f319(f152(x35731,x35732),f105(x35731)))
% 28.73/28.51 [3578]E(f319(f164(a1),f170(x35781,x35782)),f295(a1,x35781,x35782))
% 28.73/28.51 [3579]E(f319(f164(a1),f170(x35791,x35792)),f295(a1,x35791,x35792))
% 28.73/28.51 [3593]P60(x35931,f180(f932(x35931,a923)),x35932)
% 28.73/28.51 [3598]E(f319(f248(a1,a1),f40(x35981,x35982)),f39(a1,x35981,x35982))
% 28.73/28.51 [3599]E(f319(f294(a925,x35991),f319(a104,x35992)),f295(a925,x35991,x35992))
% 28.73/28.51 [3614]E(f319(f319(f143(x36141),x36142),f105(x36141)),f132(x36141,x36142,f105(x36141)))
% 28.73/28.51 [3626]E(f295(a925,f319(a104,x36261),x36262),f297(a925,x36261,x36262))
% 28.73/28.51 [3629]P57(x36291,f234(f932(x36291,a923)),f299(x36291,x36292))
% 28.73/28.51 [3691]E(f319(f319(f23(a925),x36911),f319(a104,x36912)),f319(f29(a925),f298(a925,x36912,x36911)))
% 28.73/28.51 [3746]E(f158(x37461,x37462,f105(x37461)),f319(f319(f244(f926(x37461),f926(x37461)),f105(x37461)),f105(x37461)))
% 28.73/28.51 [3764]E(f319(f249(x37641,x37642,f931(x37641,x37642)),f244(x37641,x37642)),f25(f931(x37641,x37642)))
% 28.73/28.51 [3768]P1(f319(f319(f321(f926(x37681)),f105(x37681)),f153(x37681,x37682)))
% 28.73/28.51 [3769]E(f319(f181(f926(x37691)),f106(x37691,x37692)),f319(f319(f23(a925),f319(f181(f926(x37691)),x37692)),f72(a925)))
% 28.73/28.51 [3777]P1(f319(f55(a925),f295(a925,x37771,x37772)))
% 28.73/28.51 [3778]P1(f319(f55(a925),f297(a925,x37781,x37782)))
% 28.73/28.51 [3779]P1(f319(f55(a925),f298(a925,x37791,x37792)))
% 28.73/28.51 [3780]P1(f319(f55(a1),f295(a1,x37801,x37802)))
% 28.73/28.51 [3781]P1(f319(f55(a1),f297(a1,x37811,x37812)))
% 28.73/28.51 [3782]P1(f319(f55(a1),f298(a1,x37821,x37822)))
% 28.73/28.51 [3885]E(f319(f302(a925,a925,a104),f295(a925,x38851,x38852)),f295(a925,f319(a104,x38851),f319(a104,x38852)))
% 28.73/28.51 [3907]E(f319(f319(f281(x39071,x39071,x39071),f299(x39071,x39072)),f299(x39071,x39072)),f299(x39071,x39072))
% 28.73/28.51 [3941]E(f319(f319(f244(a1,a1),f319(f319(f30(a1),x39411),x39412)),f39(a1,x39411,x39412)),f40(x39411,x39412))
% 28.73/28.51 [3942]E(f319(f319(f244(a91,a91),f319(f319(f30(a91),x39421),x39422)),f39(a91,x39421,x39422)),f21(x39421,x39422))
% 28.73/28.51 [3969]E(f319(f319(f244(a925,a925),f319(f319(f30(a925),x39691),x39692)),f39(a925,x39691,x39692)),f79(f931(a925,a925),f42(x39691,x39692)))
% 28.73/28.51 [4020]P1(f319(f319(f227(a925),f319(f319(f23(a925),x40201),x40202)),f319(a104,x40201)))
% 28.73/28.51 [4068]P39(x40681,f319(f319(f281(x40681,x40681,x40681),x40682),f299(x40681,x40682)))
% 28.73/28.51 [4108]E(f319(f319(f130(x41081),f319(f181(f926(x41081)),f169(x41081,x41082,f105(x41081)))),f105(x41081)),f105(x41081))
% 28.73/28.51 [4118]E(f319(f319(f74(a1),f319(f319(f75(a1),x41181),f319(f319(f30(a1),x41182),x41181))),f39(a1,x41182,x41181)),x41182)
% 28.73/28.51 [4122]E(f319(f319(f33(a925,f932(f931(f926(x41221),f926(x41221)),a923)),f234(f932(a925,a923))),f135(x41221,x41222)),f137(x41221,x41222))
% 28.73/28.51 [4201]E(f319(f128(x42011,f319(f319(f8(a923,a923,x42011),a314),f319(a316,x42012))),f105(x42011)),f105(x42011))
% 28.73/28.51 [4343]P1(f319(f319(f321(f931(f926(x43431),f926(x43431))),f319(f319(f244(f926(x43431),f926(x43431)),f105(x43431)),f105(x43431))),f150(x43431,x43432)))
% 28.73/28.51 [4452]E(f245(x44521,x44521,x44521,a316,f245(x44521,x44521,x44521,x44522,a316)),x44522)
% 28.73/28.51 [4495]E(f250(x44951,x44951,x44952,x44952,f25(x44951),f25(x44952)),f25(f931(x44951,x44952)))
% 28.73/28.51 [4496]E(f250(x44961,x44961,x44962,x44962,f5(x44961),f5(x44962)),f25(f931(x44961,x44962)))
% 28.73/28.51 [4497]E(f250(x44971,x44971,x44972,x44972,f25(x44971),f25(x44972)),f25(f931(x44971,x44972)))
% 28.73/28.51 [4498]E(f250(x44981,x44981,x44982,x44982,f25(x44981),f25(x44982)),f25(f931(x44981,x44982)))
% 28.73/28.51 [3505]E(f319(f160(x35051),f319(f160(x35051),x35052)),x35052)
% 28.73/28.51 [3507]E(f319(f319(f130(x35071),f2(a925)),x35072),x35072)
% 28.73/28.51 [3523]E(f319(f319(f167(x35231),f2(a925)),x35232),f105(x35231))
% 28.73/28.51 [3530]E(f319(f319(f126(x35301),f105(x35301)),x35302),x35302)
% 28.73/28.51 [3539]E(f31(f932(x35391,a923),f319(f300(x35391),x35392)),x35392)
% 28.73/28.51 [3541]E(f319(f164(x35411),f319(f159(x35411),x35412)),f319(f164(x35411),x35412))
% 28.73/28.51 [3542]E(f319(f164(x35421),f319(f160(x35421),x35422)),f319(f164(x35421),x35422))
% 28.73/28.51 [3547]E(f319(f319(f23(a91),x35471),x35472),f319(f319(a24,x35471),x35472))
% 28.73/28.51 [3560]E(f319(f319(f75(a925),x35601),x35602),f319(f319(f75(a925),x35602),x35601))
% 28.73/28.51 [3561]E(f319(f319(f75(a1),x35611),x35612),f319(f319(f75(a1),x35612),x35611))
% 28.73/28.51 [3562]E(f319(f319(f74(a925),x35621),x35622),f319(f319(f74(a925),x35622),x35621))
% 28.73/28.51 [3563]E(f319(f319(f74(a1),x35631),x35632),f319(f319(f74(a1),x35632),x35631))
% 28.73/28.51 [3585]E(f319(f319(f175(x35851,x35851),f2(a925)),x35852),f25(x35851))
% 28.73/28.51 [3586]E(f319(f181(f926(x35861)),f319(f159(x35861),x35862)),f319(f181(f926(x35861)),x35862))
% 28.73/28.51 [3587]E(f319(f181(f926(x35871)),f319(f160(x35871),x35872)),f319(f181(f926(x35871)),x35872))
% 28.73/28.51 [3588]E(f168(x35881,x35882,f180(f932(a925,a923))),f105(x35881))
% 28.73/28.51 [3589]E(f319(f319(f146(x35891,x35891),f5(x35891)),x35892),x35892)
% 28.73/28.51 [3591]E(f319(f243(a1,a1),f40(x35911,x35912)),f319(f319(f30(a1),x35911),x35912))
% 28.73/28.51 [3608]E(f319(f181(f926(x36081)),f144(x36081,x36082)),f319(f29(x36081),f319(f164(x36081),x36082)))
% 28.73/28.51 [3609]E(f319(f273(x36091),f319(f278(x36091,x36091),x36092)),f319(f273(x36091),x36092))
% 28.73/28.51 [3613]P1(f319(f55(x36131),f319(f164(x36131),x36132)))
% 28.73/28.51 [3620]E(f319(f319(f74(a1),x36201),f319(f73(a1),x36202)),f319(f319(f23(a1),x36201),x36202))
% 28.73/28.51 [3621]E(f319(f319(f74(a1),x36211),f319(f73(a1),x36212)),f319(f319(f23(a1),x36211),x36212))
% 28.73/28.51 [3627]P15(x36271,x36272,f180(f932(f924(x36271),a923)))
% 28.73/28.51 [3628]P15(x36281,x36282,f180(f932(f924(x36281),a923)))
% 28.73/28.51 [3630]E(f319(f302(x36301,x36301,f5(x36301)),x36302),x36302)
% 28.73/28.51 [3631]E(f319(f302(x36311,x36311,f25(x36311)),x36312),x36312)
% 28.73/28.51 [3632]E(f319(f303(x36321,x36321,f5(x36321)),x36322),x36322)
% 28.73/28.51 [3633]E(f319(f303(x36331,x36331,f25(x36331)),x36332),x36332)
% 28.73/28.51 [3634]P1(f319(f234(f932(x36341,a923)),x36342))
% 28.73/28.51 [3636]E(f319(f29(a925),f319(f294(a925,x36361),x36362)),f319(f319(f23(a925),x36362),x36361))
% 28.73/28.51 [3637]E(f319(f294(a925,f319(a104,x36371)),x36372),f298(a925,x36371,x36372))
% 28.73/28.51 [3650]E(f319(f319(f301(x36501),x36502),f180(f932(x36501,a923))),f319(f254(x36501),f319(a316,x36502)))
% 28.73/28.51 [3655]E(f299(x36551,f319(f278(x36551,x36551),x36552)),f319(f278(x36551,x36551),f299(x36551,x36552)))
% 28.73/28.51 [3660]E(f319(f319(f74(a925),f319(a104,x36601)),x36602),f319(f319(f74(a925),x36601),f319(a104,x36602)))
% 28.73/28.51 [3661]E(f319(f319(f23(a925),f319(a104,x36611)),f319(a104,x36612)),f319(f319(f23(a925),x36611),x36612))
% 28.73/28.51 [3667]E(f49(x36671,f2(a925),x36672),f319(f319(f143(f926(x36671)),f105(x36671)),f105(f926(x36671))))
% 28.73/28.51 [3668]E(f319(f29(a925),f297(a925,x36681,x36682)),f319(f319(f23(a925),x36682),x36681))
% 28.73/28.51 [3677]P38(x36771,f319(f319(f280(a925,x36771),a232),x36772))
% 28.73/28.51 [3679]P14(a925,f131(a925,f319(f294(a925,x36791),x36792)))
% 28.73/28.51 [3681]P1(f319(f55(a925),f319(f294(a925,x36811),x36812)))
% 28.73/28.51 [3682]P1(f319(f55(a1),f319(f294(a1,x36821),x36822)))
% 28.73/28.51 [3685]E(f319(f278(f926(x36851),f926(x36851)),f149(x36851,x36852)),f149(x36851,f319(f278(x36851,x36851),x36852)))
% 28.73/28.51 [3687]E(f319(f294(a1,x36871),f319(f319(f74(a1),x36872),f72(a1))),f295(a1,x36871,x36872))
% 28.73/28.51 [3690]E(f319(f319(f30(a1),f319(f73(a1),x36901)),f319(f73(a1),x36902)),f319(f319(f30(a1),x36901),x36902))
% 28.73/28.51 [3698]E(f319(f319(f175(f931(x36981,x36981),a923),f72(a925)),x36982),x36982)
% 28.73/28.51 [3700]E(f319(f319(f102(f932(x37001,a923)),x37002),f180(f932(x37001,a923))),x37002)
% 28.73/28.51 [3701]E(f319(f319(f93(f932(x37011,a923)),x37012),f234(f932(x37011,a923))),x37012)
% 28.73/28.51 [3702]E(f319(f319(f23(f932(x37021,a923)),x37022),f180(f932(x37021,a923))),x37022)
% 28.73/28.51 [3703]E(f319(f243(a925,a925),f79(f931(a925,a925),f42(x37031,x37032))),f319(f319(f30(a925),x37031),x37032))
% 28.73/28.51 [3709]E(f295(a1,f319(f319(f74(a1),x37091),f72(a1)),x37092),f297(a1,x37091,x37092))
% 28.73/28.51 [3714]E(f319(f248(a925,a925),f79(f931(a925,a925),f42(x37141,x37142))),f39(a925,x37141,x37142))
% 28.73/28.51 [3723]P1(f319(f319(f321(x37231),x37232),f234(f932(x37231,a923))))
% 28.73/28.51 [3724]P1(f319(f319(f321(x37241),x37242),f234(f932(x37241,a923))))
% 28.73/28.51 [3729]E(f319(f319(f23(a925),f319(a104,x37291)),x37292),f319(f29(a925),f295(a925,x37292,x37291)))
% 28.73/28.51 [3755]E(f319(f319(f102(f932(x37551,a923)),x37552),f234(f932(x37551,a923))),f234(f932(x37551,a923)))
% 28.73/28.51 [3756]E(f319(f319(f93(f932(x37561,a923)),x37562),f180(f932(x37561,a923))),f180(f932(x37561,a923)))
% 28.73/28.51 [3757]E(f319(f319(f23(f932(x37571,a923)),x37572),f234(f932(x37571,a923))),f180(f932(x37571,a923)))
% 28.73/28.51 [3771]E(f39(a1,f319(f92(a1),x37711),f319(f92(a1),x37712)),f319(f92(a1),f39(a925,x37711,x37712)))
% 28.73/28.51 [3772]E(f39(a1,f319(f73(a1),x37721),f319(f73(a1),x37722)),f319(f73(a1),f39(a1,x37721,x37722)))
% 28.73/28.51 [3773]E(f39(a1,f319(f92(a1),x37731),f319(f92(a1),x37732)),f319(f92(a1),f39(a925,x37731,x37732)))
% 28.73/28.51 [3784]E(f319(f181(f926(x37841)),f319(f163(x37841),x37842)),f319(f319(f23(a925),f319(f181(f926(x37841)),x37842)),f72(a925)))
% 28.73/28.51 [3810]E(f319(f319(f30(a1),f39(a1,x38101,x38102)),x38102),f2(a1))
% 28.73/28.51 [3819]E(f319(a3,f39(a925,f319(a20,x38191),f319(a20,x38192))),f39(a91,x38191,x38192))
% 28.73/28.51 [3852]E(f319(a3,f319(f319(f23(a925),f319(a20,x38521)),f319(a20,x38522))),f319(f319(f23(a91),x38521),x38522))
% 28.73/28.51 [3853]E(f319(a3,f319(f319(f75(a925),f319(a20,x38531)),f319(a20,x38532))),f319(f319(f75(a91),x38531),x38532))
% 28.73/28.51 [3854]E(f319(a3,f319(f319(f74(a925),f319(a20,x38541)),f319(a20,x38542))),f319(f319(f74(a91),x38541),x38542))
% 28.73/28.51 [3855]E(f319(a3,f319(f319(f30(a925),f319(a20,x38551)),f319(a20,x38552))),f319(f319(f30(a91),x38551),x38552))
% 28.73/28.51 [3863]E(f319(f302(a925,a925,a104),f319(f294(a925,x38631),x38632)),f319(f294(a925,f319(a104,x38631)),f319(a104,x38632)))
% 28.73/28.51 [3890]P1(f319(f42(x38901,x38902),f79(f931(a925,a925),f42(x38901,x38902))))
% 28.73/28.51 [3916]E(f39(a925,f319(a104,f39(a925,x39161,x39162)),x39162),f39(a925,f319(a104,x39161),x39162))
% 28.73/28.51 [3928]E(f319(f319(f34(f932(x39281,a923),f932(x39281,a923)),x39282),f5(f932(x39281,a923))),f32(f932(x39281,a923),x39282))
% 28.73/28.51 [3929]E(f319(f319(f33(f932(x39291,a923),f932(x39291,a923)),x39292),f5(f932(x39291,a923))),f31(f932(x39291,a923),x39292))
% 28.73/28.51 [3930]E(f319(f302(f926(x39301),f932(x39301,a923),f164(x39301)),f319(f164(f926(x39301)),f48(x39301,x39302))),f319(f300(x39301),f319(f164(x39301),x39302)))
% 28.73/28.51 [3934]P1(f319(f319(f321(f932(x39341,a923)),x39342),f319(f300(x39341),x39342)))
% 28.73/28.51 [3940]E(f39(a1,f319(f73(a1),f39(a1,x39401,x39402)),x39402),f39(a1,f319(f73(a1),x39401),x39402))
% 28.73/28.51 [3951]P1(f319(f319(f226(f932(x39511,a923)),x39512),f234(f932(x39511,a923))))
% 28.73/28.51 [3953]E(f319(f319(f281(x39531,x39531,x39531),f299(x39531,x39532)),f299(x39531,f299(x39531,x39532))),f299(x39531,x39532))
% 28.73/28.51 [3954]E(f319(f319(f102(f932(x39541,a923)),f319(f256(x39541,x39541),x39542)),f319(f276(x39541,x39541),x39542)),f319(f273(x39541),x39542))
% 28.73/28.51 [3975]E(f305(x39751,x39752,f234(f932(x39751,a923)),f234(f932(x39752,a923))),f234(f932(f933(x39751,x39752),a923)))
% 28.73/28.51 [4025]P1(f319(f319(f226(a925),f39(a925,x40251,x40252)),x40251))
% 28.73/28.51 [4049]P1(f319(f319(f226(a1),f319(f73(a1),f319(f92(a1),x40491))),f319(f92(a1),x40492)))
% 28.73/28.51 [4073]P1(f319(f319(f321(f932(x40731,a923)),f180(f932(x40731,a923))),f319(f300(x40731),x40732)))
% 28.73/28.51 [4078]E(f299(x40781,f319(f319(f281(x40781,x40781,x40781),x40782),f299(x40781,x40782))),f299(x40781,x40782))
% 28.73/28.51 [4080]E(f319(f319(f281(x40801,x40801,x40801),f299(x40801,x40802)),x40802),f319(f319(f281(x40801,x40801,x40801),x40802),f299(x40801,x40802)))
% 28.73/28.51 [4081]E(f319(f319(f281(x40811,x40811,x40811),f299(x40811,x40812)),x40812),f319(f319(f281(x40811,x40811,x40811),x40812),f299(x40811,x40812)))
% 28.73/28.51 [4083]E(f319(a96,f319(f319(f74(a1),f319(f319(f23(a1),x40831),x40832)),f72(a1))),f319(f29(a1),f295(a1,x40832,x40831)))
% 28.73/28.51 [4098]E(f319(f276(x40981,x40981),f319(f319(f281(x40981,x40981,x40981),x40982),f299(x40981,x40982))),f319(f276(x40981,x40981),x40982))
% 28.73/28.51 [4099]E(f319(f256(x40991,x40991),f319(f319(f281(x40991,x40991,x40991),x40992),f299(x40991,x40992))),f319(f256(x40991,x40991),x40992))
% 28.73/28.51 [4117]E(f319(f134(f926(x41171),f926(x41171),f126(x41171),f105(x41171)),f161(f926(x41171),x41172,f105(x41171))),f105(x41171))
% 28.73/28.51 [4126]P26(a925,a925,f319(f319(f7(a925,a925,a925),f74(a925)),x41261),x41262)
% 28.73/28.51 [4128]P14(a925,f319(f160(a925),f319(f319(f146(f926(x41281),a925),f181(f926(x41281))),f171(x41281,x41282))))
% 28.73/28.51 [4158]P56(x41581,f319(f319(f102(f932(f931(x41581,x41581),a923)),x41582),f319(f278(x41581,x41581),x41582)))
% 28.73/28.51 [4159]P56(x41591,f319(f319(f93(f932(f931(x41591,x41591),a923)),x41592),f319(f278(x41591,x41591),x41592)))
% 28.73/28.51 [4170]P1(f319(f319(f227(a1),f319(f73(a1),f319(f92(a1),f319(a104,x41701)))),f319(f92(a1),x41702)))
% 28.73/28.51 [4215]E(f319(f134(f926(x42151),x42151,f319(f7(x42151,f926(x42151),f926(x42151)),f143(x42151)),f105(x42151)),x42152),f319(f160(x42151),x42152))
% 28.73/28.51 [4264]P1(f319(f319(f226(f932(f931(f926(x42641),f926(x42641)),a923)),f150(x42641,x42642)),f299(f926(x42641),f149(x42641,x42642))))
% 28.73/28.51 [4293]P1(f319(f42(x42931,x42932),f319(f319(f244(a925,a925),f319(f319(f30(a925),x42931),x42932)),f39(a925,x42931,x42932))))
% 28.73/28.51 [4305]P1(f319(f319(f226(f932(f931(f926(x43051),f926(x43051)),a923)),f149(x43051,f299(x43051,x43052))),f299(f926(x43051),f149(x43051,x43052))))
% 28.73/28.51 [4521]E(f319(f319(f251(f931(a91,a91),a91,f931(a91,a91),f931(x45211,f931(a91,a91))),f259(f319(f157(a91),f319(f319(f146(f931(a91,x45211),a91),f243(a91,x45211)),x45212)))),f319(f319(f8(x45211,f932(f931(a91,a91),f931(x45211,f931(a91,a91))),a91),f244(x45211,f931(a91,a91))),f260(x45211,x45212))),f258(x45211,x45212))
% 28.73/28.51 [4598]E(f215(a925,f931(x45981,f927(x45981)),f2(a925),f319(f249(x45981,f927(x45981),a925),f319(f16(f932(f927(x45981),a925),x45981),f319(f319(f7(f927(x45981),a925,a925),f319(f319(f8(a925,f932(a925,a925),f927(x45981)),f74(a925)),f181(f927(x45981)))),f72(a925)))),f319(f127(x45981),x45982)),f319(f181(f927(x45981)),x45982))
% 28.73/28.51 [4672]E(f39(a925,f319(f319(f74(a925),f319(f95(a925),f319(f319(f23(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))),a89))),x46721),f319(f95(a925),x46722)),f39(a925,f319(a104,f319(a104,f319(a104,x46721))),f319(f95(a925),x46722)))
% 28.73/28.51 [4685]E(f319(f319(f30(a925),f319(f319(f74(a925),f319(f95(a925),f319(f319(f23(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))),a89))),x46851)),f319(f95(a925),x46852)),f319(f319(f30(a925),f319(a104,f319(a104,f319(a104,x46851)))),f319(f95(a925),x46852)))
% 28.73/28.51 [4704]E(f319(f249(f932(f931(x47041,x47041),a923),f932(f931(x47041,x47041),a923),f932(f932(x47042,x47041),f931(f932(f931(x47042,x47042),a923),f932(f931(x47042,x47042),a923)))),f319(f319(f7(f932(f931(x47041,x47041),a923),f932(f932(f931(x47041,x47041),a923),f932(f932(x47042,x47041),f932(f931(x47042,x47042),a923))),f932(f932(f931(x47041,x47041),a923),f932(f932(x47042,x47041),f931(f932(f931(x47042,x47042),a923),f932(f931(x47042,x47042),a923))))),f319(f319(f8(f932(f932(f932(x47042,x47041),f932(f931(x47042,x47042),a923)),f932(f932(x47042,x47041),f931(f932(f931(x47042,x47042),a923),f932(f931(x47042,x47042),a923)))),f932(f932(f932(f931(x47041,x47041),a923),f932(f932(x47042,x47041),f932(f931(x47042,x47042),a923))),f932(f932(f931(x47041,x47041),a923),f932(f932(x47042,x47041),f931(f932(f931(x47042,x47042),a923),f932(f931(x47042,x47042),a923))))),f932(f931(x47041,x47041),a923)),f8(f932(f932(x47042,x47041),f932(f931(x47042,x47042),a923)),f932(f932(x47042,x47041),f931(f932(f931(x47042,x47042),a923),f932(f931(x47042,x47042),a923))),f932(f931(x47041,x47041),a923))),f319(f319(f8(f932(f932(x47042,x47041),f932(f932(f931(x47042,x47042),a923),f931(f932(f931(x47042,x47042),a923),f932(f931(x47042,x47042),a923)))),f932(f932(f932(x47042,x47041),f932(f931(x47042,x47042),a923)),f932(f932(x47042,x47041),f931(f932(f931(x47042,x47042),a923),f932(f931(x47042,x47042),a923)))),f932(f931(x47041,x47041),a923)),f18(f932(x47042,x47041),f932(f931(x47042,x47042),a923),f931(f932(f931(x47042,x47042),a923),f932(f931(x47042,x47042),a923)))),f319(f319(f8(f932(f932(x47042,x47041),f932(f931(x47042,x47042),a923)),f932(f932(x47042,x47041),f932(f932(f931(x47042,x47042),a923),f931(f932(f931(x47042,x47042),a923),f932(f931(x47042,x47042),a923)))),f932(f931(x47041,x47041),a923)),f319(f8(f932(f931(x47042,x47042),a923),f932(f932(f931(x47042,x47042),a923),f931(f932(f931(x47042,x47042),a923),f932(f931(x47042,x47042),a923))),f932(x47042,x47041)),f244(f932(f931(x47042,x47042),a923),f932(f931(x47042,x47042),a923)))),f280(x47041,x47042))))),f280(x47041,x47042))),f67(x47041,x47042))
% 28.73/28.51 [4750]~E(f319(f300(x47501),x47502),f180(f932(f932(x47501,a923),a923)))
% 28.73/28.51 [4759]~P1(f319(f319(f164(x47591),f105(x47591)),x47592))
% 28.73/28.51 [4762]~P1(f319(f319(f321(x47621),x47622),f180(f932(x47621,a923))))
% 28.73/28.51 [4763]~P1(f319(f319(f321(x47631),x47632),f180(f932(x47631,a923))))
% 28.73/28.51 [4771]~P1(f319(f319(f227(f932(x47711,a923)),x47712),f180(f932(x47711,a923))))
% 28.73/28.51 [3639]E(f319(f319(f23(a925),x36391),f319(f319(f74(a925),x36391),x36392)),f2(a925))
% 28.73/28.51 [3642]E(f319(f319(f102(f932(x36421,a923)),x36422),x36422),x36422)
% 28.73/28.51 [3643]E(f319(f319(f93(f932(x36431,a923)),x36432),x36432),x36432)
% 28.73/28.51 [3671]E(f319(f319(f23(f932(x36711,a923)),x36712),x36712),f180(f932(x36711,a923)))
% 28.73/28.51 [3674]E(f319(f135(x36741,x36742),f2(a925)),f180(f932(f931(f926(x36741),f926(x36741)),a923)))
% 28.73/28.51 [3675]E(f319(f319(f74(a925),x36751),f319(a104,x36752)),f319(a104,f319(f319(f74(a925),x36751),x36752)))
% 28.73/28.51 [3686]E(f186(f319(f92(a1),x36861),f319(f92(a1),x36862)),f319(f92(a1),f319(f319(f23(a925),x36861),x36862)))
% 28.73/28.51 [3689]E(f319(f319(f30(a1),f319(f73(a1),x36891)),x36892),f319(f319(f30(a1),x36891),f319(f73(a1),x36892)))
% 28.73/28.51 [3693]E(f319(f29(a1),f319(f294(a1,x36931),x36932)),f319(a96,f319(f319(f23(a1),x36932),x36931)))
% 28.73/28.51 [3696]E(f319(f319(f74(a925),f319(a104,x36961)),x36962),f319(a104,f319(f319(f74(a925),x36961),x36962)))
% 28.73/28.51 [3699]E(f319(f73(f932(x36991,a923)),f319(f73(f932(x36991,a923)),x36992)),x36992)
% 28.73/28.51 [3711]E(f171(x37111,f319(f319(f143(f926(x37111)),f105(x37111)),x37112)),f171(x37111,x37112))
% 28.73/28.51 [3715]E(f319(f319(f74(a925),x37151),f319(f319(f75(a925),x37151),x37152)),f319(f319(f75(a925),x37151),f319(a104,x37152)))
% 28.73/28.51 [3722]E(f319(f319(a24,f319(a3,x37221)),f319(a3,x37222)),f319(a3,f319(f319(f23(a925),x37221),x37222)))
% 28.73/28.51 [3736]E(f319(f319(f236(a1),f319(f92(a1),x37361)),x37362),f319(f92(a1),f319(f319(f236(a925),x37361),x37362)))
% 28.73/28.51 [3737]E(f319(f319(f75(a1),f319(f73(a1),x37371)),x37372),f319(f73(a1),f319(f319(f75(a1),x37371),x37372)))
% 28.73/28.51 [3738]E(f319(f319(f236(a1),f319(f92(a1),x37381)),x37382),f319(f92(a1),f319(f319(f236(a925),x37381),x37382)))
% 28.73/28.51 [3739]E(f319(f319(f236(a1),f319(f92(a1),x37391)),x37392),f319(f92(a1),f319(f319(f236(a925),x37391),x37392)))
% 28.73/28.51 [3740]E(f319(f319(f75(a91),f319(a3,x37401)),f319(a3,x37402)),f319(a3,f319(f319(f75(a925),x37401),x37402)))
% 28.73/28.51 [3741]E(f319(f319(f74(a91),f319(a3,x37411)),f319(a3,x37412)),f319(a3,f319(f319(f74(a925),x37411),x37412)))
% 28.73/28.51 [3742]E(f319(f319(f224(a925),f319(a104,x37421)),f319(a104,x37422)),f319(a104,f319(f319(f224(a925),x37421),x37422)))
% 28.73/28.51 [3743]E(f319(f319(f225(a925),f319(a104,x37431)),f319(a104,x37432)),f319(a104,f319(f319(f225(a925),x37431),x37432)))
% 28.73/28.51 [3747]E(f319(f164(a925),f131(a925,f319(f294(a925,x37471),x37472))),f319(f294(a925,x37471),x37472))
% 28.73/28.51 [3748]E(f319(f164(a925),f131(a925,f319(f294(a925,x37481),x37482))),f319(f294(a925,x37481),x37482))
% 28.73/28.51 [3749]E(f304(x37491,f319(f319(f301(x37491),x37492),f180(f932(x37491,a923)))),x37492)
% 28.73/28.51 [3753]E(f319(f276(x37531,x37532),f180(f932(f931(x37531,x37532),a923))),f180(f932(x37532,a923)))
% 28.73/28.51 [3754]E(f319(f256(x37541,x37542),f180(f932(f931(x37541,x37542),a923))),f180(f932(x37541,a923)))
% 28.73/28.51 [3758]E(f319(a96,f319(f319(f23(a1),x37581),x37582)),f319(f29(a1),f297(a1,x37582,x37581)))
% 28.73/28.51 [3763]E(f319(f319(f74(a925),x37631),f319(f319(f75(a925),x37632),x37631)),f319(f319(f75(a925),f319(a104,x37632)),x37631))
% 28.73/28.51 [3765]E(f319(f319(f54(x37651),f180(f932(x37651,a923))),x37652),f180(f932(f932(x37651,a923),a923)))
% 28.73/28.51 [3774]E(f319(f181(f926(a925)),f131(a925,f319(f294(a925,x37741),x37742))),f319(f319(f23(a925),x37742),x37741))
% 28.73/28.51 [3789]E(f319(f319(f102(f932(x37891,a923)),f180(f932(x37891,a923))),x37892),x37892)
% 28.73/28.51 [3790]E(f319(f319(f93(f932(x37901,a923)),f234(f932(x37901,a923))),x37902),x37902)
% 28.73/28.51 [3791]E(f319(f319(f74(a1),f319(f73(a1),x37911)),f319(f73(a1),x37912)),f319(f73(a1),f319(f319(f74(a1),x37911),x37912)))
% 28.73/28.51 [3793]E(f319(f319(f75(a1),f319(f92(a1),x37931)),f319(f92(a1),x37932)),f319(f92(a1),f319(f319(f75(a925),x37931),x37932)))
% 28.73/28.51 [3794]E(f319(f319(f30(a1),f319(f92(a1),x37941)),f319(f92(a1),x37942)),f319(f92(a1),f319(f319(f30(a925),x37941),x37942)))
% 28.73/28.51 [3795]E(f319(f319(f75(a1),f319(f92(a1),x37951)),f319(f92(a1),x37952)),f319(f92(a1),f319(f319(f75(a925),x37951),x37952)))
% 28.73/28.51 [3796]E(f319(f319(f75(a1),f319(f92(a1),x37961)),f319(f92(a1),x37962)),f319(f92(a1),f319(f319(f75(a925),x37961),x37962)))
% 28.73/28.51 [3797]E(f319(f319(f75(a1),f319(f95(a1),x37971)),f319(f95(a1),x37972)),f319(f95(a1),f319(f319(f75(a1),x37971),x37972)))
% 28.73/28.51 [3798]E(f319(f319(f74(a1),f319(f92(a1),x37981)),f319(f92(a1),x37982)),f319(f92(a1),f319(f319(f74(a925),x37981),x37982)))
% 28.73/28.51 [3799]E(f319(f319(f74(a1),f319(f92(a1),x37991)),f319(f92(a1),x37992)),f319(f92(a1),f319(f319(f74(a925),x37991),x37992)))
% 28.73/28.51 [3800]E(f319(f319(f74(a1),f319(f95(a1),x38001)),f319(f95(a1),x38002)),f319(f95(a1),f319(f319(f74(a1),x38001),x38002)))
% 28.73/28.51 [3801]E(f319(f319(f30(a1),f319(f92(a1),x38011)),f319(f92(a1),x38012)),f319(f92(a1),f319(f319(f30(a925),x38011),x38012)))
% 28.73/28.51 [3820]E(f319(f319(f6(x38201,a925),f319(f16(a925,x38201),f72(a925))),x38202),f319(f29(x38201),x38202))
% 28.73/28.51 [3825]E(f319(f73(a1),f39(a1,f319(f73(a1),x38251),x38252)),f39(a1,x38251,f319(f73(a1),x38252)))
% 28.73/28.51 [3827]E(f319(f164(a1),f170(x38271,f319(f319(f23(a1),x38272),f72(a1)))),f319(f294(a1,x38271),x38272))
% 28.73/28.51 [3832]P1(f319(f319(f226(a925),x38321),f319(f319(f74(a925),x38322),x38321)))
% 28.73/28.51 [3833]P1(f319(f319(f226(a925),x38331),f319(f319(f74(a925),x38331),x38332)))
% 28.73/28.51 [3835]E(f319(f319(f102(f932(x38351,a923)),f234(f932(x38351,a923))),x38352),f234(f932(x38351,a923)))
% 28.73/28.51 [3836]E(f319(f319(f93(f932(x38361,a923)),f180(f932(x38361,a923))),x38362),f180(f932(x38361,a923)))
% 28.73/28.51 [3837]E(f319(f319(f23(f932(x38371,a923)),f180(f932(x38371,a923))),x38372),f180(f932(x38371,a923)))
% 28.73/28.51 [3844]E(f319(f319(f244(a1,a1),x38441),f319(f73(a1),x38442)),f319(a45,f319(f319(f244(a1,a1),x38441),x38442)))
% 28.73/28.51 [3845]E(f319(f294(a1,f319(f319(f74(a1),x38451),f72(a1))),x38452),f298(a1,x38451,x38452))
% 28.73/28.51 [3856]E(f319(f319(f75(a925),x38561),f319(f319(f30(a925),x38562),x38561)),f319(f319(f23(a925),x38562),f39(a925,x38562,x38561)))
% 28.73/28.51 [3857]E(f319(f319(f75(a1),x38571),f319(f319(f30(a1),x38572),x38571)),f319(f319(f23(a1),x38572),f39(a1,x38572,x38571)))
% 28.73/28.51 [3860]E(f319(f164(a1),f170(f319(f319(f74(a1),x38601),f72(a1)),x38602)),f297(a1,x38601,x38602))
% 28.73/28.51 [3864]P1(f319(f319(f226(f932(x38641,a923)),x38642),x38642))
% 28.73/28.51 [3867]E(f319(f319(f102(f932(x38671,a923)),x38672),f319(f73(f932(x38671,a923)),x38672)),f234(f932(x38671,a923)))
% 28.73/28.51 [3868]E(f319(f319(f93(f932(x38681,a923)),x38682),f319(f73(f932(x38681,a923)),x38682)),f180(f932(x38681,a923)))
% 28.73/28.51 [3876]E(f319(f319(f23(a925),f319(f319(f23(a925),x38761),f72(a925))),x38762),f319(f319(f23(a925),x38761),f319(a104,x38762)))
% 28.73/28.51 [3882]E(f319(f319(f23(f932(x38821,a923)),f234(f932(x38821,a923))),x38822),f319(f73(f932(x38821,a923)),x38822))
% 28.73/28.51 [3883]E(f319(f319(f23(a1),f319(f95(a1),x38831)),f319(f95(a1),x38832)),f319(f95(a1),f319(f319(f74(a1),x38831),f319(f73(a1),x38832))))
% 28.73/28.51 [3896]E(f319(f164(a925),f131(a925,f319(f294(a925,x38961),f319(a104,x38962)))),f295(a925,x38961,x38962))
% 28.73/28.51 [3914]E(f319(f181(f926(f926(x39141))),f48(x39141,x39142)),f319(f319(f236(a925),f319(a104,f319(a104,f2(a925)))),f319(f181(f926(x39141)),x39142)))
% 28.73/28.51 [3932]E(f319(f319(f175(f931(x39321,x39321),a923),f2(a925)),x39322),f299(x39321,f180(f932(f931(x39321,x39321),a923))))
% 28.73/28.51 [3936]P1(f319(f129(a925),f131(a925,f319(f294(a925,x39361),x39362))))
% 28.73/28.51 [3952]E(f319(f302(a1,a925,a96),f295(a1,f319(f92(a1),x39521),f319(f92(a1),x39522))),f295(a925,x39521,x39522))
% 28.73/28.51 [3961]E(f177(a925,f2(a925),f5(a925),f319(f319(f23(a925),x39611),x39612)),f319(f319(f23(a925),x39611),f319(a104,x39612)))
% 28.73/28.51 [3962]E(f319(a96,f319(f319(f23(a1),x39621),f319(f319(f74(a1),x39622),f72(a1)))),f319(f29(a1),f298(a1,x39622,x39621)))
% 28.73/28.51 [3997]E(f319(f319(f146(a925,a925),a104),f131(a925,f319(f294(a925,x39971),x39972))),f131(a925,f319(f294(a925,f319(a104,x39971)),f319(a104,x39972))))
% 28.73/28.51 [4005]E(f319(f164(a1),f170(f319(f319(f74(a1),x40051),f72(a1)),f319(f319(f23(a1),x40052),f72(a1)))),f298(a1,x40051,x40052))
% 28.73/28.51 [4017]P1(f319(f319(f226(f932(x40171,a923)),f180(f932(x40171,a923))),x40172))
% 28.73/28.51 [4021]E(f79(x40211,f319(f319(f7(x40211,x40211,a923),a316),x40212)),x40212)
% 28.73/28.51 [4022]E(f84(x40221,f319(f319(f7(x40221,x40221,a923),a316),x40222)),x40222)
% 28.73/28.51 [4026]E(f319(f164(a925),f131(a925,f319(f294(a925,f319(a104,x40261)),f319(a104,x40262)))),f297(a925,x40261,x40262))
% 28.73/28.51 [4052]E(f319(f319(f246(x40521,x40522),f234(f932(x40521,a923))),f319(f16(f932(x40522,a923),x40521),f234(f932(x40522,a923)))),f234(f932(f931(x40521,x40522),a923)))
% 28.73/28.51 [4085]E(f319(f254(x40851),f319(f319(f8(a923,a923,x40851),a314),x40852)),f319(f73(f932(x40851,a923)),f319(f254(x40851),x40852)))
% 28.73/28.51 [4088]E(f319(f254(x40881),f319(f319(f7(x40881,x40881,a923),a316),x40882)),f319(f319(f301(x40881),x40882),f180(f932(x40881,a923))))
% 28.73/28.51 [4095]E(f319(f319(f74(a1),f319(f319(f23(a1),x40951),x40952)),f319(f319(f23(a1),x40951),x40952)),f319(f319(f23(a1),f319(f319(f74(a1),x40951),x40951)),f319(f319(f74(a1),x40952),x40952)))
% 28.73/28.51 [4096]E(f319(f319(f74(a1),f319(f319(f74(a1),x40961),x40961)),f319(f319(f74(a1),x40962),x40962)),f319(f319(f74(a1),f319(f319(f74(a1),x40961),x40962)),f319(f319(f74(a1),x40961),x40962)))
% 28.73/28.51 [4112]P1(f319(f319(f226(a925),f319(f29(x41121),f319(f164(x41121),x41122))),f319(f181(f926(x41121)),x41122)))
% 28.73/28.51 [4113]P1(f319(f319(f226(a925),f319(f181(f926(x41131)),f144(x41131,x41132))),f319(f181(f926(x41131)),x41132)))
% 28.73/28.51 [4123]E(f319(f254(x41231),f319(f319(f7(x41231,f932(x41231,a923),a923),f321(x41231)),x41232)),x41232)
% 28.73/28.51 [4137]E(f319(f319(f167(x41371),f319(f319(f23(a925),f319(f181(f926(x41371)),x41372)),f72(a925))),x41372),f106(x41371,x41372))
% 28.73/28.51 [4157]E(f177(a925,f2(a925),f319(f319(f8(a925,a925,a925),a104),f319(f224(a925),x41571)),x41572),f319(f319(f224(a925),f319(a104,x41571)),x41572))
% 28.73/28.51 [4162]E(f31(f932(x41621,a923),f319(f302(f932(f931(x41621,x41621),a923),f932(x41621,a923),f273(x41621)),x41622)),f319(f273(x41621),f31(f932(f931(x41621,x41621),a923),x41622)))
% 28.73/28.51 [4163]E(f177(a925,f319(a104,x41631),f319(f319(f8(a925,a925,a925),a104),f319(f225(a925),x41631)),x41632),f319(f319(f225(a925),f319(a104,x41631)),x41632))
% 28.73/28.51 [4165]E(f319(f319(f244(a1,a1),f319(f319(f30(a1),f319(f69(a1),x41651)),f319(f69(a1),x41652))),f39(a1,f319(f69(a1),x41651),f319(f69(a1),x41652))),f47(x41651,x41652))
% 28.73/28.51 [4188]P1(f319(f319(f226(f932(f932(x41881,a923),a923)),x41882),f319(f300(x41881),f31(f932(x41881,a923),x41882))))
% 28.73/28.51 [4220]E(f319(f319(f33(x42201,f932(x42201,a923)),x42202),f319(f319(f7(x42201,f932(x42201,a923),f932(x42201,a923)),f301(x42201)),f180(f932(x42201,a923)))),x42202)
% 28.73/28.51 [4221]E(f319(f319(f281(x42211,x42211,x42211),f319(f278(x42211,x42211),x42212)),f299(x42211,f319(f278(x42211,x42211),x42212))),f319(f278(x42211,x42211),f319(f319(f281(x42211,x42211,x42211),x42212),f299(x42211,x42212))))
% 28.73/28.51 [4285]E(f319(f164(x42851),f319(f134(f926(x42851),f926(x42851),f126(x42851),f105(x42851)),x42852)),f319(f319(f33(f926(x42851),f932(x42851,a923)),f319(f164(f926(x42851)),x42852)),f164(x42851)))
% 28.73/28.51 [4316]E(f319(f319(f102(f932(f931(x43161,x43161),a923)),f299(x43161,f180(f932(f931(x43161,x43161),a923)))),f319(f319(f281(x43161,x43161,x43161),f299(x43161,x43162)),x43162)),f299(x43161,x43162))
% 28.73/28.51 [4352]E(f319(f319(f173(x43521,x43521),x43522),x43522),f319(f319(f146(x43521,f931(x43521,x43521)),f319(f319(f18(x43521,x43521,f931(x43521,x43521)),f244(x43521,x43521)),f5(x43521))),x43522))
% 28.73/28.51 [4463]E(f319(f134(a925,f926(x44631),f319(f7(f926(x44631),a925,a925),f319(f319(f8(a925,f932(a925,a925),f926(x44631)),f225(a925)),f181(f926(x44631)))),f2(a925)),f319(f160(f926(x44631)),x44632)),f319(f181(f926(f926(x44631))),f171(x44631,x44632)))
% 28.73/28.51 [4535]E(f319(f319(f280(f931(a925,f926(x45351)),f926(x45351)),f312(a925,f926(x45351),a232,f137(x45351,x45352))),f319(f319(f18(f926(x45351),f926(x45351),f931(a925,f926(x45351))),f319(f319(f8(a925,f932(f926(x45351),f931(a925,f926(x45351))),f926(x45351)),f244(a925,f926(x45351))),f181(f926(x45351)))),f5(f926(x45351)))),f138(x45351,x45352))
% 28.73/28.51 [4662]E(f319(f254(x46621),f319(f319(f8(f932(f932(x46621,a923),a923),a923,x46621),f82(f932(x46621,a923))),f319(f319(f8(f932(f932(x46621,a923),a923),f932(f932(x46621,a923),a923),x46621),f319(f18(f932(x46621,a923),a923,a923),f319(f319(f8(a923,f932(a923,a923),f932(x46621,a923)),a322),f319(f319(f7(f932(x46621,a923),f932(f932(x46621,a923),a923),a923),f321(f932(x46621,a923))),x46622)))),f321(x46621)))),f32(f932(x46621,a923),x46622))
% 28.73/28.51 [4663]E(f319(f254(x46631),f319(f319(f8(f932(f932(x46631,a923),a923),a923,x46631),f81(f932(x46631,a923))),f319(f319(f8(f932(f932(x46631,a923),a923),f932(f932(x46631,a923),a923),x46631),f319(f18(f932(x46631,a923),a923,a923),f319(f319(f8(a923,f932(a923,a923),f932(x46631,a923)),a317),f319(f319(f7(f932(x46631,a923),f932(f932(x46631,a923),a923),a923),f321(f932(x46631,a923))),x46632)))),f321(x46631)))),f31(f932(x46631,a923),x46632))
% 28.73/28.51 [4772]~P1(f319(f319(f227(a1),f319(f92(a1),x47721)),f319(f73(a1),f319(f92(a1),x47722))))
% 28.73/28.51 [3761]E(f319(f319(f23(a925),f319(f319(f74(a925),x37611),x37612)),x37612),x37611)
% 28.73/28.51 [3762]E(f319(f319(f23(a925),f319(f319(f74(a925),x37621),x37622)),x37621),x37622)
% 28.73/28.51 [3826]E(f319(f319(f74(a925),f319(f319(f23(a925),x38261),x38262)),x38262),f319(f319(f225(a925),x38261),x38262))
% 28.73/28.51 [3939]E(f319(f319(f75(a925),f319(f319(f30(a925),x39391),x39392)),x39392),f319(f319(f23(a925),x39391),f39(a925,x39391,x39392)))
% 28.73/28.51 [3966]E(f319(f164(a925),f131(a925,f319(f294(a925,f319(a104,x39661)),x39662))),f298(a925,x39661,x39662))
% 28.73/28.51 [3974]E(f319(f92(a1),f208(f319(a96,f319(f69(a1),x39741)),f319(a96,f319(f69(a1),x39742)))),f319(f319(a209,x39741),x39742))
% 28.73/28.51 [3976]E(f319(f319(f102(f932(x39761,a923)),f319(f73(f932(x39761,a923)),x39762)),x39762),f234(f932(x39761,a923)))
% 28.73/28.51 [3977]E(f319(f319(f93(f932(x39771,a923)),f319(f73(f932(x39771,a923)),x39772)),x39772),f180(f932(x39771,a923)))
% 28.73/28.51 [3993]P1(f319(f319(f226(a925),f319(f319(f23(a925),x39931),x39932)),x39931))
% 28.73/28.51 [3994]P1(f319(f319(f226(a925),f319(f319(f30(a925),x39941),x39942)),x39941))
% 28.73/28.51 [4018]P1(f319(f319(f227(a925),x40181),f319(a104,f319(f319(f74(a925),x40182),x40181))))
% 28.73/28.51 [4019]P1(f319(f319(f227(a925),x40191),f319(a104,f319(f319(f74(a925),x40191),x40192))))
% 28.73/28.51 [4036]E(f319(f319(f75(a925),f319(a96,f319(f69(a1),x40361))),f319(a96,f319(f69(a1),x40362))),f319(a96,f319(f69(a1),f319(f319(f75(a1),x40361),x40362))))
% 28.73/28.51 [4046]E(f319(f319(f74(a1),f319(f319(f75(a1),x40461),x40462)),f319(f319(f75(a1),x40461),x40462)),f319(f319(f75(a1),f319(f319(f74(a1),x40461),x40461)),x40462))
% 28.73/28.51 [4048]P1(f319(f319(f226(a1),f2(a1)),f319(f319(f236(a1),f319(f69(a1),x40481)),x40482)))
% 28.73/28.51 [4116]E(f319(f277(f926(x41161),f926(x41161),f150(x41161,x41162)),f319(f319(f301(f926(x41161)),f105(x41161)),f180(f932(f926(x41161),a923)))),f319(f319(f301(f926(x41161)),f105(x41161)),f180(f932(f926(x41161),a923))))
% 28.73/28.51 [4135]E(f319(f319(f102(f932(f931(x41351,x41351),a923)),f299(x41351,x41352)),f299(x41351,f180(f932(f931(x41351,x41351),a923)))),f299(x41351,x41352))
% 28.73/28.51 [4147]E(f319(f319(f30(a1),f319(f95(a1),f319(f319(f74(a1),x41471),x41471))),f319(f95(a1),f319(f319(f74(a1),x41472),x41472))),f319(f319(f30(a1),f319(f95(a1),x41471)),f319(f95(a1),x41472)))
% 28.73/28.51 [4210]E(f319(f319(f236(a1),x42101),f319(f95(a925),f319(f319(f74(a1),x42102),x42102))),f319(f319(f80(a1,a1),f319(f319(f236(a1),x42101),f319(f95(a925),x42102))),f319(f319(f18(a1,a1,a1),f75(a1)),f5(a1))))
% 28.73/28.51 [4216]E(f319(f254(f932(x42161,a923)),f319(f319(f7(f932(x42161,a923),f932(x42161,a923),a923),f226(f932(x42161,a923))),x42162)),f319(f300(x42161),x42162))
% 28.73/28.51 [4232]E(f319(f319(f146(a1,a925),a96),f319(f319(f126(a1),f319(f319(f146(a925,a1),f92(a1)),x42321)),f319(f319(f146(a925,a1),f92(a1)),x42322))),f319(f319(f126(a925),x42321),x42322))
% 28.73/28.51 [4263]E(f319(f302(a1,a1,f319(f319(f7(a1,a1,a1),f74(a1)),x42631)),f319(f294(a1,f2(a1)),f319(f319(f23(a1),x42632),x42631))),f319(f294(a1,x42631),x42632))
% 28.73/28.51 [4265]P58(x42651,f319(f319(f23(f932(f931(x42651,x42651),a923)),x42652),f299(x42651,f180(f932(f931(x42651,x42651),a923)))))
% 28.73/28.51 [4283]E(f319(f181(f926(x42831)),f319(f134(f926(x42831),f926(x42831),f126(x42831),f105(x42831)),x42832)),f319(f157(a925),f319(f319(f146(f926(x42831),a925),f181(f926(x42831))),x42832)))
% 28.73/28.51 [4287]P57(x42871,f234(f932(x42871,a923)),f319(f319(f102(f932(f931(x42871,x42871),a923)),x42872),f299(x42871,f180(f932(f931(x42871,x42871),a923)))))
% 28.73/28.51 [4326]P1(f319(f319(f321(f931(x43261,x43261)),f319(f319(f244(x43261,x43261),x43262),x43262)),f299(x43261,f180(f932(f931(x43261,x43261),a923)))))
% 28.73/28.51 [4332]E(f177(a925,f2(a925),f319(f319(f8(a925,a925,a925),a104),f319(f319(f7(a925,a925,a925),f224(a925)),x43321)),x43322),f319(f319(f224(a925),x43322),f319(a104,x43321)))
% 28.73/28.51 [4335]E(f177(a925,f319(a104,x43351),f319(f319(f8(a925,a925,a925),a104),f319(f319(f7(a925,a925,a925),f225(a925)),x43351)),x43352),f319(f319(f225(a925),x43352),f319(a104,x43351)))
% 28.73/28.51 [4338]E(f319(f302(x43381,f926(x43381),f319(f319(f7(x43381,f926(x43381),f926(x43381)),f143(x43381)),f105(x43381))),x43382),f166(x43381,x43382,f319(f319(f301(f926(x43381)),f105(x43381)),f180(f932(f926(x43381),a923)))))
% 28.73/28.51 [4340]E(f319(f319(f102(f932(f931(x43401,x43401),a923)),f319(f319(f281(x43401,x43401,x43401),x43402),f299(x43401,x43402))),f299(x43401,f180(f932(f931(x43401,x43401),a923)))),f299(x43401,x43402))
% 28.73/28.51 [4347]P1(f319(f319(f226(f932(f931(x43471,x43471),a923)),f255(x43471,x43472)),f319(f319(f246(x43471,x43471),x43472),f319(f16(f932(x43471,a923),x43471),x43472))))
% 28.73/28.51 [4350]E(f319(f302(a1,a925,a96),f319(f319(f102(f932(a1,a923)),f319(f302(a925,a1,f92(a1)),x43501)),f319(f302(a925,a1,f92(a1)),x43502))),f319(f319(f102(f932(a925,a923)),x43501),x43502))
% 28.73/28.51 [4351]E(f319(f302(a1,a925,a96),f319(f319(f93(f932(a1,a923)),f319(f302(a925,a1,f92(a1)),x43511)),f319(f302(a925,a1,f92(a1)),x43512))),f319(f319(f93(f932(a925,a923)),x43511),x43512))
% 28.73/28.51 [4354]E(f319(f254(x43541),f319(f319(f8(a923,a923,x43541),a314),f319(f319(f7(x43541,f932(x43541,a923),a923),f321(x43541)),x43542))),f319(f73(f932(x43541,a923)),x43542))
% 28.73/28.51 [4381]E(f319(f134(f926(x43811),f926(x43811),f126(x43811),f105(x43811)),f319(f319(f146(f926(x43811),f926(x43811)),f160(x43811)),f319(f160(f926(x43811)),x43812))),f319(f160(x43811),f319(f134(f926(x43811),f926(x43811),f126(x43811),f105(x43811)),x43812)))
% 28.73/28.51 [4407]E(f319(f319(f33(a925,f932(f931(x44071,x44071),a923)),f234(f932(a925,a923))),f319(f319(f7(a925,f932(f931(x44071,x44071),a923),f932(f931(x44071,x44071),a923)),f175(f931(x44071,x44071),a923)),x44072)),f299(x44071,x44072))
% 28.73/28.51 [4425]E(f79(x44251,f319(f319(f8(f932(x44251,a923),a923,x44251),f319(a316,x44252)),f319(f319(f7(x44251,f932(x44251,a923),f932(x44251,a923)),f301(x44251)),f180(f932(x44251,a923))))),f304(x44251,x44252))
% 28.73/28.51 [4433]E(f319(f181(f926(x44331)),f144(x44331,f319(f134(f926(x44331),f926(x44331),f126(x44331),f105(x44331)),x44332))),f319(f29(x44331),f319(f319(f33(f926(x44331),f932(x44331,a923)),f319(f164(f926(x44331)),x44332)),f164(x44331))))
% 28.73/28.51 [4447]E(f319(f319(f102(f932(f931(x44471,x44471),a923)),x44472),f319(f319(f281(x44471,x44471,x44471),f319(f319(f281(x44471,x44471,x44471),x44472),f299(x44471,x44472))),x44472)),f319(f319(f281(x44471,x44471,x44471),x44472),f299(x44471,x44472)))
% 28.73/28.51 [4471]P1(f319(f319(f226(f932(f931(x44711,x44711),a923)),f319(f319(f281(x44711,x44711,x44711),x44712),f299(x44711,x44712))),f319(f319(f246(x44711,x44711),f319(f273(x44711),x44712)),f319(f16(f932(x44711,a923),x44711),f319(f273(x44711),x44712)))))
% 28.73/28.51 [4512]E(f319(f254(f926(x45121)),f319(f319(f7(f926(x45121),f932(x45121,a923),a923),f319(f319(f8(f932(x45121,a923),f932(f932(x45121,a923),a923),f926(x45121)),f226(f932(x45121,a923))),f164(x45121))),x45122)),f153(x45121,x45122))
% 28.73/28.51 [4523]E(f319(f148(f926(x45231),x45231,f105(x45231),f319(f319(f8(f926(x45231),f932(f926(x45231),f926(x45231)),x45231),f319(f7(f926(x45231),f926(x45231),f926(x45231)),f126(x45231))),f319(f319(f7(x45231,f926(x45231),f926(x45231)),f143(x45231)),f105(x45231)))),x45232),f319(f159(x45231),x45232))
% 28.73/28.51 [4563]P26(f932(x45631,x45632),f932(f931(x45631,x45632),a923),f319(f319(f8(f932(f931(x45631,x45632),a923),f932(f931(x45631,x45632),a923),f932(x45631,x45632)),f254(f931(x45631,x45632))),f319(f319(f8(f932(x45631,f932(x45632,a923)),f932(f931(x45631,x45632),a923),f932(x45631,x45632)),f249(x45631,x45632,a923)),f319(f8(x45632,f932(x45632,a923),x45631),f319(f7(x45632,x45632,a923),a316)))),f234(f932(f932(x45631,x45632),a923)))
% 28.73/28.51 [4568]E(f39(a1,f319(f95(a1),f319(f319(f74(a1),x45681),x45681)),f319(f95(a1),f319(f319(f74(a1),x45682),x45682))),f319(f319(f75(a1),f319(f95(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),f39(a1,f319(f95(a1),x45681),f319(f95(a1),x45682))))
% 28.73/28.51 [4612]E(f319(f319(f33(x46121,f932(f931(x46121,x46121),a923)),x46122),f319(f319(f7(x46121,f932(f931(x46121,x46121),a923),f932(f931(x46121,x46121),a923)),f319(f319(f8(f931(x46121,x46121),f932(f932(f931(x46121,x46121),a923),f932(f931(x46121,x46121),a923)),x46121),f301(f931(x46121,x46121))),f319(f319(f18(x46121,x46121,f931(x46121,x46121)),f244(x46121,x46121)),f5(x46121)))),f180(f932(f931(x46121,x46121),a923)))),f255(x46121,x46122))
% 28.73/28.51 [4620]E(f194(x46201,f319(f319(f244(a1,a1),f319(f73(a1),f319(f319(f66(f931(a1,a1),a1,x46201,f243(a1,a1)),f204(x46201)),x46202))),f319(f319(f66(f931(a1,a1),a1,x46201,f248(a1,a1)),f204(x46201)),x46202))),f219(x46201,x46202))
% 28.73/28.51 [4701]E(f319(f254(f932(x47011,a923)),f319(f319(f8(f932(f932(x47011,a923),a923),a923,f932(x47011,a923)),f81(f932(x47011,a923))),f319(f319(f7(f932(x47011,a923),f932(f932(x47011,a923),a923),f932(f932(x47011,a923),a923)),f319(f319(f8(f932(f932(x47011,a923),f932(a923,a923)),f932(f932(f932(x47011,a923),a923),f932(f932(x47011,a923),a923)),f932(x47011,a923)),f18(f932(x47011,a923),a923,a923)),f319(f319(f8(f932(f932(x47011,a923),a923),f932(f932(x47011,a923),f932(a923,a923)),f932(x47011,a923)),f319(f8(a923,f932(a923,a923),f932(x47011,a923)),a317)),f319(f319(f7(f932(x47011,a923),f932(f932(x47011,a923),f932(x47011,a923)),f932(f932(x47011,a923),a923)),f319(f319(f8(f932(f932(x47011,a923),a923),f932(f932(f932(x47011,a923),f932(x47011,a923)),f932(f932(x47011,a923),a923)),f932(x47011,a923)),f8(f932(x47011,a923),a923,f932(x47011,a923))),a316)),f73(f932(x47011,a923)))))),f319(f319(f8(f932(f932(x47011,a923),a923),a923,f932(x47011,a923)),f319(f321(f932(x47011,a923)),x47012)),f300(x47011))))),f319(f300(x47011),f319(f73(f932(x47011,a923)),x47012)))
% 28.73/28.51 [4769]~E(f319(f319(f74(a1),x47691),x47691),f319(f319(f23(a1),f319(f319(f74(a1),x47692),x47692)),a89))
% 28.73/28.51 [4770]~E(f319(f319(f74(a1),x47701),x47701),f319(f319(f23(a1),f319(f319(f74(a1),x47702),x47702)),a89))
% 28.73/28.51 [4774]~P1(f319(f319(f227(a925),f319(f319(f74(a925),x47741),x47742)),x47742))
% 28.73/28.51 [4775]~P1(f319(f319(f227(a925),f319(f319(f74(a925),x47751),x47752)),x47751))
% 28.73/28.51 [4053]E(f319(f319(f23(a925),x40531),f319(f319(f75(a925),f319(f319(f30(a925),x40531),x40532)),x40532)),f39(a925,x40531,x40532))
% 28.73/28.51 [4054]E(f319(f319(f23(a1),x40541),f319(f319(f75(a1),f319(f319(f30(a1),x40541),x40542)),x40542)),f39(a1,x40541,x40542))
% 28.73/28.51 [4086]E(f319(f319(f146(a925,x40861),f319(f156(x40861),x40862)),f131(a925,f319(f294(a925,f2(a925)),f319(f181(f926(x40861)),x40862)))),x40862)
% 28.73/28.51 [4143]E(f319(f277(x41431,x41431,f299(x41431,f180(f932(f931(x41431,x41431),a923)))),x41432),x41432)
% 28.73/28.51 [4268]E(f299(x42681,f319(f319(f102(f932(f931(x42681,x42681),a923)),x42682),f299(x42681,f180(f932(f931(x42681,x42681),a923))))),f299(x42681,x42682))
% 28.73/28.51 [4269]E(f299(x42691,f319(f319(f23(f932(f931(x42691,x42691),a923)),x42692),f299(x42691,f180(f932(f931(x42691,x42691),a923))))),f299(x42691,x42692))
% 28.73/28.51 [4319]E(f319(f319(f23(a1),f319(f319(f23(a1),f319(f319(f74(a1),x43191),x43191)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),x43192),x43192)),a89)),f319(f319(f74(a1),f319(f319(f23(a1),x43191),x43192)),f319(f319(f23(a1),x43191),x43192)))
% 28.73/28.51 [4359]E(f319(f319(f23(a1),f319(f319(f74(a1),f319(f319(f74(a1),x43591),x43592)),f319(f319(f74(a1),x43591),x43592))),a89),f319(f319(f74(a1),f319(f319(f74(a1),x43591),x43591)),f319(f319(f23(a1),f319(f319(f74(a1),x43592),x43592)),a89)))
% 28.73/28.51 [4384]E(f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),x43841),x43841)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),x43842),x43842)),a89)),f319(f319(f74(a1),f319(f319(f74(a1),x43841),f319(f319(f23(a1),x43842),a89))),f319(f319(f74(a1),x43841),f319(f319(f23(a1),x43842),a89))))
% 28.73/28.51 [4395]E(f319(f319(f23(a1),f319(f319(f74(a1),f319(f319(f23(a1),x43951),x43952)),f319(f319(f23(a1),x43951),x43952))),a89),f319(f319(f23(a1),f319(f319(f23(a1),f319(f319(f74(a1),x43951),x43951)),a89)),f319(f319(f74(a1),x43952),x43952)))
% 28.73/28.51 [4396]E(f319(f319(f23(a1),f319(f319(f74(a1),f319(f319(f74(a1),x43961),x43962)),f319(f319(f74(a1),x43961),x43962))),a89),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),x43961),x43961)),a89)),f319(f319(f74(a1),x43962),x43962)))
% 28.73/28.51 [4444]E(f319(f92(a1),f319(f319(f30(a925),f319(f319(f75(a925),f319(a96,f319(f69(a1),x44441))),f319(a96,f319(f69(a1),x44442)))),f208(f319(a96,f319(f69(a1),x44441)),f319(a96,f319(f69(a1),x44442))))),f210(x44441,x44442))
% 28.73/28.51 [4489]E(f319(f319(f251(f931(a91,a91),a91,f931(a91,a91),f931(x44891,f931(a91,a91))),f259(f319(a3,f319(f181(f926(x44891)),x44892)))),f319(f319(f8(x44891,f932(f931(a91,a91),f931(x44891,f931(a91,a91))),a91),f244(x44891,f931(a91,a91))),f319(f319(f8(a925,x44891,a91),f319(f156(x44891),x44892)),a20))),f267(x44891,x44892))
% 28.73/28.51 [4569]E(f319(f134(a925,f926(x45691),f319(f7(f926(x45691),a925,a925),f319(f319(f8(a925,f932(a925,a925),f926(x45691)),f225(a925)),f181(f926(x45691)))),f2(a925)),f319(f160(f926(x45691)),f171(x45691,x45692))),f319(f181(f926(f926(x45691))),f319(f128(f926(x45691),f319(f319(f8(a923,a923,f926(x45691)),a314),f319(f319(f7(f926(x45691),f926(x45691),a923),a316),f105(x45691)))),x45692)))
% 28.73/28.51 [4575]E(f319(f319(f33(a925,f932(x45751,a923)),f234(f932(a925,a923))),f319(f319(f7(a925,f932(a925,f932(x45751,a923)),f932(x45751,a923)),f319(f319(f8(f932(a925,a923),f932(f932(a925,f932(x45751,a923)),f932(x45751,a923)),a925),f33(a925,f932(x45751,a923))),f294(a925,f2(a925)))),x45752)),f319(f319(f33(a925,f932(x45751,a923)),f234(f932(a925,a923))),x45752))
% 28.73/28.51 [4597]P1(f319(f55(a925),f319(f254(a925),f319(f319(f18(a925,a923,a923),f319(f319(f8(a923,f932(a923,a923),a925),a317),x45971)),f319(f319(f7(a925,a925,a923),f227(a925)),x45972)))))
% 28.73/28.51 [4709]E(f319(f254(f931(f926(x47091),f926(x47091))),f319(f249(f926(x47091),f926(x47091),a923),f319(f319(f18(f926(x47091),f932(f926(x47091),a923),f932(f926(x47091),a923)),f319(f319(f8(f932(f926(x47091),f932(a923,a923)),f932(f932(f926(x47091),a923),f932(f926(x47091),a923)),f926(x47091)),f18(f926(x47091),a923,a923)),f319(f319(f8(f932(f926(x47091),a923),f932(f926(x47091),f932(a923,a923)),f926(x47091)),f319(f8(a923,f932(a923,a923),f926(x47091)),a318)),f319(f319(f7(f926(x47091),f932(f926(x47091),a925),f932(f926(x47091),a923)),f319(f319(f8(f932(a925,a923),f932(f932(f926(x47091),a925),f932(f926(x47091),a923)),f926(x47091)),f8(a925,a923,f926(x47091))),f319(f319(f8(a925,f932(a925,a923),f926(x47091)),f227(a925)),f181(f926(x47091))))),f181(f926(x47091)))))),f319(f319(f18(f926(x47091),f932(f926(x47091),a923),f932(f926(x47091),a923)),f319(f319(f8(f932(f926(x47091),f932(a923,a923)),f932(f932(f926(x47091),a923),f932(f926(x47091),a923)),f926(x47091)),f18(f926(x47091),a923,a923)),f319(f319(f8(f932(f926(x47091),a923),f932(f926(x47091),f932(a923,a923)),f926(x47091)),f319(f8(a923,f932(a923,a923),f926(x47091)),a317)),f319(f319(f7(f926(x47091),f932(f926(x47091),a925),f932(f926(x47091),a923)),f319(f319(f8(f932(a925,a923),f932(f932(f926(x47091),a925),f932(f926(x47091),a923)),f926(x47091)),f8(a925,a923,f926(x47091))),f319(f319(f8(a925,f932(a925,a923),f926(x47091)),a316),f181(f926(x47091))))),f181(f926(x47091)))))),f319(f319(f7(f926(x47091),f932(f931(f926(x47091),f926(x47091)),a923),f932(f926(x47091),a923)),f319(f319(f8(f932(f926(x47091),f932(f932(f931(f926(x47091),f926(x47091)),a923),a923)),f932(f932(f931(f926(x47091),f926(x47091)),a923),f932(f926(x47091),a923)),f926(x47091)),f7(f926(x47091),f932(f931(f926(x47091),f926(x47091)),a923),a923)),f319(f319(f8(f932(f926(x47091),f931(f926(x47091),f926(x47091))),f932(f926(x47091),f932(f932(f931(f926(x47091),f926(x47091)),a923),a923)),f926(x47091)),f319(f8(f931(f926(x47091),f926(x47091)),f932(f932(f931(f926(x47091),f926(x47091)),a923),a923),f926(x47091)),f321(f931(f926(x47091),f926(x47091))))),f244(f926(x47091),f926(x47091))))),f137(x47091,x47092)))))),f138(x47091,x47092))
% 28.73/28.51 [4387]E(f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f75(a1),x43871),x43872)),f319(f319(f75(a1),x43871),x43872))),x43872),f319(f319(f75(a1),f319(f319(f23(a1),f319(f319(f74(a1),x43871),x43871)),a89)),x43872))
% 28.73/28.51 [4488]E(f319(a96,f319(a83,f319(f277(f931(a925,a925),f931(a925,a925),a100),f319(f319(f301(f931(a925,a925)),f319(f319(f244(a925,a925),x44881),x44882)),f180(f932(f931(a925,a925),a923)))))),f319(f319(f23(a925),x44881),x44882))
% 28.73/28.51 [4492]E(f319(f319(f281(x44921,x44921,x44921),f319(f319(f102(f932(f931(x44921,x44921),a923)),x44922),f299(x44921,f180(f932(f931(x44921,x44921),a923))))),f299(x44921,f319(f319(f102(f932(f931(x44921,x44921),a923)),x44922),f299(x44921,f180(f932(f931(x44921,x44921),a923)))))),f299(x44921,x44922))
% 28.73/28.51 [4529]E(f260(x45291,f319(f128(f931(a91,x45291),f319(f249(a91,x45291,a923),f319(f319(f8(a923,f932(x45291,a923),a91),f16(a923,x45291)),f319(f227(a91),f2(a91))))),x45292)),f260(x45291,x45292))
% 28.73/28.51 [4530]E(f258(x45301,f319(f128(f931(a91,x45301),f319(f249(a91,x45301,a923),f319(f319(f8(a923,f932(x45301,a923),a91),f16(a923,x45301)),f319(f227(a91),f2(a91))))),x45302)),f258(x45301,x45302))
% 28.73/28.51 [4532]E(f319(f73(a1),f319(a83,f319(f277(f931(a925,a925),f931(a925,a925),a100),f319(f319(f301(f931(a925,a925)),f319(f319(f244(a925,a925),x45321),x45322)),f180(f932(f931(a925,a925),a923)))))),f319(a83,f319(f277(f931(a925,a925),f931(a925,a925),a100),f319(f319(f301(f931(a925,a925)),f319(f319(f244(a925,a925),x45322),x45321)),f180(f932(f931(a925,a925),a923))))))
% 28.73/28.51 [4588]E(f319(f319(f280(f926(a925),x45881),f137(a925,a232)),f319(f319(f7(x45881,f926(f932(x45881,a925)),f926(a925)),f319(f319(f8(f932(f932(x45881,a925),a925),f932(f926(f932(x45881,a925)),f926(a925)),x45881),f146(f932(x45881,a925),a925)),f319(f7(f932(x45881,a925),x45881,a925),f5(f932(x45881,a925))))),x45882)),f145(x45881,x45882))
% 28.73/28.51 [4609]E(f319(f319(f80(a1,a925),f319(f95(a1),f319(f319(f74(a1),x46091),a89))),f319(f319(f18(a1,a925,a925),f319(f319(f7(a1,a925,f932(a925,a925)),f319(f319(f8(a923,f932(a925,f932(a925,a925)),a1),f86(a925)),a185)),f2(a925))),f319(f319(f8(a925,a925,a1),a104),f319(f319(f8(a925,a925,a1),f319(f224(a925),x46092)),a96)))),f319(f319(f224(a925),f319(a104,x46092)),f319(f95(a925),x46091)))
% 28.73/28.51 [4610]E(f319(f319(f80(a1,a925),f319(f95(a1),f319(f319(f74(a1),x46101),a89))),f319(f319(f18(a1,a925,a925),f319(f319(f7(a1,a925,f932(a925,a925)),f319(f319(f8(a923,f932(a925,f932(a925,a925)),a1),f86(a925)),a185)),f319(a104,x46102))),f319(f319(f8(a925,a925,a1),a104),f319(f319(f8(a925,a925,a1),f319(f225(a925),x46102)),a96)))),f319(f319(f225(a925),f319(a104,x46102)),f319(f95(a925),x46101)))
% 28.73/28.51 [4630]E(f319(f134(f926(x46301),f926(x46301),f126(x46301),f105(x46301)),f319(f319(f146(f926(x46301),f926(x46301)),f148(f926(x46301),x46301,f105(x46301),f319(f319(f8(f926(x46301),f932(f926(x46301),f926(x46301)),x46301),f16(f926(x46301),f926(x46301))),f319(f319(f7(x46301,f926(x46301),f926(x46301)),f143(x46301)),f105(x46301))))),x46302)),f319(f319(f146(f926(x46301),x46301),f133(x46301)),f319(f128(f926(x46301),f319(f319(f8(a923,a923,f926(x46301)),a314),f319(f319(f7(f926(x46301),f926(x46301),a923),a316),f105(x46301)))),x46302)))
% 28.73/28.51 [4692]E(f319(f249(a1,a1,a923),f319(f319(f7(a1,f932(a1,a923),f932(a1,a923)),f319(f319(f8(f932(a1,f932(a923,a923)),f932(f932(a1,a923),f932(a1,a923)),a1),f18(a1,a923,a923)),f319(f319(f8(f932(a1,a923),f932(a1,f932(a923,a923)),a1),f319(f8(a923,f932(a923,a923),a1),a317)),f319(f319(f8(f932(a1,a1),f932(a1,a923),a1),f319(f8(a1,a923,a1),f319(a316,x46921))),f319(f319(f8(a1,f932(a1,a1),a1),f74(a1)),f319(f75(a1),x46922)))))),f319(f319(f18(a1,a923,a923),f319(f319(f8(a923,f932(a923,a923),a1),a317),f319(f319(f8(a923,a923,a1),f319(a322,f319(f319(f227(a1),f2(a1)),x46922))),f319(f319(f18(a1,a923,a923),f319(f319(f8(a923,f932(a923,a923),a1),a317),f319(f226(a1),f2(a1)))),f319(f319(f7(a1,a1,a923),f227(a1)),x46922))))),f319(f319(f8(a923,a923,a1),f319(a322,f319(a314,f319(f319(f227(a1),f2(a1)),x46922)))),f319(f319(f18(a1,a923,a923),f319(f319(f8(a923,f932(a923,a923),a1),a317),f319(f227(a1),x46922))),f319(f319(f7(a1,a1,a923),f226(a1)),f2(a1))))))),f43(x46921,x46922))
% 28.73/28.51 [4695]E(f319(f254(x46951),f319(f319(f8(f932(a925,a923),a923,x46951),f81(a925)),f319(f319(f7(x46951,f932(a925,a923),f932(a925,a923)),f319(f319(f8(f932(a925,f932(a923,a923)),f932(f932(a925,a923),f932(a925,a923)),x46951),f18(a925,a923,a923)),f319(f319(f8(f932(a925,a923),f932(a925,f932(a923,a923)),x46951),f319(f8(a923,f932(a923,a923),a925),a317)),f319(f319(f7(x46951,f932(a925,x46951),f932(a925,a923)),f319(f319(f8(f932(x46951,a923),f932(f932(a925,x46951),f932(a925,a923)),x46951),f8(x46951,a923,a925)),a316)),f319(f156(x46951),x46952))))),f319(f319(f7(a925,a925,a923),f227(a925)),f319(f181(f926(x46951)),x46952))))),f319(f164(x46951),x46952))
% 28.73/28.51 [4502]E(f319(f319(f23(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),x45021),a89)),x45022)),f319(f319(f23(a1),f319(f319(f74(a1),x45021),a89)),x45022))),a89),f319(f319(f23(a1),f319(f319(f74(a1),x45021),x45021)),f319(f319(f23(a1),f319(f319(f74(a1),x45022),x45022)),a89)))
% 28.73/28.51 [4625]E(f319(f134(f926(f926(x46251)),f926(f926(x46251)),f126(f926(x46251)),f105(f926(x46251))),f319(f319(f146(f926(x46251),f926(f926(x46251))),f148(f926(f926(x46251)),x46251,f105(f926(x46251)),f319(f16(f932(f926(x46251),f926(f926(x46251))),x46251),f319(f319(f7(f926(x46251),f926(f926(x46251)),f926(f926(x46251))),f143(f926(x46251))),f105(f926(x46251)))))),x46252)),f319(f319(f146(f926(x46251),f926(x46251)),f163(x46251)),f319(f128(f926(x46251),f319(f319(f8(a923,a923,f926(x46251)),a314),f319(f319(f7(f926(x46251),f926(x46251),a923),a316),f105(x46251)))),x46252)))
% 28.73/28.51 [4635]E(f319(f319(f80(a1,a925),f319(f95(a1),f319(f319(f74(a1),x46351),a89))),f319(f319(f18(a1,a925,a925),f319(f319(f7(a1,a925,f932(a925,a925)),f319(f319(f8(a923,f932(a925,f932(a925,a925)),a1),f86(a925)),a185)),f2(a925))),f319(f319(f8(a925,a925,a1),a104),f319(f319(f7(a1,a925,a925),f319(f319(f8(a925,f932(a925,a925),a1),f224(a925)),a96)),x46352)))),f319(f319(f224(a925),f319(f95(a925),x46351)),f319(a104,x46352)))
% 28.73/28.51 [4636]E(f319(f319(f80(a1,a925),f319(f95(a1),f319(f319(f74(a1),x46361),a89))),f319(f319(f18(a1,a925,a925),f319(f319(f7(a1,a925,f932(a925,a925)),f319(f319(f8(a923,f932(a925,f932(a925,a925)),a1),f86(a925)),a185)),f319(a104,x46362))),f319(f319(f8(a925,a925,a1),a104),f319(f319(f7(a1,a925,a925),f319(f319(f8(a925,f932(a925,a925),a1),f225(a925)),a96)),x46362)))),f319(f319(f225(a925),f319(f95(a925),x46361)),f319(a104,x46362)))
% 28.73/28.51 [4624]E(f319(f249(x46241,x46241,a923),f319(f319(f18(x46241,a923,f932(x46241,a923)),f319(f319(f8(f932(x46241,f932(a923,a923)),f932(a923,f932(x46241,a923)),x46241),f7(x46241,a923,a923)),f319(f319(f8(f932(x46241,a923),f932(x46241,f932(a923,a923)),x46241),f319(f8(a923,f932(a923,a923),x46241),a317)),a316))),x46242)),f255(x46241,x46242))
% 28.73/28.51 [4669]E(f319(f319(f30(a925),x46691),f319(f319(f74(a925),f319(f95(a925),f319(f319(f23(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))),a89))),x46692)),f319(f319(f30(a925),x46691),f319(a104,f319(a104,f319(a104,x46692)))))
% 28.73/28.51 [4670]E(f39(a925,x46701,f319(f319(f74(a925),f319(f95(a925),f319(f319(f23(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))),a89))),x46702)),f39(a925,x46701,f319(a104,f319(a104,f319(a104,x46702)))))
% 28.73/28.51 [4671]E(f39(a925,f319(f319(f74(a925),f319(f95(a925),f319(f319(f23(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))),a89))),x46711),x46712),f39(a925,f319(a104,f319(a104,f319(a104,x46711))),x46712))
% 28.73/28.51 [4683]E(f115(f319(x46831,f319(f319(f75(a91),f319(f95(a91),f319(f319(f23(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))),a89))),x46832))),f319(f192(x46831),x46832))
% 28.73/28.51 [4684]E(f319(f319(f30(a925),f319(f319(f74(a925),f319(f95(a925),f319(f319(f23(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))),a89))),x46841)),x46842),f319(f319(f30(a925),f319(a104,f319(a104,f319(a104,x46841)))),x46842))
% 28.73/28.51 [4736]~E(f118(x47361,x47362,x47363),f111(x47361))
% 28.73/28.51 [4737]~E(f118(x47371,x47372,x47373),f111(x47371))
% 28.73/28.51 [3489]E(f319(f184(x34891,x34892),x34893),f113(x34891,x34892))
% 28.73/28.51 [3508]E(f319(f191(x35081,x35082),x35083),f319(f121(x35081),x35082))
% 28.73/28.51 [3584]E(f319(f319(f146(x35841,x35842),x35843),f105(x35841)),f105(x35842))
% 28.73/28.51 [3623]E(f319(f176(x36231,x36232,x36233),f2(a925)),x36232)
% 28.73/28.51 [3625]E(f319(f319(f173(x36251,x36252),x36253),f105(x36252)),f105(f931(x36251,x36252)))
% 28.73/28.51 [3640]E(f319(f181(f926(x36401)),f161(x36401,x36402,x36403)),x36402)
% 28.73/28.51 [3659]E(f79(x36591,f56(x36591,x36592,x36593)),f319(f57(x36591,x36592),x36593))
% 28.73/28.51 [3663]E(f235(x36631,x36632,f235(x36632,x36631,x36633)),x36633)
% 28.73/28.51 [3683]E(f319(f160(x36831),f161(x36831,x36832,x36833)),f161(x36831,x36832,x36833))
% 28.73/28.51 [3708]E(f132(x37081,x37082,f144(x37081,x37083)),f144(x37081,f132(x37081,x37082,x37083)))
% 28.73/28.51 [3727]E(f319(f243(f926(x37271),f926(x37271)),f158(x37271,x37272,x37273)),f319(f128(x37271,x37272),x37273))
% 28.73/28.51 [3770]E(f319(f319(f143(x37701),x37702),f161(x37701,x37703,x37702)),f161(x37701,f319(a104,x37703),x37702))
% 28.73/28.51 [3802]E(f177(x38021,x38022,x38023,f2(a925)),x38022)
% 28.73/28.51 [3803]E(f17(x38031,x38032,x38033,f2(a91)),x38032)
% 28.73/28.51 [3804]E(f19(x38041,x38042,x38043,f2(a91)),x38042)
% 28.73/28.51 [3811]E(f155(x38111,x38112,x38113,f105(x38111)),f105(x38112))
% 28.73/28.51 [3812]E(f122(x38121,x38122,x38123,f111(x38121)),f111(x38122))
% 28.73/28.51 [3818]E(f319(f319(f156(x38181),f319(f319(f143(x38181),x38182),x38183)),f2(a925)),x38182)
% 28.73/28.51 [3846]E(f53(x38461,x38462,f105(x38461),x38463),f105(f931(x38461,x38462)))
% 28.73/28.51 [3866]P26(x38661,x38662,x38663,f180(f932(x38661,a923)))
% 28.73/28.51 [3970]E(f257(x39701,x39702,x39703),f319(f244(f932(a91,f932(a923,f929(f927(x39701)))),f931(a91,a91)),f35(x39701)))
% 28.73/28.51 [4027]E(f319(f66(x40271,x40272,x40271,x40273),f25(x40271)),x40273)
% 28.73/28.51 [4202]P1(f319(f319(f321(f931(x42021,x42021)),f319(f319(f244(x42021,x42021),x42022),x42022)),f299(x42021,x42023)))
% 28.73/28.51 [4779]~P1(f319(f319(f321(f931(f926(x47791),f926(x47791))),f319(f319(f244(f926(x47791),f926(x47791)),x47792),f105(x47791))),f137(x47791,x47793)))
% 28.73/28.51 [4780]~P1(f319(f319(f321(f931(f926(x47801),f926(x47801))),f319(f319(f244(f926(x47801),f926(x47801)),x47802),f105(x47801))),f139(x47801,x47803)))
% 28.73/28.51 [4781]~P1(f319(f319(f321(f931(f926(x47811),f926(x47811))),f319(f319(f244(f926(x47811),f926(x47811)),x47812),f105(x47811))),f149(x47811,x47813)))
% 28.73/28.51 [4782]~P1(f319(f319(f321(f931(f926(x47821),f926(x47821))),f319(f319(f244(f926(x47821),f926(x47821)),f105(x47821)),x47822)),f137(x47821,x47823)))
% 28.73/28.51 [4783]~P1(f319(f319(f321(f931(f926(x47831),f926(x47831))),f319(f319(f244(f926(x47831),f926(x47831)),f105(x47831)),x47832)),f149(x47831,x47833)))
% 28.73/28.51 [3559]E(f319(f319(f193(x35591),x35592),x35593),f194(x35591,f207(x35592,x35593)))
% 28.73/28.51 [3612]E(f319(f278(x36121,x36122),f319(f278(x36122,x36121),x36123)),x36123)
% 28.73/28.51 [3635]E(f319(f319(f173(x36351,x36352),f105(x36351)),x36353),f105(f931(x36351,x36352)))
% 28.73/28.51 [3638]E(f168(x36381,x36382,f319(f274(a925),x36383)),f319(f319(f167(x36381),x36383),x36382))
% 28.73/28.51 [3654]E(f319(f256(x36541,x36542),f319(f278(x36542,x36541),x36543)),f319(f276(x36542,x36541),x36543))
% 28.73/28.51 [3656]E(f144(x36561,f319(f128(x36561,x36562),x36563)),f319(f128(x36561,x36562),f144(x36561,x36563)))
% 28.73/28.51 [3657]E(f319(f276(x36571,x36572),f319(f278(x36572,x36571),x36573)),f319(f256(x36572,x36571),x36573))
% 28.73/28.51 [3658]E(f319(f256(x36581,x36582),f319(f278(x36582,x36581),x36583)),f319(f276(x36582,x36581),x36583))
% 28.73/28.51 [3676]E(f319(f128(x36761,x36762),f319(f160(x36761),x36763)),f319(f160(x36761),f319(f128(x36761,x36762),x36763)))
% 28.73/28.51 [3688]E(f319(f319(f130(x36881),x36882),f319(f163(x36881),x36883)),f319(f319(f130(x36881),f319(a104,x36882)),x36883))
% 28.73/28.51 [3704]E(f319(f302(x37041,x37042,x37043),f180(f932(x37041,a923))),f180(f932(x37042,a923)))
% 28.73/28.51 [3705]E(f319(f303(x37051,x37052,x37053),f234(f932(x37052,a923))),f234(f932(x37051,a923)))
% 28.73/28.51 [3706]E(f319(f303(x37061,x37062,x37063),f180(f932(x37062,a923))),f180(f932(x37061,a923)))
% 28.73/28.51 [3707]E(f319(f277(x37071,x37072,x37073),f180(f932(x37071,a923))),f180(f932(x37072,a923)))
% 28.73/28.51 [3733]E(f112(x37331,f118(f927(x37331),x37332,x37333)),f108(x37331,x37332,f112(x37331,x37333)))
% 28.73/28.51 [3734]E(f165(x37341,f319(f319(f143(x37341),x37342),x37343),f105(x37341)),f319(f319(f143(x37341),x37342),x37343))
% 28.73/28.51 [3735]E(f319(f319(f301(x37351),x37352),f319(f164(x37351),x37353)),f319(f164(x37351),f132(x37351,x37352,x37353)))
% 28.73/28.51 [3822]E(f319(f302(f931(x38221,x38222),x38222,f248(x38221,x38222)),x38223),f319(f276(x38221,x38222),x38223))
% 28.73/28.51 [3823]E(f319(f302(f931(x38231,x38232),x38231,f243(x38231,x38232)),x38233),f319(f256(x38231,x38232),x38233))
% 28.73/28.51 [3838]E(f319(f164(x38381),f161(x38381,f319(a104,x38382),x38383)),f319(f319(f301(x38381),x38383),f180(f932(x38381,a923))))
% 28.73/28.51 [3894]E(f319(f319(f244(x38941,x38942),f319(f243(x38941,x38942),x38943)),f319(f248(x38941,x38942),x38943)),x38943)
% 28.73/28.51 [3895]E(f319(f319(f244(x38951,x38952),f319(f243(x38951,x38952),x38953)),f319(f248(x38951,x38952),x38953)),x38953)
% 28.73/28.51 [3904]E(f319(f181(f927(x39041)),f118(x39041,x39042,x39043)),f319(f319(f74(a925),f319(f181(f927(x39041)),x39043)),f319(a104,f2(a925))))
% 28.73/28.51 [3906]E(f319(f319(f249(x39061,x39062,x39061),f16(x39061,x39062)),x39063),f319(f243(x39061,x39062),x39063))
% 28.73/28.51 [4032]E(f319(f66(x40321,x40321,x40322,f25(x40321)),x40323),x40323)
% 28.73/28.51 [4039]E(f319(f319(f126(x40391),f161(x40391,x40392,x40393)),f319(f319(f143(x40391),x40393),f105(x40391))),f319(f319(f143(x40391),x40393),f161(x40391,x40392,x40393)))
% 28.73/28.51 [4211]P1(f319(f319(f226(f932(x42111,a923)),f319(f164(x42111),f319(f128(x42111,x42112),x42113))),f319(f164(x42111),x42113)))
% 28.73/28.51 [4254]P1(f319(f319(f226(f932(x42541,a923)),f319(f164(x42541),f319(f319(f167(x42541),x42542),x42543))),f319(f164(x42541),x42543)))
% 28.73/28.51 [4255]P1(f319(f319(f226(f932(x42551,a923)),f319(f164(x42551),f319(f319(f130(x42551),x42552),x42553))),f319(f164(x42551),x42553)))
% 28.73/28.51 [4259]P1(f319(f319(f226(f932(x42591,a923)),f319(f164(x42591),f168(x42591,x42592,x42593))),f319(f164(x42591),x42592)))
% 28.73/28.51 [4260]P1(f319(f319(f226(f932(x42601,a923)),f319(f164(x42601),f162(x42601,x42602,x42603))),f319(f164(x42601),x42603)))
% 28.73/28.51 [4281]P26(f931(x42811,x42812),f931(x42812,x42811),f319(f249(x42811,x42812,f931(x42812,x42811)),f319(f7(x42812,x42811,f931(x42812,x42811)),f244(x42812,x42811))),x42813)
% 28.73/28.51 [4292]E(f319(f319(f319(f175(f926(x42921),f926(x42921)),f39(a925,x42922,f319(f181(f926(x42921)),x42923))),f159(x42921)),x42923),f319(f319(f319(f175(f926(x42921),f926(x42921)),x42922),f159(x42921)),x42923))
% 28.73/28.51 [4333]E(f319(f66(f926(x43331),f926(x43331),f926(x43331),f319(f319(f175(f926(x43331),f926(x43331)),x43332),f159(x43331))),f319(f319(f175(f926(x43331),f926(x43331)),x43333),f159(x43331))),f319(f319(f175(f926(x43331),f926(x43331)),f319(f319(f74(a925),x43332),x43333)),f159(x43331)))
% 28.73/28.51 [4336]P1(f319(f319(f321(f931(f926(x43361),f926(x43361))),f319(f319(f244(f926(x43361),f926(x43361)),x43362),x43362)),f150(x43361,f299(x43361,x43363))))
% 28.73/28.51 [4475]E(f79(f931(x44751,x44752),f319(f319(f18(f931(x44751,x44752),x44752,a923),f319(f319(f8(x44751,f932(x44752,a923),f931(x44751,x44752)),x44753),f243(x44751,x44752))),f248(x44751,x44752))),f79(f931(x44751,x44752),f319(f249(x44751,x44752,a923),x44753)))
% 28.73/28.51 [4476]E(f84(f931(x44761,x44762),f319(f319(f18(f931(x44761,x44762),x44762,a923),f319(f319(f8(x44761,f932(x44762,a923),f931(x44761,x44762)),x44763),f243(x44761,x44762))),f248(x44761,x44762))),f84(f931(x44761,x44762),f319(f249(x44761,x44762,a923),x44763)))
% 28.73/28.51 [4509]E(f319(f319(f280(f931(a925,x45091),x45091),f312(a925,x45091,a232,x45092)),f319(f319(f18(x45091,x45091,f931(a925,x45091)),f319(f319(f8(a925,f932(x45091,f931(a925,x45091)),x45091),f244(a925,x45091)),x45093)),f5(x45091))),f313(x45091,x45093,x45092))
% 28.73/28.51 [4571]E(f319(f250(x45711,x45711,x45712,x45712,f5(x45711),f5(x45712)),x45713),x45713)
% 28.73/28.51 [4644]E(f319(f134(f926(f926(x46441)),f926(f926(x46441)),f126(f926(x46441)),f105(f926(x46441))),f319(f319(f146(f926(x46441),f926(f926(x46441))),f319(f319(f7(f926(x46441),f926(x46441),f926(f926(x46441))),f319(f319(f8(f932(x46441,f926(x46441)),f932(f926(x46441),f926(f926(x46441))),f926(x46441)),f146(x46441,f926(x46441))),f319(f7(x46441,f926(x46441),f926(x46441)),f143(x46441)))),x46442)),f49(x46441,x46443,x46442))),f49(x46441,f319(a104,x46443),x46442))
% 28.73/28.51 [4700]E(f215(a925,f931(x47001,f927(x47001)),f2(a925),f319(f249(x47001,f927(x47001),a925),f319(f319(f7(x47001,a925,f932(f927(x47001),a925)),f319(f319(f8(f932(f927(x47001),f932(a925,a925)),f932(a925,f932(f927(x47001),a925)),x47001),f7(f927(x47001),a925,a925)),f319(f319(f8(f932(f927(x47001),a925),f932(f927(x47001),f932(a925,a925)),x47001),f319(f8(a925,f932(a925,a925),f927(x47001)),f74(a925))),f319(f319(f7(x47001,f932(f927(x47001),a925),f932(f927(x47001),a925)),f319(f319(f8(f932(a925,a925),f932(f932(f927(x47001),a925),f932(f927(x47001),a925)),x47001),f8(a925,a925,f927(x47001))),f319(f319(f8(a925,f932(a925,a925),x47001),f74(a925)),x47002))),f117(x47001,x47002))))),f72(a925))),f319(f127(x47001),x47003)),f319(f117(x47001,x47002),x47003))
% 28.73/28.51 [4708]E(f319(f319(f80(a1,x47081),f210(f319(f319(f66(f931(a1,a1),a1,x47081,f248(a1,a1)),f204(x47081)),x47082),f319(f319(f66(f931(a1,a1),a1,x47081,f248(a1,a1)),f204(x47081)),x47083))),f319(f319(f18(a1,a1,x47081),f319(f319(f8(a1,f932(a1,x47081),a1),f193(x47081)),f319(f319(f18(a1,a1,a1),f319(f319(f8(a1,f932(a1,a1),a1),f74(a1)),f319(f319(f8(a1,a1,a1),f319(f75(a1),f319(f319(f66(f931(a1,a1),a1,x47081,f243(a1,a1)),f204(x47081)),x47082))),f319(f319(f7(a1,a1,a1),f30(a1)),f319(f319(f66(f931(a1,a1),a1,x47081,f248(a1,a1)),f204(x47081)),x47082))))),f319(f319(f8(a1,a1,a1),f319(f75(a1),f319(f319(f66(f931(a1,a1),a1,x47081,f243(a1,a1)),f204(x47081)),x47083))),f319(f319(f7(a1,a1,a1),f30(a1)),f319(f319(f66(f931(a1,a1),a1,x47081,f248(a1,a1)),f204(x47081)),x47083)))))),f5(a1))),f222(x47081,x47082,x47083))
% 28.73/28.51 [4731]~E(f319(f319(f143(x47311),x47312),x47313),x47313)
% 28.73/28.51 [4732]~E(f319(f319(f143(x47321),x47322),x47323),x47323)
% 28.73/28.51 [4734]~E(f319(f319(f143(x47341),x47342),x47343),f105(x47341))
% 28.73/28.51 [4735]~E(f319(f319(f143(x47351),x47352),x47353),f105(x47351))
% 28.73/28.51 [4740]~E(f319(f319(f301(x47401),x47402),x47403),f180(f932(x47401,a923)))
% 28.73/28.51 [4741]~E(f319(f319(f301(x47411),x47412),x47413),f180(f932(x47411,a923)))
% 28.73/28.51 [4761]~E(f319(f302(x47611,f932(x47611,a923),x47612),x47613),f319(f300(x47611),x47613))
% 28.73/28.51 [3616]E(f319(f319(f151(x36161,f105(x36161)),x36162),x36163),f105(x36161))
% 28.73/28.51 [3617]E(f319(f319(f151(x36171,f105(x36171)),x36172),x36173),f105(x36171))
% 28.73/28.51 [3618]E(f319(f133(x36181),f319(f319(f143(x36181),x36182),x36183)),x36182)
% 28.73/28.51 [3619]E(f319(f163(x36191),f319(f319(f143(x36191),x36192),x36193)),x36193)
% 28.73/28.51 [3662]E(f319(f319(f130(x36621),f72(a925)),f319(f319(f143(x36621),x36622),x36623)),x36623)
% 28.73/28.51 [3694]E(f106(x36941,f319(f319(f130(x36941),x36942),x36943)),f319(f319(f130(x36941),x36942),f106(x36941,x36943)))
% 28.73/28.51 [3695]E(f106(x36951,f319(f319(f130(x36951),x36952),x36953)),f319(f319(f130(x36951),x36952),f106(x36951,x36953)))
% 28.73/28.51 [3697]E(f319(f319(f151(x36971,x36972),x36973),f319(f319(f156(x36971),x36972),x36973)),x36972)
% 28.73/28.51 [3717]E(f319(f319(f301(x37171),x37172),f319(f319(f301(x37171),x37172),x37173)),f319(f319(f301(x37171),x37172),x37173))
% 28.73/28.51 [3730]E(f319(f319(f301(x37301),x37302),f319(f164(x37301),x37303)),f319(f164(x37301),f319(f319(f143(x37301),x37302),x37303)))
% 28.73/28.51 [3731]E(f319(f319(f130(x37311),x37312),f319(f163(x37311),x37313)),f319(f163(x37311),f319(f319(f130(x37311),x37312),x37313)))
% 28.73/28.51 [3732]E(f319(f319(f130(x37321),x37322),f319(f163(x37321),x37323)),f319(f163(x37321),f319(f319(f130(x37321),x37322),x37323)))
% 28.73/28.51 [3744]E(f319(f319(f167(x37441),f72(a925)),f319(f319(f143(x37441),x37442),x37443)),f319(f319(f143(x37441),x37442),f105(x37441)))
% 28.73/28.51 [3787]E(f319(f57(x37871,x37872),f319(f319(f301(x37871),x37873),f180(f932(x37871,a923)))),x37873)
% 28.73/28.51 [3828]E(f319(f319(f74(a925),x38281),f319(f319(f74(a925),x38282),x38283)),f319(f319(f74(a925),x38282),f319(f319(f74(a925),x38281),x38283)))
% 28.73/28.51 [3829]E(f319(f319(f74(a1),x38291),f319(f319(f74(a1),x38292),x38293)),f319(f319(f74(a1),x38292),f319(f319(f74(a1),x38291),x38293)))
% 28.73/28.51 [3834]E(f319(f319(f246(x38341,x38342),f180(f932(x38341,a923))),x38343),f180(f932(f931(x38341,x38342),a923)))
% 28.73/28.51 [3858]E(f319(f319(f102(f932(x38581,a923)),x38582),x38583),f319(f319(f102(f932(x38581,a923)),x38583),x38582))
% 28.73/28.51 [3859]E(f319(f319(f93(f932(x38591,a923)),x38592),x38593),f319(f319(f93(f932(x38591,a923)),x38593),x38592))
% 28.73/28.51 [3861]E(f319(f319(f126(x38611),x38612),f319(f319(f143(x38611),x38613),f105(x38611))),f319(f159(x38611),f319(f319(f143(x38611),x38613),x38612)))
% 28.73/28.51 [3862]E(f319(f319(f126(x38621),f319(f160(x38621),x38622)),f319(f160(x38621),x38623)),f319(f160(x38621),f319(f319(f126(x38621),x38623),x38622)))
% 28.73/28.51 [3872]E(f319(f163(x38721),f319(f319(f167(x38721),f319(a104,x38722)),x38723)),f319(f319(f167(x38721),x38722),f319(f163(x38721),x38723)))
% 28.73/28.51 [3880]P1(f319(f319(f321(x38801),x38802),f319(f319(f301(x38801),x38802),x38803)))
% 28.73/28.51 [3884]E(f319(f319(f34(x38841,f932(x38842,a923)),f180(f932(x38841,a923))),x38843),f234(f932(x38842,a923)))
% 28.73/28.51 [3887]E(f319(f277(x38871,x38871,f255(x38871,x38872)),x38873),f319(f319(f93(f932(x38871,a923)),x38872),x38873))
% 28.73/28.51 [3903]E(f319(f181(f926(x39031)),f319(f319(f143(x39031),x39032),x39033)),f319(f319(f74(a925),f319(f181(f926(x39031)),x39033)),f319(a104,f2(a925))))
% 28.73/28.51 [3908]E(f106(x39081,f319(f319(f126(x39081),x39082),f319(f319(f143(x39081),x39083),f105(x39081)))),x39082)
% 28.73/28.51 [3909]E(f136(x39091,f319(f319(f126(x39091),x39092),f319(f319(f143(x39091),x39093),f105(x39091)))),x39093)
% 28.73/28.51 [3917]E(f319(f319(f126(x39171),f319(f319(f167(x39171),x39172),x39173)),f319(f319(f130(x39171),x39172),x39173)),x39173)
% 28.73/28.51 [3926]E(f319(f319(f23(a925),f319(f319(f74(a925),x39261),x39262)),f319(f319(f74(a925),x39263),x39262)),f319(f319(f23(a925),x39261),x39263))
% 28.73/28.51 [3927]E(f319(f319(f23(a925),f319(f319(f74(a925),x39271),x39272)),f319(f319(f74(a925),x39271),x39273)),f319(f319(f23(a925),x39272),x39273))
% 28.73/28.51 [3933]E(f319(f319(f126(x39331),f319(f160(x39331),x39332)),f319(f319(f143(x39331),x39333),f105(x39331))),f319(f160(x39331),f319(f319(f143(x39331),x39333),x39332)))
% 28.73/28.51 [3935]E(f319(f319(f74(a925),f319(f181(f926(x39351)),x39352)),f319(f181(f926(x39351)),x39353)),f319(f181(f926(x39351)),f319(f319(f126(x39351),x39352),x39353)))
% 28.73/28.51 [3938]E(f319(f319(f74(a925),f319(f181(f926(x39381)),x39382)),f319(f181(f926(x39381)),x39383)),f319(f181(f926(x39381)),f165(x39381,x39382,x39383)))
% 28.73/28.51 [3945]E(f319(f319(f102(f932(x39451,a923)),f319(f164(x39451),x39452)),f319(f164(x39451),x39453)),f319(f164(x39451),f319(f319(f126(x39451),x39452),x39453)))
% 28.73/28.51 [3946]E(f39(a925,f319(f319(f75(a925),x39461),x39462),f319(f319(f75(a925),x39461),x39463)),f319(f319(f75(a925),x39461),f39(a925,x39462,x39463)))
% 28.73/28.51 [3958]E(f319(f319(f167(x39581),f319(f319(f23(a925),x39582),f72(a925))),f319(f163(x39581),x39583)),f319(f163(x39581),f319(f319(f167(x39581),x39582),x39583)))
% 28.73/28.51 [3963]E(f319(f319(f93(f932(x39631,a923)),x39632),f319(f73(f932(x39631,a923)),x39633)),f319(f319(f23(f932(x39631,a923)),x39632),x39633))
% 28.73/28.51 [3964]E(f319(f319(f23(f932(x39641,a923)),x39642),f319(f73(f932(x39641,a923)),x39643)),f319(f319(f93(f932(x39641,a923)),x39642),x39643))
% 28.73/28.51 [3986]E(f319(f319(f246(x39861,x39862),x39863),f319(f16(f932(x39862,a923),x39861),f180(f932(x39862,a923)))),f180(f932(f931(x39861,x39862),a923)))
% 28.73/28.51 [3988]E(f319(f319(f23(a925),f319(f319(f75(a925),x39881),x39882)),f319(f319(f75(a925),x39881),x39883)),f319(f319(f75(a925),x39881),f319(f319(f23(a925),x39882),x39883)))
% 28.73/28.51 [3989]E(f319(f319(f74(a925),f319(f319(f75(a925),x39891),x39892)),f319(f319(f75(a925),x39891),x39893)),f319(f319(f75(a925),x39891),f319(f319(f74(a925),x39892),x39893)))
% 28.73/28.51 [3990]E(f319(f319(f23(a1),f319(f319(f75(a1),x39901),x39902)),f319(f319(f75(a1),x39901),x39903)),f319(f319(f75(a1),x39901),f319(f319(f23(a1),x39902),x39903)))
% 28.73/28.51 [3991]E(f319(f319(f74(a1),f319(f319(f75(a1),x39911),x39912)),f319(f319(f75(a1),x39911),x39913)),f319(f319(f75(a1),x39911),f319(f319(f74(a1),x39912),x39913)))
% 28.73/28.51 [3992]E(f319(f319(f75(a1),f319(f319(f236(a1),x39921),x39922)),f319(f319(f236(a1),x39921),x39923)),f319(f319(f236(a1),x39921),f319(f319(f74(a925),x39922),x39923)))
% 28.73/28.51 [4006]E(f319(f319(f33(x40061,f932(x40062,a923)),x40063),f319(f16(f932(x40062,a923),x40061),f180(f932(x40062,a923)))),f180(f932(x40062,a923)))
% 28.73/28.51 [4008]E(f39(a925,f319(f319(f75(a925),x40081),x40082),f319(f319(f75(a925),x40083),x40082)),f319(f319(f75(a925),f39(a925,x40081,x40083)),x40082))
% 28.73/28.51 [4012]E(f39(a1,f319(f319(f75(a1),x40121),f39(a1,x40122,x40123)),x40123),f39(a1,f319(f319(f75(a1),x40121),x40122),x40123))
% 28.73/28.51 [4013]E(f39(a1,f319(f319(f23(a1),x40131),f39(a1,x40132,x40133)),x40133),f39(a1,f319(f319(f23(a1),x40131),x40132),x40133))
% 28.73/28.51 [4014]E(f39(a1,f319(f319(f75(a1),x40141),f39(a1,x40142,x40143)),x40143),f39(a1,f319(f319(f75(a1),x40141),x40142),x40143))
% 28.73/28.51 [4015]P1(f319(f319(f226(f932(x40151,a923)),x40152),f319(f319(f301(x40151),x40153),x40152)))
% 28.73/28.51 [4090]E(f319(f319(f34(f932(x40901,a923),f932(x40901,a923)),x40902),f319(f102(f932(x40901,a923)),x40903)),f319(f319(f102(f932(x40901,a923)),x40903),f32(f932(x40901,a923),x40902)))
% 28.73/28.51 [4091]E(f319(f319(f33(f932(x40911,a923),f932(x40911,a923)),x40912),f319(f93(f932(x40911,a923)),x40913)),f319(f319(f93(f932(x40911,a923)),x40913),f31(f932(x40911,a923),x40912)))
% 28.73/28.51 [4103]E(f319(f164(x41031),f319(f319(f319(f175(f926(x41031),f926(x41031)),x41032),f159(x41031)),x41033)),f319(f164(x41031),x41033))
% 28.73/28.51 [4107]E(f319(f319(f167(x41071),f319(f181(f926(x41071)),f169(x41071,x41072,x41073))),x41073),f169(x41071,x41072,x41073))
% 28.73/28.51 [4111]E(f319(f181(f926(x41111)),f319(f319(f319(f175(f926(x41111),f926(x41111)),x41112),f159(x41111)),x41113)),f319(f181(f926(x41111)),x41113))
% 28.73/28.51 [4114]E(f319(f319(f249(x41141,x41142,x41142),f319(f16(f932(x41142,x41142),x41141),f5(x41142))),x41143),f319(f248(x41141,x41142),x41143))
% 28.73/28.51 [4120]E(f39(a1,f319(f319(f23(a1),f39(a1,x41201,x41202)),x41203),x41202),f39(a1,f319(f319(f23(a1),x41201),x41203),x41202))
% 28.73/28.51 [4121]E(f39(a1,f319(f319(f236(a1),f39(a1,x41211,x41212)),x41213),x41212),f39(a1,f319(f319(f236(a1),x41211),x41213),x41212))
% 28.73/28.51 [4124]E(f319(f319(f33(f932(f931(x41241,x41242),a923),f932(x41242,a923)),x41243),f276(x41241,x41242)),f319(f276(x41241,x41242),f31(f932(f931(x41241,x41242),a923),x41243)))
% 28.73/28.51 [4125]E(f319(f319(f33(f932(f931(x41251,x41252),a923),f932(x41251,a923)),x41253),f256(x41251,x41252)),f319(f256(x41251,x41252),f31(f932(f931(x41251,x41252),a923),x41253)))
% 28.73/28.51 [4148]E(f319(f66(x41481,x41481,x41481,x41482),f319(f319(f175(x41481,x41481),x41483),x41482)),f319(f319(f175(x41481,x41481),f319(a104,x41483)),x41482))
% 28.73/28.51 [4166]E(f319(f319(f130(x41661),f319(f319(f23(a925),f319(f181(f926(x41661)),x41662)),x41663)),f319(f160(x41661),x41662)),f319(f160(x41661),f319(f319(f167(x41661),x41663),x41662)))
% 28.73/28.51 [4167]E(f319(f319(f167(x41671),f319(f319(f23(a925),f319(f181(f926(x41671)),x41672)),x41673)),f319(f160(x41671),x41672)),f319(f160(x41671),f319(f319(f130(x41671),x41673),x41672)))
% 28.73/28.51 [4169]E(f319(f319(f74(a925),f319(f157(a925),f319(f319(f146(x41691,a925),x41692),x41693))),f319(f181(f926(x41691)),x41693)),f147(x41691,x41692,x41693))
% 28.73/28.51 [4182]E(f319(f319(f319(f175(f926(x41821),f926(x41821)),x41822),f159(x41821)),f319(f159(x41821),x41823)),f319(f159(x41821),f319(f319(f319(f175(f926(x41821),f926(x41821)),x41822),f159(x41821)),x41823)))
% 28.73/28.51 [4189]E(f319(f159(x41891),f319(f319(f319(f175(f926(x41891),f926(x41891)),x41892),f159(x41891)),x41893)),f319(f319(f319(f175(f926(x41891),f926(x41891)),f319(a104,x41892)),f159(x41891)),x41893))
% 28.73/28.51 [4203]P1(f319(f319(f226(a925),f319(f181(f926(x42031)),f319(f128(x42031,x42032),x42033))),f319(f181(f926(x42031)),x42033)))
% 28.73/28.51 [4219]E(f319(f319(f102(f932(f932(x42191,a923),a923)),f319(f300(x42191),x42192)),f319(f302(f932(x42191,a923),f932(x42191,a923),f319(f301(x42191),x42193)),f319(f300(x42191),x42192))),f319(f300(x42191),f319(f319(f301(x42191),x42193),x42192)))
% 28.73/28.51 [4251]P1(f319(f319(f226(a925),f319(f181(f926(x42511)),f169(x42511,x42512,x42513))),f319(f181(f926(x42511)),x42513)))
% 28.73/28.51 [4258]E(f319(f256(x42581,x42582),f319(f254(f931(x42581,x42582)),f319(f249(x42581,x42582,a923),x42583))),f319(f254(x42581),f319(f319(f8(f932(x42582,a923),a923,x42581),f81(x42582)),x42583)))
% 28.73/28.51 [4270]E(f319(f302(a925,a925,f319(f319(f7(a925,a925,a925),f74(a925)),x42701)),f295(a925,x42702,x42703)),f295(a925,f319(f319(f74(a925),x42702),x42701),f319(f319(f74(a925),x42703),x42701)))
% 28.73/28.51 [4284]E(f319(f302(a925,a925,f319(f319(f7(a925,a925,a925),f74(a925)),x42841)),f319(f294(a925,x42842),x42843)),f319(f294(a925,f319(f319(f74(a925),x42842),x42841)),f319(f319(f74(a925),x42843),x42841)))
% 28.73/28.51 [4302]E(f319(f319(f173(x43021,x43022),f319(f319(f146(f931(x43021,x43022),x43021),f243(x43021,x43022)),x43023)),f319(f319(f146(f931(x43021,x43022),x43022),f248(x43021,x43022)),x43023)),x43023)
% 28.73/28.51 [4307]E(f319(f319(f74(a925),f319(f319(f75(a925),x43071),f39(a925,f319(f319(f30(a925),x43072),x43071),x43073))),f39(a925,x43072,x43071)),f39(a925,x43072,f319(f319(f75(a925),x43071),x43073)))
% 28.73/28.51 [4320]E(f319(f319(f126(x43201),x43202),f319(f134(f926(x43201),f926(x43201),f126(x43201),f105(x43201)),x43203)),f319(f134(f926(x43201),f926(x43201),f126(x43201),x43202),x43203))
% 28.73/28.51 [4341]P1(f319(f319(f321(f931(x43411,x43411)),f319(f319(f244(x43411,x43411),x43412),x43412)),f319(f319(f175(f931(x43411,x43411),a923),f2(a925)),x43413)))
% 28.73/28.51 [4346]E(f319(f254(x43461),f319(f319(f8(f932(x43462,a923),a923,x43461),f81(x43462)),f319(f7(x43462,x43461,a923),x43463))),f319(f276(x43462,x43461),f319(f254(f931(x43462,x43461)),f319(f249(x43462,x43461,a923),x43463))))
% 28.73/28.51 [4363]E(f319(f319(f102(f932(x43631,a923)),f319(f319(f33(a925,f932(x43631,a923)),f295(a925,f72(a925),x43632)),x43633)),f319(x43633,f2(a925))),f319(f319(f33(a925,f932(x43631,a923)),f319(f293(a925),x43632)),x43633))
% 28.73/28.51 [4378]E(f319(f134(f926(x43781),f926(x43781),f126(x43781),f105(x43781)),f319(f319(f146(f926(x43781),f926(x43781)),f128(x43781,x43782)),x43783)),f319(f128(x43781,x43782),f319(f134(f926(x43781),f926(x43781),f126(x43781),f105(x43781)),x43783)))
% 28.73/28.51 [4382]E(f319(f248(f926(x43821),f926(x43821)),f158(x43821,x43822,x43823)),f319(f128(x43821,f319(f66(a923,a923,x43821,a314),x43822)),x43823))
% 28.73/28.51 [4427]E(f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f75(a1),x44271),f319(f319(f30(a1),x44272),x44271))),f39(a1,x44272,x44271))),x44273),f319(f319(f74(a1),x44272),x44273))
% 28.73/28.51 [4464]E(f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f75(a1),f319(f319(f30(a1),x44641),x44642)),x44642)),f39(a1,x44641,x44642))),x44643),f319(f319(f74(a1),x44641),x44643))
% 28.73/28.51 [4490]E(f79(f931(x44901,x44902),f319(f249(x44901,x44902,a923),f319(f319(f8(f932(x44902,f931(x44901,x44902)),f932(x44902,a923),x44901),f319(f8(f931(x44901,x44902),a923,x44902),x44903)),f244(x44901,x44902)))),f79(f931(x44901,x44902),x44903))
% 28.73/28.51 [4491]E(f84(f931(x44911,x44912),f319(f249(x44911,x44912,a923),f319(f319(f8(f932(x44912,f931(x44911,x44912)),f932(x44912,a923),x44911),f319(f8(f931(x44911,x44912),a923,x44912),x44913)),f244(x44911,x44912)))),f84(f931(x44911,x44912),x44913))
% 28.73/28.51 [4518]P1(f319(f319(f226(f932(x45181,a923)),f31(f932(x45181,a923),f319(f319(f93(f932(f932(x45181,a923),a923)),x45182),x45183))),f319(f319(f93(f932(x45181,a923)),f31(f932(x45181,a923),x45182)),f31(f932(x45181,a923),x45183))))
% 28.73/28.51 [4519]E(f319(f160(x45191),f319(f319(f319(f175(f926(x45191),f926(x45191)),f319(f319(f23(a925),f319(f181(f926(x45191)),x45192)),f39(a925,x45193,f319(f181(f926(x45191)),x45192)))),f159(x45191)),x45192)),f319(f319(f319(f175(f926(x45191),f926(x45191)),x45193),f159(x45191)),f319(f160(x45191),x45192)))
% 28.73/28.51 [4556]P1(f319(f319(f226(a925),f319(f181(f926(x45561)),f319(f319(f130(x45561),f319(f181(f926(x45561)),f169(x45561,x45562,x45563))),x45563))),f319(f181(f926(x45561)),x45563)))
% 28.73/28.51 [4773]~P1(f319(f56(x47731,x47732,f180(f932(x47731,a923))),x47733))
% 28.73/28.51 [4778]~P1(f319(f319(f321(f931(x47781,x47781)),f319(f319(f244(x47781,x47781),x47782),x47783)),f145(x47781,f105(f932(x47781,a925)))))
% 28.73/28.51 [3873]E(f319(f181(f926(x38731)),f319(f319(f167(x38731),x38732),x38733)),f319(f319(f224(a925),f319(f181(f926(x38731)),x38733)),x38732))
% 28.73/28.51 [3874]E(f319(f181(f926(x38741)),f319(f319(f130(x38741),x38742),x38743)),f319(f319(f23(a925),f319(f181(f926(x38741)),x38743)),x38742))
% 28.73/28.51 [3902]E(f319(f181(f926(f926(x39021))),f49(x39021,x39022,x39023)),f319(f319(f236(a925),f319(f181(f926(x39021)),x39023)),x39022))
% 28.73/28.51 [3919]E(f319(f319(f30(a925),f319(f319(f30(a925),x39191),x39192)),x39193),f319(f319(f30(a925),x39191),f319(f319(f75(a925),x39192),x39193)))
% 28.73/28.51 [3920]E(f319(f319(f23(a925),f319(f319(f23(a925),x39201),x39202)),x39203),f319(f319(f23(a925),x39201),f319(f319(f74(a925),x39202),x39203)))
% 28.73/28.51 [3921]E(f319(f319(f75(a925),f319(f319(f75(a925),x39211),x39212)),x39213),f319(f319(f75(a925),x39211),f319(f319(f75(a925),x39212),x39213)))
% 28.73/28.51 [3922]E(f319(f319(f75(a1),f319(f319(f75(a1),x39221),x39222)),x39223),f319(f319(f75(a1),x39221),f319(f319(f75(a1),x39222),x39223)))
% 28.73/28.51 [3923]E(f319(f319(f74(a925),f319(f319(f74(a925),x39231),x39232)),x39233),f319(f319(f74(a925),x39231),f319(f319(f74(a925),x39232),x39233)))
% 28.73/28.51 [3924]E(f319(f319(f74(a1),f319(f319(f74(a1),x39241),x39242)),x39243),f319(f319(f74(a1),x39241),f319(f319(f74(a1),x39242),x39243)))
% 28.73/28.51 [3925]E(f319(f319(f236(a1),f319(f319(f236(a1),x39251),x39252)),x39253),f319(f319(f236(a1),x39251),f319(f319(f75(a925),x39252),x39253)))
% 28.73/28.51 [3944]E(f154(x39441,f319(f319(f143(f932(x39441,a923)),x39442),x39443)),f166(x39441,x39442,f154(x39441,x39443)))
% 28.73/28.51 [3987]E(f319(f319(f23(a925),f319(f319(f23(a925),x39871),x39872)),x39873),f319(f319(f23(a925),f319(f319(f23(a925),x39871),x39873)),x39872))
% 28.73/28.51 [3995]E(f319(f319(f93(f932(x39951,a923)),x39952),f319(f319(f23(f932(x39951,a923)),x39953),x39952)),f180(f932(x39951,a923)))
% 28.73/28.51 [3999]E(f319(f319(f146(a925,x39991),f319(f16(x39991,a925),x39992)),f131(a925,f319(f294(a925,f2(a925)),x39993))),f161(x39991,x39993,x39992))
% 28.73/28.51 [4037]E(f32(f932(x40371,a923),f319(f319(f301(f932(x40371,a923)),x40372),x40373)),f319(f319(f93(f932(x40371,a923)),x40372),f32(f932(x40371,a923),x40373)))
% 28.73/28.51 [4038]E(f31(f932(x40381,a923),f319(f319(f301(f932(x40381,a923)),x40382),x40383)),f319(f319(f102(f932(x40381,a923)),x40382),f31(f932(x40381,a923),x40383)))
% 28.73/28.51 [4040]E(f161(x40401,f319(f181(f926(x40401)),f319(f128(x40401,f319(a316,x40402)),x40403)),x40402),f319(f128(x40401,f319(a316,x40402)),x40403))
% 28.73/28.51 [4042]E(f319(f319(f23(a925),f319(f319(f75(a925),x40421),x40422)),f319(f319(f75(a925),x40423),x40422)),f319(f319(f75(a925),f319(f319(f23(a925),x40421),x40423)),x40422))
% 28.73/28.51 [4043]E(f319(f319(f74(a925),f319(f319(f75(a925),x40431),x40432)),f319(f319(f75(a925),x40433),x40432)),f319(f319(f75(a925),f319(f319(f74(a925),x40431),x40433)),x40432))
% 28.73/28.51 [4044]E(f319(f319(f23(a1),f319(f319(f75(a1),x40441),x40442)),f319(f319(f75(a1),x40443),x40442)),f319(f319(f75(a1),f319(f319(f23(a1),x40441),x40443)),x40442))
% 28.73/28.51 [4045]E(f319(f319(f74(a1),f319(f319(f75(a1),x40451),x40452)),f319(f319(f75(a1),x40453),x40452)),f319(f319(f75(a1),f319(f319(f74(a1),x40451),x40453)),x40452))
% 28.73/28.51 [4047]E(f319(f319(f224(a925),f319(f319(f23(a925),x40471),x40472)),f319(f319(f23(a925),x40473),x40472)),f319(f319(f23(a925),f319(f319(f224(a925),x40471),x40473)),x40472))
% 28.73/28.51 [4067]E(f319(f319(f93(f932(f926(x40671),a923)),f152(x40671,x40672)),f152(x40671,x40673)),f152(x40671,f319(f319(f93(f932(x40671,a923)),x40672),x40673)))
% 28.73/28.51 [4070]E(f319(f319(f102(f932(x40701,a923)),x40702),f319(f319(f102(f932(x40701,a923)),x40702),x40703)),f319(f319(f102(f932(x40701,a923)),x40702),x40703))
% 28.73/28.51 [4071]E(f319(f319(f102(f932(x40711,a923)),x40712),f319(f319(f23(f932(x40711,a923)),x40713),x40712)),f319(f319(f102(f932(x40711,a923)),x40712),x40713))
% 28.73/28.51 [4072]E(f319(f319(f93(f932(x40721,a923)),x40722),f319(f319(f93(f932(x40721,a923)),x40722),x40723)),f319(f319(f93(f932(x40721,a923)),x40722),x40723))
% 28.73/28.51 [4084]E(f319(f319(f281(x40841,x40842,x40842),x40843),f299(x40842,f180(f932(f931(x40842,x40842),a923)))),x40843)
% 28.73/28.51 [4087]E(f319(f319(f102(f932(x40871,a923)),f319(f319(f301(x40871),x40872),f180(f932(x40871,a923)))),x40873),f319(f319(f301(x40871),x40872),x40873))
% 28.73/28.51 [4106]E(f319(f319(f23(a925),f319(f319(f23(a925),f319(a104,x41061)),x41062)),f319(a104,x41063)),f319(f319(f23(a925),f319(f319(f23(a925),x41061),x41062)),x41063))
% 28.73/28.51 [4133]E(f319(f319(f93(f932(f932(x41331,a923),a923)),f319(f300(x41331),x41332)),f319(f300(x41331),x41333)),f319(f300(x41331),f319(f319(f93(f932(x41331,a923)),x41332),x41333)))
% 28.73/28.51 [4136]E(f319(f319(f102(f932(x41361,a923)),f319(f73(f932(x41361,a923)),x41362)),x41363),f319(f73(f932(x41361,a923)),f319(f319(f23(f932(x41361,a923)),x41362),x41363)))
% 28.73/28.51 [4145]E(f319(f319(f301(x41451),x41452),f319(f319(f23(f932(x41451,a923)),x41453),f319(f319(f301(x41451),x41452),f180(f932(x41451,a923))))),f319(f319(f301(x41451),x41452),x41453))
% 28.73/28.51 [4155]P1(f319(f319(f226(f932(x41551,a923)),x41552),f319(f319(f102(f932(x41551,a923)),x41553),x41552)))
% 28.73/28.51 [4156]P1(f319(f319(f226(f932(x41561,a923)),x41562),f319(f319(f102(f932(x41561,a923)),x41562),x41563)))
% 28.73/28.51 [4160]E(f319(f319(f93(f932(x41601,a923)),f319(f73(f932(x41601,a923)),x41602)),f319(f73(f932(x41601,a923)),x41603)),f319(f73(f932(x41601,a923)),f319(f319(f102(f932(x41601,a923)),x41602),x41603)))
% 28.73/28.51 [4161]E(f319(f319(f102(f932(x41611,a923)),f319(f73(f932(x41611,a923)),x41612)),f319(f73(f932(x41611,a923)),x41613)),f319(f73(f932(x41611,a923)),f319(f319(f93(f932(x41611,a923)),x41612),x41613)))
% 28.73/28.51 [4175]P1(f319(f319(f226(f932(x41751,a923)),f319(f164(x41751),x41752)),f319(f164(x41751),f319(f319(f143(x41751),x41753),x41752))))
% 28.73/28.51 [4187]E(f319(f319(f102(f932(x41871,a923)),f319(f319(f23(f932(x41871,a923)),x41872),x41873)),f319(f319(f93(f932(x41871,a923)),x41872),x41873)),x41872)
% 28.73/28.51 [4238]E(f319(f319(f6(x42381,a1),f319(f319(f8(a925,a1,x42381),f92(a1)),x42382)),x42383),f319(f92(a1),f319(f319(f6(x42381,a925),x42382),x42383)))
% 28.73/28.51 [4239]E(f319(f319(f9(x42391,a1),f319(f319(f8(a925,a1,x42391),f92(a1)),x42392)),x42393),f319(f92(a1),f319(f319(f9(x42391,a925),x42392),x42393)))
% 28.73/28.51 [4286]E(f319(f319(f126(x42861),f169(x42861,x42862,x42863)),f319(f319(f130(x42861),f319(f181(f926(x42861)),f169(x42861,x42862,x42863))),x42863)),x42863)
% 28.73/28.51 [4290]E(f319(f73(f932(f931(x42901,x42902),a923)),f319(f319(f246(x42901,x42902),x42903),f319(f16(f932(x42902,a923),x42901),f234(f932(x42902,a923))))),f319(f319(f246(x42901,x42902),f319(f73(f932(x42901,a923)),x42903)),f319(f16(f932(x42902,a923),x42901),f234(f932(x42902,a923)))))
% 28.73/28.51 [4291]E(f319(f73(f932(f931(x42911,x42912),a923)),f319(f319(f246(x42911,x42912),f234(f932(x42911,a923))),f319(f16(f932(x42912,a923),x42911),x42913))),f319(f319(f246(x42911,x42912),f234(f932(x42911,a923))),f319(f16(f932(x42912,a923),x42911),f319(f73(f932(x42912,a923)),x42913))))
% 28.73/28.51 [4342]E(f319(f319(f33(f932(x43421,a923),f932(x43421,a923)),x43422),f319(f319(f7(f932(x43421,a923),f932(x43421,a923),f932(x43421,a923)),f93(f932(x43421,a923))),x43423)),f319(f319(f93(f932(x43421,a923)),f31(f932(x43421,a923),x43422)),x43423))
% 28.73/28.51 [4348]E(f319(f134(f926(x43481),f926(x43481),f126(x43481),f105(x43481)),f319(f319(f143(f926(x43481)),x43482),x43483)),f319(f319(f126(x43481),x43482),f319(f134(f926(x43481),f926(x43481),f126(x43481),f105(x43481)),x43483)))
% 28.73/28.51 [4369]E(f319(f319(f301(f932(x43691,a923)),f319(f277(x43691,x43691,x43692),f319(f319(f301(x43691),x43693),f180(f932(x43691,a923))))),f180(f932(f932(x43691,a923),a923))),f319(f319(f54(x43691),f319(f319(f301(x43691),x43693),f180(f932(x43691,a923)))),x43692))
% 28.73/28.51 [4379]E(f319(f319(f74(a925),f319(f319(f75(a925),x43791),f319(f319(f30(a925),x43792),x43793))),f319(f319(f30(a925),f319(f319(f75(a925),x43791),f39(a925,x43792,x43793))),x43793)),f319(f319(f30(a925),f319(f319(f75(a925),x43791),x43792)),x43793))
% 28.73/28.51 [4380]E(f319(f319(f74(a1),f319(f319(f75(a1),x43801),f319(f319(f30(a1),x43802),x43803))),f319(f319(f30(a1),f319(f319(f75(a1),x43801),f39(a1,x43802,x43803))),x43803)),f319(f319(f30(a1),f319(f319(f75(a1),x43801),x43802)),x43803))
% 28.73/28.51 [4412]E(f319(f319(f23(f932(x44121,a923)),f319(f164(x44121),x44122)),f319(f319(f301(x44121),x44123),f180(f932(x44121,a923)))),f319(f164(x44121),f319(f128(x44121,f319(f319(f8(a923,a923,x44121),a314),f319(a316,x44123))),x44122)))
% 28.73/28.51 [4462]E(f319(f319(f126(x44621),f319(f134(f926(x44621),f926(x44621),f126(x44621),f105(x44621)),x44622)),f319(f134(f926(x44621),f926(x44621),f126(x44621),f105(x44621)),x44623)),f319(f134(f926(x44621),f926(x44621),f126(x44621),f105(x44621)),f319(f319(f126(f926(x44621)),x44622),x44623)))
% 28.73/28.51 [4465]E(f319(f319(f244(f926(x44651),f926(x44651)),f319(f128(x44651,x44652),x44653)),f319(f128(x44651,f319(f66(a923,a923,x44651,a314),x44652)),x44653)),f158(x44651,x44652,x44653))
% 28.73/28.51 [4468]E(f319(f319(f74(a925),f319(f319(f74(a925),f319(f319(f30(a925),x44681),x44682)),f319(f319(f30(a925),x44683),x44682))),f319(f319(f30(a925),f319(f319(f74(a925),f39(a925,x44681,x44682)),f39(a925,x44683,x44682))),x44682)),f319(f319(f30(a925),f319(f319(f74(a925),x44681),x44683)),x44682))
% 28.73/28.51 [4469]E(f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f30(a1),x44691),x44692)),f319(f319(f30(a1),x44693),x44692))),f319(f319(f30(a1),f319(f319(f74(a1),f39(a1,x44691,x44692)),f39(a1,x44693,x44692))),x44692)),f319(f319(f30(a1),f319(f319(f74(a1),x44691),x44693)),x44692))
% 28.73/28.51 [4522]E(f319(f319(f93(f932(f926(x45221),a923)),f319(f319(f7(f926(x45221),f932(f926(x45221),a923),a923),f321(f926(x45221))),f153(x45221,x45222))),f319(f319(f7(f926(x45221),f932(f926(x45221),a923),a923),f321(f926(x45221))),f153(x45221,x45223))),f152(x45221,f319(f319(f93(f932(x45221,a923)),f319(f319(f7(x45221,f932(x45221,a923),a923),f321(x45221)),x45222)),f319(f319(f7(x45221,f932(x45221,a923),a923),f321(x45221)),x45223))))
% 28.73/28.51 [4533]E(f319(f254(x45331),f319(f319(f18(x45331,a923,a923),f319(f319(f8(a923,f932(a923,a923),x45331),a318),f319(f319(f7(x45331,x45331,a923),a316),x45332))),f319(f319(f7(x45331,f932(x45331,a923),a923),f321(x45331)),x45333))),f319(f319(f301(x45331),x45332),x45333))
% 28.73/28.51 [4534]E(f319(f254(x45341),f319(f319(f18(x45341,a923,a923),f319(f319(f8(a923,f932(a923,a923),x45341),a318),f319(f319(f7(x45341,x45341,a923),a316),x45342))),f319(f319(f7(x45341,f932(x45341,a923),a923),f321(x45341)),x45343))),f319(f319(f301(x45341),x45342),x45343))
% 28.73/28.51 [4554]E(f319(f319(f80(f926(f926(x45541)),f926(f926(x45541))),f48(x45541,x45542)),f319(f319(f18(f926(f926(x45541)),f926(f926(x45541)),f926(f926(x45541))),f319(f319(f8(f926(f926(x45541)),f932(f926(f926(x45541)),f926(f926(x45541))),f926(f926(x45541))),f126(f926(x45541))),f319(f146(f926(x45541),f926(x45541)),f319(f143(x45541),x45543)))),f5(f926(f926(x45541))))),f48(x45541,f319(f319(f143(x45541),x45543),x45542)))
% 28.73/28.51 [4557]E(f319(f254(x45571),f319(f319(f18(x45571,a923,a923),f319(f319(f8(a923,f932(a923,a923),x45571),a318),f319(f319(f7(x45571,f932(x45571,a923),a923),f321(x45571)),x45572))),f319(f319(f7(x45571,f932(x45571,a923),a923),f321(x45571)),x45573))),f319(f319(f102(f932(x45571,a923)),x45572),x45573))
% 28.73/28.51 [4558]E(f319(f254(x45581),f319(f319(f18(x45581,a923,a923),f319(f319(f8(a923,f932(a923,a923),x45581),a317),f319(f319(f7(x45581,f932(x45581,a923),a923),f321(x45581)),x45582))),f319(f319(f7(x45581,f932(x45581,a923),a923),f321(x45581)),x45583))),f319(f319(f93(f932(x45581,a923)),x45582),x45583))
% 28.73/28.51 [4647]E(f319(f319(f33(x46471,f932(f932(x46471,a923),a923)),x46472),f319(f319(f7(x46471,f932(f932(x46471,a923),a923),f932(f932(x46471,a923),a923)),f319(f319(f8(f932(x46471,a923),f932(f932(f932(x46471,a923),a923),f932(f932(x46471,a923),a923)),x46471),f301(f932(x46471,a923))),f319(f319(f8(f932(x46471,a923),f932(x46471,a923),x46471),f277(x46471,x46471,x46473)),f319(f319(f7(x46471,f932(x46471,a923),f932(x46471,a923)),f301(x46471)),f180(f932(x46471,a923)))))),f180(f932(f932(x46471,a923),a923)))),f319(f319(f54(x46471),x46472),x46473))
% 28.73/28.51 [4649]E(f319(f319(f193(x46491),f319(f319(f75(a1),f319(f319(f66(f931(a1,a1),a1,x46491,f243(a1,a1)),f204(x46491)),x46492)),f319(f319(f66(f931(a1,a1),a1,x46491,f243(a1,a1)),f204(x46491)),x46493))),f319(f319(f75(a1),f319(f319(f66(f931(a1,a1),a1,x46491,f248(a1,a1)),f204(x46491)),x46492)),f319(f319(f66(f931(a1,a1),a1,x46491,f248(a1,a1)),f204(x46491)),x46493))),f220(x46491,x46492,x46493))
% 28.73/28.51 [4652]E(f319(f254(f926(x46521)),f319(f319(f18(f926(x46521),a923,a923),f319(f319(f8(a923,f932(a923,a923),f926(x46521)),a317),f319(f319(f7(f926(x46521),a925,a923),f319(f319(f8(a925,f932(a925,a923),f926(x46521)),a316),f181(f926(x46521)))),x46522))),f319(f319(f7(f926(x46521),f932(x46521,a923),a923),f319(f319(f8(f932(x46521,a923),f932(f932(x46521,a923),a923),f926(x46521)),f226(f932(x46521,a923))),f164(x46521))),f319(f164(x46521),x46523)))),f319(f164(f926(x46521)),f49(x46521,x46522,x46523)))
% 28.73/28.51 [4060]E(f39(a925,f319(f319(f74(a925),f319(f319(f75(a925),x40601),x40602)),x40603),x40602),f39(a925,x40603,x40602))
% 28.73/28.51 [4105]E(f131(a925,f319(f294(a925,f319(f319(f74(a925),x41051),x41052)),x41053)),f319(f319(f130(a925),x41052),f131(a925,f319(f294(a925,x41051),x41053))))
% 28.73/28.51 [4144]E(f319(f319(f74(a1),f319(f92(a1),x41441)),f319(f319(f74(a1),f319(f92(a1),x41442)),x41443)),f319(f319(f74(a1),f319(f92(a1),f319(f319(f74(a925),x41441),x41442))),x41443))
% 28.73/28.51 [4151]E(f319(f319(f102(f932(x41511,a923)),f319(f319(f23(f932(x41511,a923)),x41512),x41513)),x41513),f319(f319(f102(f932(x41511,a923)),x41512),x41513))
% 28.73/28.51 [4152]E(f319(f319(f23(f932(x41521,a923)),f319(f319(f23(f932(x41521,a923)),x41522),x41523)),x41523),f319(f319(f23(f932(x41521,a923)),x41522),x41523))
% 28.73/28.51 [4176]E(f319(f319(f281(x41761,x41761,x41762),f299(x41761,f180(f932(f931(x41761,x41761),a923)))),x41763),x41763)
% 28.73/28.51 [4184]E(f319(f319(f102(f932(x41841,a923)),f319(f273(x41841),x41842)),f319(f273(x41841),x41843)),f319(f273(x41841),f319(f319(f102(f932(f931(x41841,x41841),a923)),x41842),x41843)))
% 28.73/28.51 [4194]E(f258(x41941,f319(f319(f143(f931(a91,x41941)),f319(f319(f244(a91,x41941),f2(a91)),x41942)),x41943)),f258(x41941,x41943))
% 28.73/28.51 [4196]E(f319(f319(f93(f932(x41961,a923)),f32(f932(x41961,a923),x41962)),f32(f932(x41961,a923),x41963)),f32(f932(x41961,a923),f319(f319(f102(f932(f932(x41961,a923),a923)),x41962),x41963)))
% 28.73/28.51 [4197]E(f319(f319(f102(f932(x41971,a923)),f31(f932(x41971,a923),x41972)),f31(f932(x41971,a923),x41973)),f31(f932(x41971,a923),f319(f319(f102(f932(f932(x41971,a923),a923)),x41972),x41973)))
% 28.73/28.51 [4234]E(f319(f319(f281(x42341,x42341,x42341),f319(f319(f175(f931(x42341,x42341),a923),x42342),x42343)),x42343),f319(f319(f175(f931(x42341,x42341),a923),f319(a104,x42342)),x42343))
% 28.73/28.51 [4278]P1(f319(f319(f226(f932(x42781,a923)),f319(f319(f93(f932(x42781,a923)),x42782),x42783)),x42783))
% 28.73/28.51 [4279]P1(f319(f319(f226(f932(x42791,a923)),f319(f319(f93(f932(x42791,a923)),x42792),x42793)),x42792))
% 28.73/28.51 [4280]P1(f319(f319(f226(f932(x42801,a923)),f319(f319(f23(f932(x42801,a923)),x42802),x42803)),x42802))
% 28.73/28.51 [4304]E(f299(x43041,f319(f319(f102(f932(f931(x43041,x43041),a923)),f299(x43041,x43042)),f299(x43041,x43043))),f299(x43041,f319(f319(f102(f932(f931(x43041,x43041),a923)),x43042),x43043)))
% 28.73/28.51 [4308]E(f31(f932(x43081,a923),f319(f319(f301(f932(x43081,a923)),x43082),f319(f319(f301(f932(x43081,a923)),x43083),f180(f932(f932(x43081,a923),a923))))),f319(f319(f102(f932(x43081,a923)),x43082),x43083))
% 28.73/28.51 [4309]E(f32(f932(x43091,a923),f319(f319(f301(f932(x43091,a923)),x43092),f319(f319(f301(f932(x43091,a923)),x43093),f180(f932(f932(x43091,a923),a923))))),f319(f319(f93(f932(x43091,a923)),x43092),x43093))
% 28.73/28.51 [4314]E(f319(f319(f281(x43141,x43141,x43141),f319(f319(f175(f931(x43141,x43141),a923),x43142),x43143)),x43143),f319(f319(f281(x43141,x43141,x43141),x43143),f319(f319(f175(f931(x43141,x43141),a923),x43142),x43143)))
% 28.73/28.51 [4383]E(f319(f319(f102(f932(x43831,a923)),f319(f254(x43831),f319(f319(f7(x43831,x43831,a923),a316),x43832))),x43833),f319(f319(f301(x43831),x43832),x43833))
% 28.73/28.51 [4385]E(f319(a96,f319(f319(f6(x43851,a1),f319(f319(f8(a925,a1,x43851),f92(a1)),x43852)),x43853)),f319(f319(f6(x43851,a925),x43852),x43853))
% 28.73/28.51 [4386]E(f319(a96,f319(f319(f9(x43861,a1),f319(f319(f8(a925,a1,x43861),f92(a1)),x43862)),x43863)),f319(f319(f9(x43861,a925),x43862),x43863))
% 28.73/28.51 [4459]E(f319(f148(f926(x44591),x44591,f319(f163(x44591),x44592),f319(f16(f932(f926(x44591),f926(x44591)),x44591),f319(f319(f7(f926(x44591),f926(x44591),f926(x44591)),f126(x44591)),x44592))),x44593),f319(f163(x44591),f319(f319(f126(x44591),x44593),x44592)))
% 28.73/28.51 [4487]P1(f319(f319(f226(f932(f932(x44871,a923),a923)),f319(f319(f102(f932(f932(x44871,a923),a923)),f319(f300(x44871),x44872)),f319(f300(x44871),x44873))),f319(f300(x44871),f319(f319(f102(f932(x44871,a923)),x44872),x44873))))
% 28.73/28.51 [4576]E(f319(f254(x45761),f319(f319(f18(x45761,a923,a923),f319(f319(f8(a923,f932(a923,a923),x45761),a317),f319(f319(f7(x45761,f932(x45761,a923),a923),f321(x45761)),x45762))),f319(f319(f8(a923,a923,x45761),a314),f319(f319(f7(x45761,f932(x45761,a923),a923),f321(x45761)),x45763)))),f319(f319(f23(f932(x45761,a923)),x45762),x45763))
% 28.73/28.51 [4600]E(f319(f29(a925),f319(f254(a925),f319(f319(f18(a925,a923,a923),f319(f319(f8(a923,f932(a923,a923),a925),a317),f319(f319(f7(a925,a925,a923),f227(a925)),f319(f181(f926(x46001)),x46002)))),f319(f319(f8(x46001,a923,a925),x46003),f319(f156(x46001),x46002))))),f319(f181(f926(x46001)),f319(f128(x46001,x46003),x46002)))
% 28.73/28.51 [4602]E(f319(f181(f926(x46021)),f168(x46021,x46022,x46023)),f319(f29(a925),f319(f254(a925),f319(f319(f18(a925,a923,a923),f319(f319(f8(a923,f932(a923,a923),a925),a317),f319(f319(f7(a925,a925,a923),f227(a925)),f319(f181(f926(x46021)),x46022)))),f319(f319(f7(a925,f932(a925,a923),a923),f321(a925)),x46023)))))
% 28.73/28.51 [4698]E(f319(f319(f93(f932(f931(f926(x46981),f926(x46981)),a923)),f319(f302(f931(f931(x46981,f926(x46981)),f931(x46981,f926(x46981))),f931(f926(x46981),f926(x46981)),f250(f931(x46981,f926(x46981)),f926(x46981),f931(x46981,f926(x46981)),f926(x46981),f319(f249(x46981,f926(x46981),f926(x46981)),f143(x46981)),f319(f249(x46981,f926(x46981),f926(x46981)),f143(x46981)))),f312(x46981,f926(x46981),x46982,f319(f135(x46981,x46982),x46983)))),f319(f254(f931(f926(x46981),f926(x46981))),f319(f249(f926(x46981),f926(x46981),a923),f319(f319(f7(f926(x46981),f932(f926(x46981),a923),f932(f926(x46981),a923)),f319(f319(f8(f932(a923,a923),f932(f932(f926(x46981),a923),f932(f926(x46981),a923)),f926(x46981)),f8(a923,a923,f926(x46981))),f319(f319(f8(a923,f932(a923,a923),f926(x46981)),a317),f319(f319(f7(f926(x46981),a925,a923),f319(f319(f8(a925,f932(a925,a923),f926(x46981)),a316),f181(f926(x46981)))),f319(a104,x46983))))),f319(f319(f7(f926(x46981),a925,a923),f319(f319(f8(a925,f932(a925,a923),f926(x46981)),a316),f181(f926(x46981)))),f319(a104,x46983)))))),f319(f135(x46981,x46982),f319(a104,x46983)))
% 28.73/28.51 [4198]E(f39(a925,f319(a104,f319(f319(f74(a925),f319(f319(f75(a925),x41981),x41982)),x41983)),x41982),f39(a925,f319(a104,x41983),x41982))
% 28.73/28.51 [4445]E(f319(f254(x44451),f319(f319(f18(x44451,a923,a923),f319(f319(f8(a923,f932(a923,a923),x44451),a317),x44452)),x44453)),f319(f319(f93(f932(x44451,a923)),f319(f254(x44451),x44452)),f319(f254(x44451),x44453)))
% 28.73/28.51 [4446]E(f319(f254(x44461),f319(f319(f18(x44461,a923,a923),f319(f319(f8(a923,f932(a923,a923),x44461),a318),x44462)),x44463)),f319(f319(f102(f932(x44461,a923)),f319(f254(x44461),x44462)),f319(f254(x44461),x44463)))
% 28.73/28.51 [4448]E(f319(f319(f126(x44481),f319(f319(f130(x44481),f39(a925,x44482,f319(f181(f926(x44481)),x44483))),x44483)),f319(f319(f167(x44481),f39(a925,x44482,f319(f181(f926(x44481)),x44483))),x44483)),f319(f319(f319(f175(f926(x44481),f926(x44481)),x44482),f159(x44481)),x44483))
% 28.73/28.51 [4454]E(f319(f254(x44541),f319(f319(f18(x44541,a923,a923),f319(f319(f8(a923,f932(a923,a923),x44541),a322),x44542)),x44543)),f319(f319(f102(f932(x44541,a923)),f319(f73(f932(x44541,a923)),f319(f254(x44541),x44542))),f319(f254(x44541),x44543)))
% 28.73/28.51 [4470]E(f319(f319(f74(a925),f319(f181(f926(x44701)),f319(f128(x44701,x44702),x44703))),f319(f181(f926(x44701)),f319(f128(x44701,f319(f319(f8(a923,a923,x44701),a314),x44702)),x44703))),f319(f181(f926(x44701)),x44703))
% 28.73/28.51 [4493]P1(f319(f319(f226(f932(x44931,a923)),f319(f319(f102(f932(x44931,a923)),f32(f932(x44931,a923),x44932)),f32(f932(x44931,a923),x44933))),f32(f932(x44931,a923),f319(f319(f93(f932(f932(x44931,a923),a923)),x44932),x44933))))
% 28.73/28.51 [4507]E(f319(f164(x45071),f319(f128(x45071,f319(f319(f8(a923,a923,x45071),a314),f319(f319(f7(x45071,x45071,a923),a316),x45072))),x45073)),f319(f319(f23(f932(x45071,a923)),f319(f164(x45071),x45073)),f319(f319(f301(x45071),x45072),f180(f932(x45071,a923)))))
% 28.73/28.51 [4516]P1(f319(f319(f226(f932(f931(x45161,x45161),a923)),f319(f319(f102(f932(f931(x45161,x45161),a923)),f299(x45161,x45162)),f299(x45161,x45163))),f299(x45161,f319(f319(f102(f932(f931(x45161,x45161),a923)),x45162),x45163))))
% 28.73/28.51 [4539]E(f319(f319(f75(a925),f319(a104,f319(a104,f2(a925)))),f319(f319(f6(a925,a925),f319(f319(f8(a925,a925,a925),f319(f74(a925),x45391)),f319(f319(f7(a925,a925,a925),f75(a925)),x45392))),f319(f274(a925),x45393))),f319(f319(f75(a925),x45393),f319(f319(f74(a925),x45391),f319(f319(f74(a925),x45391),f319(f319(f75(a925),f319(f319(f23(a925),x45393),f72(a925))),x45392)))))
% 28.73/28.51 [4549]E(f319(f254(x45491),f319(f319(f18(x45491,a923,a923),f319(f319(f8(a923,f932(a923,a923),x45491),a317),f319(f319(f7(x45491,f932(x45491,a923),a923),f321(x45491)),f319(f164(x45491),x45492)))),x45493)),f319(f164(x45491),f319(f128(x45491,x45493),x45492)))
% 28.73/28.51 [4697]E(f319(f254(x46971),f319(f319(f8(f932(a925,a923),a923,x46971),f81(a925)),f319(f319(f7(x46971,f932(a925,a923),f932(a925,a923)),f319(f319(f8(f932(a925,f932(a923,a923)),f932(f932(a925,a923),f932(a925,a923)),x46971),f18(a925,a923,a923)),f319(f319(f8(f932(a925,a923),f932(a925,f932(a923,a923)),x46971),f319(f8(a923,f932(a923,a923),a925),a317)),f319(f319(f7(x46971,f932(a925,x46971),f932(a925,a923)),f319(f319(f8(f932(x46971,a923),f932(f932(a925,x46971),f932(a925,a923)),x46971),f8(x46971,a923,a925)),a316)),f319(f156(x46971),x46972))))),f319(f319(f18(a925,a923,a923),f319(f319(f8(a923,f932(a923,a923),a925),a317),f319(f319(f7(a925,a925,a923),f227(a925)),f319(f181(f926(x46971)),x46972)))),f319(f319(f7(a925,f932(a925,a923),a923),f321(a925)),x46973))))),f319(f164(x46971),f168(x46971,x46972,x46973)))
% 28.73/28.51 [4589]E(f319(f254(x45891),f319(f319(f18(x45891,a923,a923),f319(f319(f8(a923,f932(a923,a923),x45891),a322),f319(f319(f8(a923,a923,x45891),a314),f319(f319(f7(x45891,x45891,a923),a316),x45892)))),x45893)),f319(f319(f301(x45891),x45892),f319(f254(x45891),x45893)))
% 28.73/28.51 [4621]E(f319(f319(f146(f931(x46211,a925),x46211),f243(x46211,a925)),f319(f128(f931(x46211,a925),f319(f319(f7(f931(x46211,a925),f932(a925,a923),a923),f319(f319(f8(a925,f932(f932(a925,a923),a923),f931(x46211,a925)),f321(a925)),f248(x46211,a925))),x46212)),f319(f319(f173(x46211,a925),x46213),f131(a925,f319(f294(a925,f2(a925)),f319(f181(f926(x46211)),x46213)))))),f168(x46211,x46213,x46212))
% 28.73/28.51 [4648]E(f319(f319(f75(a1),f319(f95(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),f319(f319(f6(a925,a1),f319(f319(f8(a1,a1,a925),f319(f74(a1),x46481)),f319(f319(f7(a925,a1,a1),f319(f319(f8(a1,f932(a1,a1),a925),f75(a1)),f92(a1))),x46482))),f319(f274(a925),x46483))),f319(f319(f75(a1),f319(f92(a1),x46483)),f319(f319(f74(a1),x46481),f319(f319(f74(a1),x46481),f319(f319(f75(a1),f319(f92(a1),f319(f319(f23(a925),x46483),f72(a925)))),x46482)))))
% 28.73/28.51 [4690]E(f319(f254(f931(x46901,x46902)),f319(f249(x46901,x46902,a923),f319(f319(f7(x46901,f932(f931(x46902,x46901),a923),f932(x46902,a923)),f319(f319(f8(f932(x46902,f932(f932(f931(x46902,x46901),a923),a923)),f932(f932(f931(x46902,x46901),a923),f932(x46902,a923)),x46901),f7(x46902,f932(f931(x46902,x46901),a923),a923)),f319(f319(f8(f932(x46902,f931(x46902,x46901)),f932(x46902,f932(f932(f931(x46902,x46901),a923),a923)),x46901),f319(f8(f931(x46902,x46901),f932(f932(f931(x46902,x46901),a923),a923),x46902),f321(f931(x46902,x46901)))),f319(f7(x46902,x46901,f931(x46902,x46901)),f244(x46902,x46901))))),x46903))),f319(f278(x46902,x46901),x46903))
% 28.73/28.51 [4710]E(f319(f254(f926(x47101)),f319(f319(f8(f932(x47101,a923),a923,f926(x47101)),f81(x47101)),f319(f319(f8(f932(x47101,f932(f926(x47101),a923)),f932(x47101,a923),f926(x47101)),f319(f8(f932(f926(x47101),a923),a923,x47101),f81(f926(x47101)))),f319(f319(f7(f926(x47101),f932(x47101,f932(f926(x47101),a923)),f932(x47101,f932(f926(x47101),a923))),f319(f319(f8(f932(x47101,f932(f932(f926(x47101),a923),f932(f926(x47101),a923))),f932(f932(x47101,f932(f926(x47101),a923)),f932(x47101,f932(f926(x47101),a923))),f926(x47101)),f18(x47101,f932(f926(x47101),a923),f932(f926(x47101),a923))),f319(f319(f8(f932(x47101,f932(f926(x47101),f932(a923,a923))),f932(x47101,f932(f932(f926(x47101),a923),f932(f926(x47101),a923))),f926(x47101)),f319(f8(f932(f926(x47101),f932(a923,a923)),f932(f932(f926(x47101),a923),f932(f926(x47101),a923)),x47101),f18(f926(x47101),a923,a923))),f319(f319(f8(f932(x47101,f932(f926(x47101),a923)),f932(x47101,f932(f926(x47101),f932(a923,a923))),f926(x47101)),f319(f8(f932(f926(x47101),a923),f932(f926(x47101),f932(a923,a923)),x47101),f319(f8(a923,f932(a923,a923),f926(x47101)),a317))),f319(f319(f7(f926(x47101),f932(x47101,f932(f926(x47101),f926(x47101))),f932(x47101,f932(f926(x47101),a923))),f319(f319(f8(f932(f932(f926(x47101),f926(x47101)),f932(f926(x47101),a923)),f932(f932(x47101,f932(f926(x47101),f926(x47101))),f932(x47101,f932(f926(x47101),a923))),f926(x47101)),f8(f932(f926(x47101),f926(x47101)),f932(f926(x47101),a923),x47101)),f319(f319(f8(f932(f926(x47101),a923),f932(f932(f926(x47101),f926(x47101)),f932(f926(x47101),a923)),f926(x47101)),f8(f926(x47101),a923,f926(x47101))),a316))),f143(x47101)))))),f319(f319(f7(x47101,f932(f926(x47101),a923),f932(f926(x47101),a923)),f319(f319(f8(f932(a923,a923),f932(f932(f926(x47101),a923),f932(f926(x47101),a923)),x47101),f8(a923,a923,f926(x47101))),f319(f319(f8(a923,f932(a923,a923),x47101),a317),f319(f319(f7(x47101,f932(x47101,a923),a923),f321(x47101)),x47102)))),f319(f319(f7(f926(x47101),f932(f926(x47101),a923),a923),f321(f926(x47101))),x47103)))))),f166(x47101,x47102,x47103))
% 28.73/28.51 [4707]E(f319(f319(f80(a1,f931(a1,a1)),f319(f319(f23(a1),x47071),x47072)),f319(f319(f7(a1,f931(a1,a1),f931(a1,a1)),f319(f319(f18(a1,f931(a1,a1),f932(f931(a1,a1),f931(a1,a1))),f319(f319(f8(a923,f932(f931(a1,a1),f932(f931(a1,a1),f931(a1,a1))),a1),f86(f931(a1,a1))),f319(f226(a1),f2(a1)))),f319(f244(a1,a1),f319(f319(f74(a1),f319(f319(f75(a1),f319(f95(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),x47073)),f72(a1))))),f319(f319(f244(a1,a1),f319(f319(f75(a1),f319(f95(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),x47073)),x47071))),f319(f37(x47072),f319(f319(f244(a1,a1),x47073),x47071)))
% 28.73/28.51 [3760]E(f108(x37601,f319(x37602,x37603),f319(x37604,x37603)),f319(f195(x37601,x37602,x37604),x37603))
% 28.73/28.51 [3813]E(f319(f319(f237(x38131,x38132,x38133),x38134),f2(a925)),x38132)
% 28.73/28.51 [3851]E(f177(x38511,x38512,x38513,f319(a104,x38514)),f319(x38513,x38514))
% 28.73/28.51 [3892]E(f162(x38921,x38922,f162(x38921,x38923,x38924)),f162(x38921,x38923,f162(x38921,x38922,x38924)))
% 28.73/28.51 [3893]E(f118(x38931,x38932,f108(x38931,x38933,x38934)),f108(x38931,f118(x38931,x38932,x38933),x38934))
% 28.73/28.51 [4028]E(f319(f148(x40281,x40282,x40283,x40284),f105(x40282)),x40283)
% 28.73/28.51 [4029]E(f319(f134(x40291,x40292,x40293,x40294),f105(x40292)),x40294)
% 28.73/28.51 [4066]E(f319(f181(f930(x40661,x40662)),f212(x40661,x40662,x40663,x40664)),f2(a925))
% 28.73/28.51 [4089]E(f319(f249(x40891,x40892,x40893),f247(x40891,x40892,x40893,x40894)),x40894)
% 28.73/28.51 [4132]E(f319(f319(f126(x41321),f161(x41321,x41322,x41323)),f161(x41321,x41324,x41323)),f319(f319(f126(x41321),f161(x41321,x41324,x41323)),f161(x41321,x41322,x41323)))
% 28.73/28.51 [4217]E(f319(f319(f251(x42171,x42172,x42173,f931(x42172,x42173)),x42174),f244(x42172,x42173)),x42174)
% 28.73/28.51 [4227]E(f119(x42271,x42272,x42273,x42274,f111(x42272)),x42273)
% 28.73/28.51 [4233]E(f68(x42331,x42332,x42333,x42334,f319(x42333,x42334)),x42333)
% 28.73/28.51 [4499]P44(x44991,x44992,x44993,x44994,f180(f932(x44991,a923)),x44994)
% 28.73/28.51 [4500]P44(x45001,x45002,x45003,x45004,f180(f932(x45001,a923)),x45004)
% 28.73/28.51 [3565]E(f319(f319(f16(x35651,x35652),x35653),x35654),x35653)
% 28.73/28.51 [3841]E(f162(x38411,x38412,f319(f128(x38411,x38413),x38414)),f319(f128(x38411,x38413),f162(x38411,x38412,x38414)))
% 28.73/28.51 [3875]E(f319(f319(f58(x38751,x38752,x38753),x38754),f180(f932(x38751,a923))),x38754)
% 28.73/28.51 [3901]E(f319(f319(f156(x39011),f319(f319(f143(x39011),x39012),x39013)),f319(a104,x39014)),f319(f319(f156(x39011),x39013),x39014))
% 28.73/28.51 [3968]E(f319(f319(x39681,x39682),f319(f176(x39683,x39684,x39681),x39682)),f319(f176(x39683,x39684,x39681),f319(a104,x39682)))
% 28.73/28.51 [4009]E(f247(x40091,x40092,x40093,f319(f249(x40091,x40092,x40093),x40094)),x40094)
% 28.73/28.51 [4064]E(f319(f319(f151(x40641,f319(f319(f143(x40641),x40642),x40643)),f2(a925)),x40644),f319(f319(f143(x40641),x40644),x40643))
% 28.73/28.51 [4074]E(f319(f319(f33(f932(x40741,a923),f932(x40742,a923)),x40743),f302(x40741,x40742,x40744)),f319(f302(x40741,x40742,x40744),f31(f932(x40741,a923),x40743)))
% 28.73/28.51 [4075]E(f319(f319(f33(f932(x40751,a923),f932(x40752,a923)),x40753),f303(x40752,x40751,x40754)),f319(f303(x40752,x40751,x40754),f31(f932(x40751,a923),x40753)))
% 28.73/28.51 [4100]E(f112(x41001,f122(x41002,f927(x41001),x41003,x41004)),f319(f110(x41002,x41001,x41004),x41003))
% 28.73/28.51 [4172]E(f319(f117(x41721,x41722),f118(x41721,x41723,x41724)),f319(f319(f74(a925),f319(f319(f74(a925),f319(x41722,x41723)),f319(f117(x41721,x41722),x41724))),f319(a104,f2(a925))))
% 28.73/28.51 [4193]E(f319(f134(x41931,x41932,f319(f7(x41932,x41931,x41931),x41933),x41934),f319(f160(x41932),f105(x41932))),x41934)
% 28.73/28.51 [4237]E(f70(x42371,x42372,x42373,x42374,f180(f932(x42371,a923))),x42373)
% 28.73/28.51 [4298]E(f215(x42981,f931(x42982,f927(x42982)),x42983,f319(f249(x42982,f927(x42982),x42981),x42984),f319(f127(x42982),f111(x42982))),x42983)
% 28.73/28.51 [4430]E(f319(f249(x44301,x44302,x44303),f319(f319(f8(f932(x44302,f931(x44301,x44302)),f932(x44302,x44303),x44301),f319(f8(f931(x44301,x44302),x44303,x44302),x44304)),f244(x44301,x44302))),x44304)
% 28.73/28.51 [3751]E(f319(f248(x37511,x37512),f319(f319(f244(x37511,x37512),x37513),x37514)),x37514)
% 28.73/28.51 [3752]E(f319(f243(x37521,x37522),f319(f319(f244(x37521,x37522),x37523),x37524)),x37523)
% 28.73/28.51 [3785]E(f319(f181(f926(x37851)),f319(f319(f151(x37851,x37852),x37853),x37854)),f319(f181(f926(x37851)),x37852))
% 28.73/28.51 [3786]E(f319(f181(f926(x37861)),f319(f319(f146(x37862,x37861),x37863),x37864)),f319(f181(f926(x37862)),x37864))
% 28.73/28.51 [3807]E(f319(f319(f130(x38071),f319(a104,x38072)),f319(f319(f143(x38071),x38073),x38074)),f319(f319(f130(x38071),x38072),x38074))
% 28.73/28.51 [3870]E(f319(f319(f167(x38701),x38702),f161(x38701,x38703,x38704)),f161(x38701,f319(f319(f224(a925),x38702),x38703),x38704))
% 28.73/28.51 [3871]E(f319(f319(f130(x38711),x38712),f161(x38711,x38713,x38714)),f161(x38711,f319(f319(f23(a925),x38713),x38712),x38714))
% 28.73/28.51 [3877]E(f319(f319(f301(x38771),x38772),f319(f319(f301(x38771),x38773),x38774)),f319(f319(f301(x38771),x38773),f319(f319(f301(x38771),x38772),x38774)))
% 28.73/28.51 [3881]E(f319(f319(f146(x38811,x38812),x38813),f106(x38811,x38814)),f106(x38812,f319(f319(f146(x38811,x38812),x38813),x38814)))
% 28.73/28.51 [3899]E(f319(f160(x38991),f319(f319(f146(x38992,x38991),x38993),x38994)),f319(f319(f146(x38992,x38991),x38993),f319(f160(x38992),x38994)))
% 28.73/28.51 [3900]E(f319(f319(f146(x39001,x39002),x39003),f319(f163(x39001),x39004)),f319(f163(x39002),f319(f319(f146(x39001,x39002),x39003),x39004)))
% 28.73/28.51 [3915]E(f319(f319(f167(x39151),f319(a104,x39152)),f319(f319(f143(x39151),x39153),x39154)),f319(f319(f143(x39151),x39153),f319(f319(f167(x39151),x39152),x39154)))
% 28.73/28.51 [3918]E(f319(f164(x39181),f319(f319(f146(x39182,x39181),x39183),x39184)),f319(f302(x39182,x39181,x39183),f319(f164(x39182),x39184)))
% 28.73/28.51 [3931]E(f319(f319(f146(x39311,x39312),f319(f16(x39312,x39311),x39313)),x39314),f161(x39312,f319(f181(f926(x39311)),x39314),x39313))
% 28.73/28.51 [3967]E(f17(x39671,x39672,x39673,f319(a3,f319(a104,f319(a20,x39674)))),f319(x39673,x39674))
% 28.73/28.51 [3971]E(f319(f319(f126(x39711),f319(f128(x39711,x39712),x39713)),f319(f128(x39711,x39712),x39714)),f319(f128(x39711,x39712),f319(f319(f126(x39711),x39713),x39714)))
% 28.73/28.51 [3983]E(f144(x39831,f319(f319(f146(x39832,x39831),x39833),f144(x39832,x39834))),f144(x39831,f319(f319(f146(x39832,x39831),x39833),x39834)))
% 28.73/28.51 [3998]E(f319(f278(x39981,x39981),f319(f319(f280(x39982,x39981),x39983),x39984)),f319(f319(f280(x39982,x39981),f319(f278(x39982,x39982),x39983)),x39984))
% 28.73/28.51 [4010]E(f319(f319(f281(x40101,x40102,x40103),x40104),f180(f932(f931(x40102,x40103),a923))),f180(f932(f931(x40101,x40103),a923)))
% 28.73/28.51 [4011]E(f319(f319(f167(x40111),f319(f319(f23(a925),x40112),x40113)),f319(f319(f130(x40111),x40113),x40114)),f319(f319(f130(x40111),x40113),f319(f319(f167(x40111),x40112),x40114)))
% 28.73/28.51 [4030]E(f319(f319(f126(x40301),f161(x40301,x40302,x40303)),f161(x40301,x40304,x40303)),f161(x40301,f319(f319(f74(a925),x40302),x40304),x40303))
% 28.73/28.51 [4031]E(f319(f319(f319(f270(x40311),x40312),x40313),x40314),f319(f244(f932(a91,f932(a923,f929(f927(x40311)))),f931(a91,a91)),f319(f36(x40311),x40312)))
% 28.73/28.51 [4055]E(f31(f932(x40551,a923),f319(f302(x40552,f932(x40551,a923),x40553),x40554)),f319(f319(f33(x40552,f932(x40551,a923)),x40554),x40553))
% 28.73/28.51 [4056]E(f32(f932(x40561,a923),f319(f302(x40562,f932(x40561,a923),x40563),x40564)),f319(f319(f34(x40562,f932(x40561,a923)),x40564),x40563))
% 28.73/28.51 [4057]E(f32(f932(x40571,a923),f319(f302(x40572,f932(x40571,a923),x40573),x40574)),f319(f319(f34(x40572,f932(x40571,a923)),x40574),x40573))
% 28.73/28.51 [4058]E(f31(f932(x40581,a923),f319(f302(x40582,f932(x40581,a923),x40583),x40584)),f319(f319(f33(x40582,f932(x40581,a923)),x40584),x40583))
% 28.73/28.51 [4059]E(f319(f181(f926(f931(x40591,x40592))),f319(f319(f173(x40591,x40592),x40593),x40594)),f319(f319(f224(a925),f319(f181(f926(x40591)),x40593)),f319(f181(f926(x40592)),x40594)))
% 28.73/28.51 [4061]E(f319(f303(x40611,x40612,x40613),f319(f73(f932(x40612,a923)),x40614)),f319(f73(f932(x40611,a923)),f319(f303(x40611,x40612,x40613),x40614)))
% 28.73/28.51 [4110]E(f319(f303(x41101,x41102,x41103),f319(f254(x41102),x41104)),f319(f254(x41101),f319(f319(f8(x41102,a923,x41101),x41104),x41103)))
% 28.73/28.51 [4127]E(f319(f319(f156(x41271),f319(f319(f126(x41271),x41272),f319(f319(f143(x41271),x41273),x41274))),f319(f181(f926(x41271)),x41272)),x41273)
% 28.73/28.51 [4149]E(f319(f302(x41491,x41492,x41493),f319(f303(x41491,x41492,x41493),x41494)),f319(f319(f93(f932(x41492,a923)),x41494),f319(f302(x41491,x41492,x41493),f234(f932(x41491,a923)))))
% 28.73/28.51 [4168]P1(f319(f319(f321(x41681),f319(x41682,x41683)),f319(f302(x41684,x41681,x41682),f234(f932(x41684,a923)))))
% 28.73/28.51 [4177]E(f19(x41771,x41772,x41773,f319(a3,f319(a104,f319(a20,x41774)))),f319(f319(x41773,x41774),f19(x41771,x41772,x41773,x41774)))
% 28.73/28.51 [4181]E(f319(f319(f126(x41811),f161(x41811,x41812,x41813)),f319(f319(f143(x41811),x41813),x41814)),f319(f319(f143(x41811),x41813),f319(f319(f126(x41811),f161(x41811,x41812,x41813)),x41814)))
% 28.73/28.51 [4183]E(f319(f319(f246(x41831,x41832),f319(f164(x41831),x41833)),f319(f16(f932(x41832,a923),x41831),f319(f164(x41832),x41834))),f319(f164(f931(x41831,x41832)),f53(x41831,x41832,x41833,x41834)))
% 28.73/28.51 [4195]E(f147(x41951,x41952,f319(f319(f143(x41951),x41953),x41954)),f319(f319(f74(a925),f319(f319(f74(a925),f319(x41952,x41953)),f147(x41951,x41952,x41954))),f319(a104,f2(a925))))
% 28.73/28.51 [4208]E(f177(f926(x42081),f319(f319(f143(x42081),x42082),x42083),f319(f319(f7(a925,f926(x42081),f926(x42081)),f130(x42081)),x42083),x42084),f319(f319(f130(x42081),x42084),f319(f319(f143(x42081),x42082),x42083)))
% 28.73/28.51 [4209]P26(x42091,f931(x42092,x42091),f323(x42093,x42094,x42092,x42091),f319(f319(f33(x42092,f932(x42091,a923)),x42094),x42093))
% 28.73/28.51 [4218]E(f319(f319(f23(f932(x42181,a923)),f319(f319(f23(f932(x42181,a923)),x42182),x42183)),f319(f319(f301(x42181),x42184),f180(f932(x42181,a923)))),f319(f319(f23(f932(x42181,a923)),x42182),f319(f319(f301(x42181),x42184),x42183)))
% 28.73/28.51 [4231]E(f319(f319(f175(f932(x42311,x42312),f932(x42311,x42312)),x42313),f66(x42312,x42312,x42311,x42314)),f66(x42312,x42312,x42311,f319(f319(f175(x42312,x42312),x42313),x42314)))
% 28.73/28.51 [4303]E(f319(f319(f319(f175(f926(x43031),f926(x43031)),x43032),f159(x43031)),f319(f319(f319(f175(f926(x43031),f926(x43031)),x43033),f159(x43031)),x43034)),f319(f319(f319(f175(f926(x43031),f926(x43031)),f319(f319(f74(a925),x43032),x43033)),f159(x43031)),x43034))
% 28.73/28.51 [4388]P1(f319(f319(f226(f932(x43881,a923)),f319(f164(x43881),f319(f319(f151(x43881,x43882),x43883),x43884))),f319(f319(f301(x43881),x43884),f319(f164(x43881),x43882))))
% 28.73/28.51 [4420]E(f319(f319(f33(f932(x44201,a923),f932(f931(x44201,x44202),a923)),x44203),f319(f319(f7(f932(x44201,a923),f932(x44201,f932(x44202,a923)),f932(f931(x44201,x44202),a923)),f246(x44201,x44202)),x44204)),f319(f319(f246(x44201,x44202),f31(f932(x44201,a923),x44203)),x44204))
% 28.73/28.51 [4458]E(f201(x44581,x44582,x44583,f319(f66(x44582,f932(a91,f932(a91,f932(f931(a91,a91),f932(a91,f927(x44582))))),x44581,f200(x44582)),x44584)),f202(x44581,x44582,x44584,x44583))
% 28.73/28.51 [4473]E(f197(x44731,x44732,x44733,f319(f66(x44732,f932(a91,f932(a91,f932(f931(a91,a91),f932(a91,f927(f929(x44732)))))),x44731,f196(x44732)),x44734)),f198(x44731,x44732,x44734,x44733))
% 28.73/28.51 [4477]P1(f319(f60(x44771,x44772,x44773,x44774,f180(f932(x44771,a923))),x44774))
% 28.73/28.51 [4478]P1(f319(f60(x44781,x44782,x44783,x44784,f180(f932(x44781,a923))),x44784))
% 28.73/28.51 [4517]E(f319(f319(f33(x45171,f932(x45172,a923)),x45173),f319(f319(f7(x45171,f932(x45172,a923),f932(x45172,a923)),f319(f319(f8(x45172,f932(f932(x45172,a923),f932(x45172,a923)),x45171),f301(x45172)),x45174)),f180(f932(x45172,a923)))),f319(f302(x45171,x45172,x45174),x45173))
% 28.73/28.51 [4524]P1(f319(f319(f226(f932(x45241,a923)),f319(f276(x45242,x45241),f319(f319(f93(f932(f931(x45242,x45241),a923)),x45243),x45244))),f319(f319(f93(f932(x45241,a923)),f319(f276(x45242,x45241),x45243)),f319(f276(x45242,x45241),x45244))))
% 28.73/28.51 [4525]P1(f319(f319(f226(f932(x45251,a923)),f319(f256(x45251,x45252),f319(f319(f93(f932(f931(x45251,x45252),a923)),x45253),x45254))),f319(f319(f93(f932(x45251,a923)),f319(f256(x45251,x45252),x45253)),f319(f256(x45251,x45252),x45254))))
% 28.73/28.51 [4585]P1(f319(f319(f226(f932(f931(x45851,x45852),a923)),f319(f302(x45852,f931(x45851,x45852),f323(x45853,x45854,x45851,x45852)),f319(f319(f33(x45851,f932(x45852,a923)),x45854),x45853))),f319(f319(f246(x45851,x45852),x45854),x45853)))
% 28.73/28.51 [4586]E(f319(f110(x45861,f931(x45861,x45862),x45863),f319(f319(f8(f932(x45862,f927(f931(x45861,x45862))),f927(f931(x45861,x45862)),x45861),f110(x45862,f931(x45861,x45862),x45864)),f319(f319(f8(f932(x45862,f931(x45861,x45862)),f932(x45862,f927(f931(x45861,x45862))),x45861),f319(f8(f931(x45861,x45862),f927(f931(x45861,x45862)),x45862),f121(f931(x45861,x45862)))),f244(x45861,x45862)))),f123(x45861,x45862,x45863,x45864))
% 28.73/28.51 [4587]E(f268(x45871,x45872,x45873,f319(f66(x45872,f932(a91,f932(a91,f932(f931(a91,a91),f931(f932(a91,f932(a923,f929(f927(x45872)))),f931(a91,a91))))),x45871,f270(x45872)),x45874)),f271(x45871,x45872,x45874,x45873))
% 28.73/28.51 [4627]E(f79(f931(x46271,x46272),f319(f249(x46271,x46272,a923),f319(f319(f7(x46271,f932(x46272,a923),f932(x46272,a923)),f319(f319(f8(f932(a923,a923),f932(f932(x46272,a923),f932(x46272,a923)),x46271),f8(a923,a923,x46272)),f319(f319(f8(a923,f932(a923,a923),x46271),a317),f319(a316,x46273)))),f319(a316,x46274)))),f319(f319(f244(x46271,x46272),x46273),x46274))
% 28.73/28.51 [4628]E(f84(f931(x46281,x46282),f319(f249(x46281,x46282,a923),f319(f319(f7(x46281,f932(x46282,a923),f932(x46282,a923)),f319(f319(f8(f932(a923,a923),f932(f932(x46282,a923),f932(x46282,a923)),x46281),f8(a923,a923,x46282)),f319(f319(f8(a923,f932(a923,a923),x46281),a317),f319(a316,x46283)))),f319(a316,x46284)))),f319(f319(f244(x46281,x46282),x46283),x46284))
% 28.73/28.51 [4699]E(f319(f319(f249(f926(x46991),f926(x46991),f931(f926(x46991),f926(x46991))),f319(f319(f18(f926(x46991),f932(f926(x46991),f931(f926(x46991),f926(x46991))),f932(f926(x46991),f931(f926(x46991),f926(x46991)))),f319(f319(f8(f932(f926(x46991),f932(f931(f926(x46991),f926(x46991)),f931(f926(x46991),f926(x46991)))),f932(f932(f926(x46991),f931(f926(x46991),f926(x46991))),f932(f926(x46991),f931(f926(x46991),f926(x46991)))),f926(x46991)),f18(f926(x46991),f931(f926(x46991),f926(x46991)),f931(f926(x46991),f926(x46991)))),f319(f319(f8(f932(f926(x46991),f931(f926(x46991),f926(x46991))),f932(f926(x46991),f932(f931(f926(x46991),f926(x46991)),f931(f926(x46991),f926(x46991)))),f926(x46991)),f319(f8(f931(f926(x46991),f926(x46991)),f932(f931(f926(x46991),f926(x46991)),f931(f926(x46991),f926(x46991))),f926(x46991)),f319(f86(f931(f926(x46991),f926(x46991))),f319(x46992,x46993)))),f319(f319(f8(f926(x46991),f932(f926(x46991),f931(f926(x46991),f926(x46991))),f926(x46991)),f244(f926(x46991),f926(x46991))),f319(f143(x46991),x46993))))),f319(f319(f7(f926(x46991),f932(f926(x46991),f926(x46991)),f932(f926(x46991),f931(f926(x46991),f926(x46991)))),f319(f319(f8(f932(f926(x46991),f931(f926(x46991),f926(x46991))),f932(f932(f926(x46991),f926(x46991)),f932(f926(x46991),f931(f926(x46991),f926(x46991)))),f926(x46991)),f8(f926(x46991),f931(f926(x46991),f926(x46991)),f926(x46991))),f244(f926(x46991),f926(x46991)))),f319(f143(x46991),x46993)))),f158(x46991,x46992,x46994)),f158(x46991,x46992,f319(f319(f143(x46991),x46993),x46994)))
% 28.73/28.51 [3947]E(f319(f319(f167(x39471),x39472),f319(f319(f167(x39471),x39473),x39474)),f319(f319(f167(x39471),f319(f319(f224(a925),x39472),x39473)),x39474))
% 28.73/28.51 [3948]E(f319(f319(f130(x39481),x39482),f319(f319(f130(x39481),x39483),x39484)),f319(f319(f130(x39481),f319(f319(f74(a925),x39482),x39483)),x39484))
% 28.73/28.51 [3959]E(f319(f319(f126(x39591),f319(f319(f143(x39591),x39592),x39593)),x39594),f319(f319(f143(x39591),x39592),f319(f319(f126(x39591),x39593),x39594)))
% 28.73/28.51 [3960]E(f319(f319(f126(x39601),f319(f319(f126(x39601),x39602),x39603)),x39604),f319(f319(f126(x39601),x39602),f319(f319(f126(x39601),x39603),x39604)))
% 28.73/28.51 [4041]E(f319(f319(f156(x40411),f319(f319(f143(x40411),x40412),x40413)),x40414),f177(x40411,x40412,f319(f156(x40411),x40413),x40414))
% 28.73/28.51 [4050]E(f319(f319(f175(x40501,x40501),x40502),f319(f319(f175(x40501,x40501),x40503),x40504)),f319(f319(f175(x40501,x40501),f319(f319(f75(a925),x40503),x40502)),x40504))
% 28.73/28.51 [4077]E(f319(f319(f102(f932(x40771,a923)),x40772),f319(f319(f301(x40771),x40773),x40774)),f319(f319(f301(x40771),x40773),f319(f319(f102(f932(x40771,a923)),x40772),x40774)))
% 28.73/28.51 [4092]E(f319(f319(f319(f175(x40921,x40921),x40922),x40923),f319(x40923,x40924)),f319(x40923,f319(f319(f319(f175(x40921,x40921),x40922),x40923),x40924)))
% 28.73/28.51 [4101]E(f319(f319(f281(x41011,x41012,x41013),f180(f932(f931(x41011,x41012),a923))),x41014),f180(f932(f931(x41011,x41013),a923)))
% 28.73/28.51 [4115]E(f319(f319(f102(f932(x41151,a923)),f319(f319(f301(x41151),x41152),x41153)),x41154),f319(f319(f301(x41151),x41152),f319(f319(f102(f932(x41151,a923)),x41153),x41154)))
% 28.73/28.51 [4134]E(f319(f29(f931(x41341,x41342)),f319(f319(f246(x41341,x41342),x41343),f319(f16(f932(x41342,a923),x41341),x41344))),f319(f319(f75(a925),f319(f29(x41341),x41343)),f319(f29(x41342),x41344)))
% 28.73/28.51 [4140]E(f319(f319(f93(f932(x41401,a923)),f319(f319(f301(x41401),x41402),x41403)),f319(f319(f301(x41401),x41402),x41404)),f319(f319(f301(x41401),x41402),f319(f319(f93(f932(x41401,a923)),x41403),x41404)))
% 28.73/28.51 [4153]E(f319(f319(f102(f932(x41531,a923)),x41532),f319(f319(f102(f932(x41531,a923)),x41533),x41534)),f319(f319(f102(f932(x41531,a923)),x41533),f319(f319(f102(f932(x41531,a923)),x41532),x41534)))
% 28.73/28.51 [4154]E(f319(f319(f93(f932(x41541,a923)),x41542),f319(f319(f93(f932(x41541,a923)),x41543),x41544)),f319(f319(f93(f932(x41541,a923)),x41543),f319(f319(f93(f932(x41541,a923)),x41542),x41544)))
% 28.73/28.51 [4164]E(f58(x41641,x41642,f319(f319(f8(x41642,f932(x41642,x41642),x41641),x41643),x41644)),f319(f59(x41642,x41641,x41643),x41644))
% 28.73/28.51 [4173]E(f171(x41731,f319(f319(f146(f926(x41732),f926(x41731)),f319(f146(x41732,x41731),x41733)),x41734)),f319(f319(f146(f926(x41732),f926(x41731)),f319(f146(x41732,x41731),x41733)),f171(x41732,x41734)))
% 28.73/28.51 [4191]E(f319(f134(f926(x41911),f926(x41911),f126(x41911),f105(x41911)),f319(f319(f146(x41912,f926(x41911)),x41913),x41914)),f155(x41912,x41911,x41913,x41914))
% 28.73/28.51 [4192]E(f319(f134(f926(x41921),f926(x41921),f126(x41921),f105(x41921)),f319(f319(f146(x41922,f926(x41921)),x41923),x41924)),f155(x41922,x41921,x41923,x41924))
% 28.73/28.51 [4250]E(f319(f66(x42501,x42501,x42501,f319(f319(f175(x42501,x42501),x42502),x42503)),f319(f319(f175(x42501,x42501),x42504),x42503)),f319(f319(f175(x42501,x42501),f319(f319(f74(a925),x42502),x42504)),x42503))
% 28.73/28.51 [4273]E(f319(f319(f93(f932(x42731,a923)),f319(f319(f102(f932(x42731,a923)),x42732),x42733)),f319(f319(f102(f932(x42731,a923)),x42732),x42734)),f319(f319(f102(f932(x42731,a923)),x42732),f319(f319(f93(f932(x42731,a923)),x42733),x42734)))
% 28.73/28.51 [4274]E(f319(f319(f102(f932(x42741,a923)),f319(f319(f93(f932(x42741,a923)),x42742),x42743)),f319(f319(f93(f932(x42741,a923)),x42742),x42744)),f319(f319(f93(f932(x42741,a923)),x42742),f319(f319(f102(f932(x42741,a923)),x42743),x42744)))
% 28.73/28.51 [4275]E(f319(f319(f23(f932(x42751,a923)),f319(f319(f93(f932(x42751,a923)),x42752),x42753)),f319(f319(f93(f932(x42751,a923)),x42752),x42754)),f319(f319(f93(f932(x42751,a923)),x42752),f319(f319(f23(f932(x42751,a923)),x42753),x42754)))
% 28.73/28.51 [4276]E(f319(f319(f93(f932(x42761,a923)),f319(f319(f23(f932(x42761,a923)),x42762),x42763)),f319(f319(f23(f932(x42761,a923)),x42762),x42764)),f319(f319(f23(f932(x42761,a923)),x42762),f319(f319(f102(f932(x42761,a923)),x42763),x42764)))
% 28.73/28.51 [4277]E(f319(f319(f102(f932(x42771,a923)),f319(f319(f23(f932(x42771,a923)),x42772),x42773)),f319(f319(f23(f932(x42771,a923)),x42772),x42774)),f319(f319(f23(f932(x42771,a923)),x42772),f319(f319(f93(f932(x42771,a923)),x42773),x42774)))
% 28.73/28.51 [4282]E(f319(f29(f931(x42821,x42822)),f319(f319(f246(x42821,x42822),f319(f319(f301(x42821),x42823),f180(f932(x42821,a923)))),f319(f16(f932(x42822,a923),x42821),x42824))),f319(f29(x42822),x42824))
% 28.73/28.51 [4317]E(f319(f319(f34(x43171,f932(x43172,a923)),x43173),f319(f319(f8(f932(x43172,a923),f932(x43172,a923),x43171),f73(f932(x43172,a923))),x43174)),f319(f73(f932(x43172,a923)),f319(f319(f33(x43171,f932(x43172,a923)),x43173),x43174)))
% 28.73/28.51 [4318]E(f319(f319(f33(x43181,f932(x43182,a923)),x43183),f319(f319(f8(f932(x43182,a923),f932(x43182,a923),x43181),f73(f932(x43182,a923))),x43184)),f319(f73(f932(x43182,a923)),f319(f319(f34(x43181,f932(x43182,a923)),x43183),x43184)))
% 28.73/28.51 [4334]E(f319(f319(f281(x43341,x43341,x43341),f319(f319(f175(f931(x43341,x43341),a923),x43342),x43343)),f319(f319(f175(f931(x43341,x43341),a923),x43344),x43343)),f319(f319(f175(f931(x43341,x43341),a923),f319(f319(f74(a925),x43342),x43344)),x43343))
% 28.73/28.51 [4364]E(f319(f319(f34(x43641,f932(f932(x43642,a923),a923)),x43643),f319(f319(f8(f932(x43642,a923),f932(f932(x43642,a923),a923),x43641),f300(x43642)),x43644)),f319(f300(x43642),f319(f319(f34(x43641,f932(x43642,a923)),x43643),x43644)))
% 28.73/28.51 [4391]E(f319(f319(f33(f932(x43911,a923),f932(x43912,a923)),x43913),f319(f319(f7(f932(x43911,a923),f932(x43911,f932(x43912,a923)),f932(x43912,a923)),f33(x43911,f932(x43912,a923))),x43914)),f319(f319(f33(x43911,f932(x43912,a923)),f31(f932(x43911,a923),x43913)),x43914))
% 28.73/28.51 [4392]E(f319(f319(f34(f932(x43921,a923),f932(x43922,a923)),x43923),f319(f319(f7(f932(x43921,a923),f932(x43921,f932(x43922,a923)),f932(x43922,a923)),f34(x43921,f932(x43922,a923))),x43924)),f319(f319(f34(x43921,f932(x43922,a923)),f31(f932(x43921,a923),x43923)),x43924))
% 28.73/28.51 [4393]E(f319(f319(f33(f932(x43931,a923),f932(x43932,a923)),x43933),f319(f319(f7(f932(x43931,a923),f932(x43931,f932(x43932,a923)),f932(x43932,a923)),f33(x43931,f932(x43932,a923))),x43934)),f319(f319(f33(x43931,f932(x43932,a923)),f31(f932(x43931,a923),x43933)),x43934))
% 28.73/28.51 [4394]E(f319(f319(f34(f932(x43941,a923),f932(x43942,a923)),x43943),f319(f319(f7(f932(x43941,a923),f932(x43941,f932(x43942,a923)),f932(x43942,a923)),f34(x43941,f932(x43942,a923))),x43944)),f319(f319(f34(x43941,f932(x43942,a923)),f31(f932(x43941,a923),x43943)),x43944))
% 28.73/28.51 [4399]E(f319(f319(f146(x43991,x43992),x43993),f319(f134(f926(x43991),f926(x43991),f126(x43991),f105(x43991)),x43994)),f319(f134(f926(x43992),f926(x43992),f126(x43992),f105(x43992)),f319(f319(f146(f926(x43991),f926(x43992)),f319(f146(x43991,x43992),x43993)),x43994)))
% 28.73/28.51 [4401]E(f177(f926(x44011),f105(x44011),f319(f319(f8(f926(x44011),f926(x44011),a925),f319(f143(x44011),x44012)),f319(f319(f7(a925,f926(x44011),f926(x44011)),f167(x44011)),x44013)),x44014),f319(f319(f167(x44011),x44014),f319(f319(f143(x44011),x44012),x44013)))
% 28.73/28.51 [4439]P1(f319(f319(f226(f932(x44391,a923)),f319(f302(x44392,x44391,x44393),f319(f303(x44392,x44391,x44393),x44394))),x44394))
% 28.73/28.51 [4441]E(f319(f302(f931(x44411,x44412),f931(x44412,x44411),f319(f249(x44411,x44412,f931(x44412,x44411)),f319(f7(x44412,x44411,f931(x44412,x44411)),f244(x44412,x44411)))),f319(f319(f246(x44411,x44412),x44413),f319(f16(f932(x44412,a923),x44411),x44414))),f319(f319(f246(x44412,x44411),x44414),f319(f16(f932(x44411,a923),x44412),x44413)))
% 28.73/28.51 [4450]E(f319(f319(f33(x44501,f932(x44502,a923)),x44503),f319(f319(f8(f932(x44501,a923),f932(x44502,a923),x44501),f303(x44502,x44501,x44504)),f319(f319(f7(x44501,f932(x44501,a923),f932(x44501,a923)),f301(x44501)),f180(f932(x44501,a923))))),f319(f303(x44502,x44501,x44504),x44503))
% 28.73/28.51 [4451]E(f319(f319(f33(x44511,f932(x44512,a923)),x44513),f319(f319(f8(f932(x44511,a923),f932(x44512,a923),x44511),f277(x44511,x44512,x44514)),f319(f319(f7(x44511,f932(x44511,a923),f932(x44511,a923)),f301(x44511)),f180(f932(x44511,a923))))),f319(f277(x44511,x44512,x44514),x44513))
% 28.73/28.51 [4526]E(f319(f319(f126(x45261),f319(f128(x45261,f319(f319(f8(a923,a923,x45261),a314),f319(a316,x45262))),x45263)),f319(f128(x45261,f319(f319(f8(a923,a923,x45261),a314),f319(a316,x45262))),x45264)),f319(f128(x45261,f319(f319(f8(a923,a923,x45261),a314),f319(a316,x45262))),f319(f319(f126(x45261),x45263),x45264)))
% 28.73/28.51 [4538]E(f319(f319(f102(f932(x45381,a923)),f319(f319(f102(f932(x45381,a923)),f319(f319(f93(f932(x45381,a923)),x45382),x45383)),f319(f319(f93(f932(x45381,a923)),x45383),x45384))),f319(f319(f93(f932(x45381,a923)),x45384),x45382)),f319(f319(f93(f932(x45381,a923)),f319(f319(f93(f932(x45381,a923)),f319(f319(f102(f932(x45381,a923)),x45382),x45383)),f319(f319(f102(f932(x45381,a923)),x45383),x45384))),f319(f319(f102(f932(x45381,a923)),x45384),x45382)))
% 28.73/28.51 [4601]E(f319(f134(f926(x46011),f926(x46011),f126(x46011),f105(x46011)),f319(f319(f146(x46012,f926(x46011)),f319(f319(f7(x46012,f926(x46011),f926(x46011)),f319(f319(f8(x46011,f932(f926(x46011),f926(x46011)),x46012),f143(x46011)),x46013)),f105(x46011))),x46014)),f319(f319(f146(x46012,x46011),x46013),x46014))
% 28.73/28.51 [4611]E(f319(f319(f80(a1,x46111),f319(f95(a1),f319(f319(f74(a1),x46112),a89))),f319(f319(f18(a1,x46111,x46111),f319(f319(f7(a1,x46111,f932(x46111,x46111)),f319(f319(f8(a923,f932(x46111,f932(x46111,x46111)),a1),f86(x46111)),a185)),x46113)),f319(f319(f8(a925,x46111,a1),x46114),a96))),f177(x46111,x46113,x46114,f319(f95(a925),x46112)))
% 28.73/28.51 [4642]E(f319(f254(x46421),f319(f319(f8(f932(x46422,a923),a923,x46421),f81(x46422)),f319(f319(f8(f932(x46422,a923),f932(x46422,a923),x46421),f319(f18(x46422,a923,a923),f319(f319(f8(a923,f932(a923,a923),x46422),a317),f319(f319(f7(x46422,f932(x46422,a923),a923),f321(x46422)),x46423)))),f319(f7(x46422,x46421,a923),x46424)))),f319(f277(x46422,x46421,f319(f254(f931(x46422,x46421)),f319(f249(x46422,x46421,a923),x46424))),x46423))
% 28.73/28.51 [4777]~P1(f319(f319(f180(f932(x47771,f932(x47772,a923))),x47773),x47774))
% 28.73/28.51 [4104]E(f319(f319(f156(x41041),f319(f319(f126(x41041),x41042),x41043)),f319(f319(f74(a925),f319(f181(f926(x41041)),x41042)),x41044)),f319(f319(f156(x41041),x41043),x41044))
% 28.73/28.51 [4109]E(f319(f319(f130(x41091),x41092),f319(f319(f167(x41091),f319(f319(f74(a925),x41093),x41092)),x41094)),f319(f319(f167(x41091),x41093),f319(f319(f130(x41091),x41092),x41094)))
% 28.73/28.51 [4206]E(f319(f319(f102(f932(x42061,a923)),f319(f276(x42062,x42061),x42063)),f319(f276(x42062,x42061),x42064)),f319(f276(x42062,x42061),f319(f319(f102(f932(f931(x42062,x42061),a923)),x42063),x42064)))
% 28.73/28.51 [4207]E(f319(f319(f102(f932(x42071,a923)),f319(f256(x42071,x42072),x42073)),f319(f256(x42071,x42072),x42074)),f319(f256(x42071,x42072),f319(f319(f102(f932(f931(x42071,x42072),a923)),x42073),x42074)))
% 28.73/28.51 [4212]E(f319(f319(f102(f932(x42121,a923)),f319(f319(f102(f932(x42121,a923)),x42122),x42123)),x42124),f319(f319(f102(f932(x42121,a923)),x42122),f319(f319(f102(f932(x42121,a923)),x42123),x42124)))
% 28.73/28.51 [4213]E(f319(f319(f93(f932(x42131,a923)),f319(f319(f93(f932(x42131,a923)),x42132),x42133)),x42134),f319(f319(f93(f932(x42131,a923)),x42132),f319(f319(f93(f932(x42131,a923)),x42133),x42134)))
% 28.73/28.51 [4214]E(f319(f319(f23(f932(x42141,a923)),f319(f319(f93(f932(x42141,a923)),x42142),x42143)),x42144),f319(f319(f93(f932(x42141,a923)),x42142),f319(f319(f23(f932(x42141,a923)),x42143),x42144)))
% 28.73/28.51 [4252]E(f319(f319(f102(f932(f931(x42521,x42522),a923)),f319(f278(x42522,x42521),x42523)),f319(f278(x42522,x42521),x42524)),f319(f278(x42522,x42521),f319(f319(f102(f932(f931(x42522,x42521),a923)),x42523),x42524)))
% 28.73/28.51 [4253]E(f319(f319(f93(f932(f931(x42531,x42532),a923)),f319(f278(x42532,x42531),x42533)),f319(f278(x42532,x42531),x42534)),f319(f278(x42532,x42531),f319(f319(f93(f932(f931(x42532,x42531),a923)),x42533),x42534)))
% 28.73/28.51 [4266]E(f319(f319(f102(f932(x42661,f932(x42662,a923))),f235(x42662,x42661,x42663)),f235(x42662,x42661,x42664)),f235(x42662,x42661,f319(f319(f102(f932(x42662,f932(x42661,a923))),x42663),x42664)))
% 28.73/28.51 [4267]E(f319(f319(f93(f932(x42671,f932(x42672,a923))),f235(x42672,x42671,x42673)),f235(x42672,x42671,x42674)),f235(x42672,x42671,f319(f319(f93(f932(x42672,f932(x42671,a923))),x42673),x42674)))
% 28.73/28.51 [4321]E(f319(f319(f93(f932(x43211,a923)),f319(f319(f102(f932(x43211,a923)),x43212),x43213)),f319(f319(f102(f932(x43211,a923)),x43214),x43213)),f319(f319(f102(f932(x43211,a923)),f319(f319(f93(f932(x43211,a923)),x43212),x43214)),x43213))
% 28.73/28.51 [4322]E(f319(f319(f102(f932(x43221,a923)),f319(f319(f93(f932(x43221,a923)),x43222),x43223)),f319(f319(f93(f932(x43221,a923)),x43224),x43223)),f319(f319(f93(f932(x43221,a923)),f319(f319(f102(f932(x43221,a923)),x43222),x43224)),x43223))
% 28.73/28.51 [4323]E(f319(f319(f23(f932(x43231,a923)),f319(f319(f93(f932(x43231,a923)),x43232),x43233)),f319(f319(f93(f932(x43231,a923)),x43234),x43233)),f319(f319(f93(f932(x43231,a923)),f319(f319(f23(f932(x43231,a923)),x43232),x43234)),x43233))
% 28.73/28.51 [4324]E(f319(f319(f102(f932(x43241,a923)),f319(f319(f23(f932(x43241,a923)),x43242),x43243)),f319(f319(f23(f932(x43241,a923)),x43244),x43243)),f319(f319(f23(f932(x43241,a923)),f319(f319(f102(f932(x43241,a923)),x43242),x43244)),x43243))
% 28.73/28.51 [4325]E(f319(f319(f23(f932(x43251,a923)),f319(f319(f93(f932(x43251,a923)),x43252),x43253)),f319(f319(f93(f932(x43251,a923)),x43254),x43253)),f319(f319(f23(f932(x43251,a923)),f319(f319(f93(f932(x43251,a923)),x43252),x43253)),x43254))
% 28.73/28.51 [4337]E(f319(f319(f23(f932(x43371,a923)),f319(f319(f23(f932(x43371,a923)),x43372),f319(f319(f301(x43371),x43373),f180(f932(x43371,a923))))),x43374),f319(f319(f23(f932(x43371,a923)),x43372),f319(f319(f301(x43371),x43373),x43374)))
% 28.73/28.51 [4390]E(f319(f319(f102(f932(x43901,a923)),f319(f319(f301(x43901),x43902),f319(f319(f301(x43901),x43903),f180(f932(x43901,a923))))),f319(f273(x43901),x43904)),f319(f273(x43901),f319(f319(f301(f931(x43901,x43901)),f319(f319(f244(x43901,x43901),x43902),x43903)),x43904)))
% 28.73/28.51 [4415]E(f319(f319(f33(a925,f932(x44151,a923)),f319(f293(a925),x44152)),f319(f319(f8(a925,f932(x44151,a923),a925),x44153),f319(f319(f7(a925,a925,a925),f74(a925)),x44154))),f319(f319(f33(a925,f932(x44151,a923)),f295(a925,x44154,f319(f319(f74(a925),x44152),x44154))),x44153))
% 28.73/28.51 [4416]E(f166(x44161,f319(f277(x44161,x44161,x44162),f319(f319(f301(x44161),x44163),f180(f932(x44161,a923)))),f319(f277(f926(x44161),f926(x44161),f150(x44161,x44162)),f319(f319(f301(f926(x44161)),x44164),f180(f932(f926(x44161),a923))))),f319(f277(f926(x44161),f926(x44161),f150(x44161,x44162)),f319(f319(f301(f926(x44161)),f319(f319(f143(x44161),x44163),x44164)),f180(f932(f926(x44161),a923)))))
% 28.73/28.51 [4480]E(f319(f254(x44801),f319(f319(f7(x44801,f932(x44802,a923),a923),f319(f319(f8(x44802,f932(f932(x44802,a923),a923),x44801),f321(x44802)),x44803)),x44804)),f319(f303(x44801,x44802,x44803),x44804))
% 28.73/28.51 [4570]E(f319(f254(x45701),f319(f319(f7(x45701,f932(f931(x45702,x45701),a923),a923),f319(f319(f8(f931(x45702,x45701),f932(f932(f931(x45702,x45701),a923),a923),x45701),f321(f931(x45702,x45701))),f319(f244(x45702,x45701),x45703))),x45704)),f319(f277(x45702,x45701,x45704),f319(f319(f301(x45702),x45703),f180(f932(x45702,a923)))))
% 28.73/28.51 [4584]E(f319(f319(f146(f931(x45841,a925),x45841),f243(x45841,a925)),f319(f128(f931(x45841,a925),f319(f319(f8(a925,a923,f931(x45841,a925)),x45842),f319(f319(f8(a925,a925,f931(x45841,a925)),a104),f248(x45841,a925)))),f319(f319(f173(x45841,a925),x45843),x45844))),f319(f319(f146(f931(x45841,a925),x45841),f243(x45841,a925)),f319(f128(f931(x45841,a925),f319(f319(f8(a925,a923,f931(x45841,a925)),x45842),f248(x45841,a925))),f319(f319(f173(x45841,a925),x45843),f319(f319(f146(a925,a925),a104),x45844)))))
% 28.73/28.51 [4593]P1(f319(f319(f226(f932(f932(x45931,a923),a923)),f319(f319(f33(x45932,f932(f932(x45931,a923),a923)),x45933),f319(f319(f8(f932(x45931,a923),f932(f932(x45931,a923),a923),x45932),f300(x45931)),x45934))),f319(f300(x45931),f319(f319(f33(x45932,f932(x45931,a923)),x45933),x45934))))
% 28.73/28.51 [4634]E(f319(f319(f80(a1,x46341),f319(f95(a1),f319(f319(f74(a1),x46342),a89))),f319(f319(f18(a1,x46341,x46341),f319(f319(f7(a1,x46341,f932(x46341,x46341)),f319(f319(f8(a923,f932(x46341,f932(x46341,x46341)),a1),f86(x46341)),a185)),x46343)),f319(f319(f18(a1,x46341,x46341),f319(f319(f8(a925,f932(x46341,x46341),a1),x46344),a96)),f319(f319(f8(a925,x46341,a1),f176(x46341,x46343,x46344)),a96)))),f319(f176(x46341,x46343,x46344),f319(f95(a925),x46342)))
% 28.73/28.51 [4658]E(f319(f254(f931(x46581,x46582)),f319(f249(x46581,x46582,a923),f319(f319(f7(x46581,f932(x46582,a923),f932(x46582,a923)),f319(f319(f8(f932(a923,a923),f932(f932(x46582,a923),f932(x46582,a923)),x46581),f8(a923,a923,x46582)),f319(f319(f8(a923,f932(a923,a923),x46581),a317),f319(f319(f7(x46581,f932(x46581,a923),a923),f321(x46581)),x46583)))),f319(f319(f7(x46582,f932(x46582,a923),a923),f321(x46582)),x46584)))),f221(x46581,x46582,x46583,x46584))
% 28.73/28.51 [4694]E(f319(f319(f33(x46941,f932(f931(x46941,x46942),a923)),x46943),f319(f319(f18(x46941,f932(x46942,f932(f931(x46941,x46942),a923)),f932(f931(x46941,x46942),a923)),f319(f319(f8(f932(x46942,a923),f932(f932(x46942,f932(f931(x46941,x46942),a923)),f932(f931(x46941,x46942),a923)),x46941),f33(x46942,f932(f931(x46941,x46942),a923))),x46944)),f319(f319(f7(x46941,f932(f931(x46941,x46942),a923),f932(x46942,f932(f931(x46941,x46942),a923))),f319(f319(f8(f932(x46942,f932(f932(f931(x46941,x46942),a923),f932(f931(x46941,x46942),a923))),f932(f932(f931(x46941,x46942),a923),f932(x46942,f932(f931(x46941,x46942),a923))),x46941),f7(x46942,f932(f931(x46941,x46942),a923),f932(f931(x46941,x46942),a923))),f319(f319(f8(f932(x46942,f931(x46941,x46942)),f932(x46942,f932(f932(f931(x46941,x46942),a923),f932(f931(x46941,x46942),a923))),x46941),f319(f8(f931(x46941,x46942),f932(f932(f931(x46941,x46942),a923),f932(f931(x46941,x46942),a923)),x46942),f301(f931(x46941,x46942)))),f244(x46941,x46942)))),f180(f932(f931(x46941,x46942),a923))))),f319(f319(f246(x46941,x46942),x46943),x46944))
% 28.73/28.51 [4261]E(f319(f319(f126(x42611),f319(f319(f167(x42611),x42612),x42613)),f319(f319(f167(x42611),f319(f319(f23(a925),x42612),f319(f181(f926(x42611)),x42613))),x42614)),f319(f319(f167(x42611),x42612),f319(f319(f126(x42611),x42613),x42614)))
% 28.73/28.51 [4262]E(f319(f319(f126(x42621),f319(f319(f130(x42621),x42622),x42623)),f319(f319(f130(x42621),f319(f319(f23(a925),x42622),f319(f181(f926(x42621)),x42623))),x42624)),f319(f319(f130(x42621),x42622),f319(f319(f126(x42621),x42623),x42624)))
% 28.73/28.51 [4311]E(f319(f319(f74(a925),f319(f319(f75(a925),x43111),x43112)),f319(f319(f74(a925),f319(f319(f75(a925),x43113),x43112)),x43114)),f319(f319(f74(a925),f319(f319(f75(a925),f319(f319(f74(a925),x43111),x43113)),x43112)),x43114))
% 28.73/28.51 [4456]E(f84(x44561,f319(f319(f7(x44561,x44562,a923),f319(f319(f8(x44562,f932(x44562,a923),x44561),a316),x44563)),x44564)),f319(f85(x44561,x44562,f234(f932(x44561,a923)),x44563),x44564))
% 28.73/28.51 [4504]P1(f319(f319(f226(f932(x45041,a923)),f319(f319(f23(f932(x45041,a923)),f319(f276(x45042,x45041),x45043)),f319(f276(x45042,x45041),x45044))),f319(f276(x45042,x45041),f319(f319(f23(f932(f931(x45042,x45041),a923)),x45043),x45044))))
% 28.73/28.51 [4505]P1(f319(f319(f226(f932(x45051,a923)),f319(f319(f23(f932(x45051,a923)),f319(f256(x45051,x45052),x45053)),f319(f256(x45051,x45052),x45054))),f319(f256(x45051,x45052),f319(f319(f23(f932(f931(x45051,x45052),a923)),x45053),x45054))))
% 28.73/28.51 [4613]E(f319(f319(f74(a1),f319(a83,f319(f277(f931(a925,a925),f931(a925,a925),a100),f319(f319(f301(f931(a925,a925)),f319(f319(f244(a925,a925),x46131),x46132)),f180(f932(f931(a925,a925),a923)))))),f319(a83,f319(f277(f931(a925,a925),f931(a925,a925),a100),f319(f319(f301(f931(a925,a925)),f319(f319(f244(a925,a925),x46133),x46134)),f180(f932(f931(a925,a925),a923)))))),f319(a83,f319(f277(f931(a925,a925),f931(a925,a925),a100),f319(f319(f301(f931(a925,a925)),f319(f319(f244(a925,a925),f319(f319(f74(a925),x46131),x46133)),f319(f319(f74(a925),x46132),x46134))),f180(f932(f931(a925,a925),a923))))))
% 28.73/28.51 [4653]E(f319(f319(f75(a1),f319(a83,f319(f277(f931(a925,a925),f931(a925,a925),a100),f319(f319(f301(f931(a925,a925)),f319(f319(f244(a925,a925),x46531),x46532)),f180(f932(f931(a925,a925),a923)))))),f319(a83,f319(f277(f931(a925,a925),f931(a925,a925),a100),f319(f319(f301(f931(a925,a925)),f319(f319(f244(a925,a925),x46533),x46534)),f180(f932(f931(a925,a925),a923)))))),f319(a83,f319(f277(f931(a925,a925),f931(a925,a925),a100),f319(f319(f301(f931(a925,a925)),f319(f319(f244(a925,a925),f319(f319(f74(a925),f319(f319(f75(a925),x46531),x46533)),f319(f319(f75(a925),x46532),x46534))),f319(f319(f74(a925),f319(f319(f75(a925),x46531),x46534)),f319(f319(f75(a925),x46532),x46533)))),f180(f932(f931(a925,a925),a923))))))
% 28.73/28.51 [4674]E(f319(f254(x46741),f319(f319(f8(f932(x46742,a923),a923,x46741),f82(x46742)),f319(f319(f8(f932(x46742,a923),f932(x46742,a923),x46741),f319(f18(x46742,a923,a923),f319(f319(f8(a923,f932(a923,a923),x46742),a322),f319(f319(f7(x46742,f932(x46742,a923),a923),f321(x46742)),x46743)))),f319(f319(f7(x46741,f932(x46742,f932(x46741,a923)),f932(x46742,a923)),f319(f319(f8(f932(f932(x46741,a923),a923),f932(f932(x46742,f932(x46741,a923)),f932(x46742,a923)),x46741),f8(f932(x46741,a923),a923,x46742)),f321(x46741))),x46744)))),f319(f319(f34(x46742,f932(x46741,a923)),x46743),x46744))
% 28.73/28.51 [4706]E(f319(f319(f281(x47061,x47061,x47061),f319(f319(f301(f931(x47061,x47061)),f319(f319(f244(x47061,x47061),x47062),x47063)),x47064)),f299(x47061,f319(f319(f301(f931(x47061,x47061)),f319(f319(f244(x47061,x47061),x47062),x47063)),x47064))),f319(f319(f102(f932(f931(x47061,x47061),a923)),f319(f319(f281(x47061,x47061,x47061),x47064),f299(x47061,x47064))),f319(f254(f931(x47061,x47061)),f319(f249(x47061,x47061,a923),f319(f319(f7(x47061,f932(x47061,a923),f932(x47061,a923)),f319(f319(f8(f932(a923,a923),f932(f932(x47061,a923),f932(x47061,a923)),x47061),f8(a923,a923,x47061)),f319(f319(f8(a923,f932(a923,a923),x47061),a317),f319(f319(f7(x47061,f932(f931(x47061,x47061),a923),a923),f319(f319(f8(f931(x47061,x47061),f932(f932(f931(x47061,x47061),a923),a923),x47061),f321(f931(x47061,x47061))),f319(f319(f7(x47061,x47061,f931(x47061,x47061)),f244(x47061,x47061)),x47062))),f299(x47061,x47064))))),f319(f319(f7(x47061,f932(f931(x47061,x47061),a923),a923),f319(f319(f8(f931(x47061,x47061),f932(f932(f931(x47061,x47061),a923),a923),x47061),f321(f931(x47061,x47061))),f319(f244(x47061,x47061),x47063))),f299(x47061,x47064)))))))
% 28.73/28.51 [4506]E(f319(f128(x45061,f319(f319(f18(x45061,a923,a923),f319(f319(f8(a923,f932(a923,a923),x45061),a317),x45062)),x45063)),x45064),f319(f128(x45061,x45063),f319(f128(x45061,x45062),x45064)))
% 28.73/28.51 [4607]E(f319(f319(f126(x46071),f319(f319(f319(f86(f926(x46071)),f319(f319(f321(a925),f2(a925)),x46072)),f319(f319(f143(x46071),x46073),f105(x46071))),f105(x46071))),f168(x46071,x46074,f319(f254(a925),f319(f319(f7(a925,f932(a925,a923),a923),f319(f319(f8(a925,f932(f932(a925,a923),a923),a925),f321(a925)),a104)),x46072)))),f168(x46071,f319(f319(f143(x46071),x46073),x46074),x46072))
% 28.73/28.51 [4702]E(f319(f254(f931(x47021,x47022)),f319(f319(f8(f932(a925,a923),a923,f931(x47021,x47022)),f81(a925)),f319(f319(f7(f931(x47021,x47022),f932(a925,a923),f932(a925,a923)),f319(f319(f8(f932(a925,f932(a923,a923)),f932(f932(a925,a923),f932(a925,a923)),f931(x47021,x47022)),f18(a925,a923,a923)),f319(f319(f8(f932(a925,a923),f932(a925,f932(a923,a923)),f931(x47021,x47022)),f319(f8(a923,f932(a923,a923),a925),a317)),f319(f319(f7(f931(x47021,x47022),f932(a925,f931(x47021,x47022)),f932(a925,a923)),f319(f319(f8(f932(f931(x47021,x47022),a923),f932(f932(a925,f931(x47021,x47022)),f932(a925,a923)),f931(x47021,x47022)),f8(f931(x47021,x47022),a923,a925)),a316)),f319(f319(f18(a925,x47022,f931(x47021,x47022)),f319(f319(f8(x47021,f932(x47022,f931(x47021,x47022)),a925),f244(x47021,x47022)),f319(f156(x47021),x47023))),f319(f156(x47022),x47024)))))),f319(f319(f7(a925,a925,a923),f227(a925)),f319(f319(f224(a925),f319(f181(f926(x47021)),x47023)),f319(f181(f926(x47022)),x47024)))))),f319(f164(f931(x47021,x47022)),f319(f319(f173(x47021,x47022),x47023),x47024)))
% 28.73/28.51 [4626]E(f319(f254(f931(x46261,x46262)),f319(f249(x46261,x46262,a923),f319(f319(f7(x46261,f932(x46262,a923),f932(x46262,a923)),f319(f319(f8(f932(a923,a923),f932(f932(x46262,a923),f932(x46262,a923)),x46261),f8(a923,a923,x46262)),f319(f319(f8(a923,f932(a923,a923),x46261),a317),x46263))),x46264))),f319(f319(f246(x46261,x46262),f319(f254(x46261),x46263)),f319(f16(f932(x46262,a923),x46261),f319(f254(x46262),x46264))))
% 28.73/28.51 [4629]E(f319(f254(f931(x46291,x46292)),f319(f249(x46291,x46292,a923),f319(f319(f18(x46291,f932(x46292,a923),f932(x46292,a923)),f319(f319(f8(f932(a923,a923),f932(f932(x46292,a923),f932(x46292,a923)),x46291),f8(a923,a923,x46292)),f319(f319(f8(a923,f932(a923,a923),x46291),a317),x46293))),x46294))),f319(f319(f246(x46291,x46292),f319(f254(x46291),x46293)),f319(f319(f8(f932(x46292,a923),f932(x46292,a923),x46291),f254(x46292)),x46294)))
% 28.73/28.51 [4641]E(f319(f254(x46411),f319(f319(f8(f932(x46412,a923),a923,x46411),f82(x46412)),f319(f319(f8(f932(x46412,a923),f932(x46412,a923),x46411),f319(f18(x46412,a923,a923),f319(f319(f8(a923,f932(a923,a923),x46412),a322),f319(f319(f7(x46412,f932(x46412,a923),a923),f321(x46412)),x46413)))),x46414))),f319(f319(f34(x46412,f932(x46411,a923)),x46413),f319(f319(f8(f932(x46411,a923),f932(x46411,a923),x46412),f254(x46411)),f319(f7(x46411,x46412,a923),x46414))))
% 28.73/28.51 [4686]E(f319(f319(f146(f931(x46861,a925),x46861),f243(x46861,a925)),f319(f128(f931(x46861,a925),f319(f319(f7(f931(x46861,a925),f932(a925,a923),a923),f319(f319(f8(a925,f932(f932(a925,a923),a923),f931(x46861,a925)),f321(a925)),f248(x46861,a925))),x46862)),f319(f319(f173(x46861,a925),x46863),f131(a925,f319(f294(a925,x46864),f319(f319(f74(a925),x46864),f319(f181(f926(x46861)),x46863))))))),f319(f319(f146(f931(x46861,a925),x46861),f243(x46861,a925)),f319(f128(f931(x46861,a925),f319(f319(f7(f931(x46861,a925),f932(a925,a923),a923),f319(f319(f8(a925,f932(f932(a925,a923),a923),f931(x46861,a925)),f321(a925)),f319(f319(f7(f931(x46861,a925),a925,a925),f319(f319(f8(a925,f932(a925,a925),f931(x46861,a925)),f74(a925)),f248(x46861,a925))),x46864))),x46862)),f319(f319(f173(x46861,a925),x46863),f131(a925,f319(f294(a925,f2(a925)),f319(f181(f926(x46861)),x46863)))))))
% 28.73/28.51 [4687]E(f319(a104,f319(f319(f225(a925),f319(f181(f926(x46871)),x46872)),f319(f134(a925,f926(x46873),f319(f7(f926(x46873),a925,a925),f319(f319(f8(a925,f932(a925,a925),f926(x46873)),f225(a925)),f319(f319(f7(f926(x46873),a925,a925),f319(f319(f8(a925,f932(a925,a925),f926(x46873)),f23(a925)),f181(f926(x46873)))),f319(a104,f2(a925))))),f2(a925)),f319(f160(f926(x46873)),f319(f128(f926(x46873),f319(f319(f8(a923,a923,f926(x46873)),a314),f319(f319(f7(f926(x46873),f926(x46873),a923),a316),f105(x46873)))),x46874))))),f319(f319(f225(a925),f319(a104,f319(f181(f926(x46871)),x46872))),f319(f134(a925,f926(x46873),f319(f7(f926(x46873),a925,a925),f319(f319(f8(a925,f932(a925,a925),f926(x46873)),f225(a925)),f181(f926(x46873)))),f2(a925)),f319(f160(f926(x46873)),x46874))))
% 28.73/28.51 [4640]E(f319(f319(f126(x46401),f168(x46401,x46402,x46403)),f168(x46401,x46404,f319(f254(a925),f319(f319(f7(a925,f932(a925,a923),a923),f319(f319(f8(a925,f932(f932(a925,a923),a923),a925),f321(a925)),f319(f319(f7(a925,a925,a925),f74(a925)),f319(f181(f926(x46401)),x46402)))),x46403)))),f168(x46401,f319(f319(f126(x46401),x46402),x46404),x46403))
% 28.73/28.51 [4688]E(f31(f932(x46881,a923),f319(f254(f932(x46881,a923)),f319(f319(f8(f932(x46882,a923),a923,f932(x46881,a923)),f81(x46882)),f319(f319(f8(f932(x46882,a923),f932(x46882,a923),f932(x46881,a923)),f319(f18(x46882,a923,a923),f319(f319(f8(a923,f932(a923,a923),x46882),a317),f319(f319(f7(x46882,f932(x46882,a923),a923),f321(x46882)),x46883)))),f319(f319(f7(f932(x46881,a923),f932(x46882,f932(x46881,a923)),f932(x46882,a923)),f319(f319(f8(f932(f932(x46881,a923),a923),f932(f932(x46882,f932(x46881,a923)),f932(x46882,a923)),f932(x46881,a923)),f8(f932(x46881,a923),a923,x46882)),a316)),x46884))))),f319(f319(f33(x46882,f932(x46881,a923)),x46883),x46884))
% 28.73/28.51 [4689]E(f32(f932(x46891,a923),f319(f254(f932(x46891,a923)),f319(f319(f8(f932(x46892,a923),a923,f932(x46891,a923)),f81(x46892)),f319(f319(f8(f932(x46892,a923),f932(x46892,a923),f932(x46891,a923)),f319(f18(x46892,a923,a923),f319(f319(f8(a923,f932(a923,a923),x46892),a317),f319(f319(f7(x46892,f932(x46892,a923),a923),f321(x46892)),x46893)))),f319(f319(f7(f932(x46891,a923),f932(x46892,f932(x46891,a923)),f932(x46892,a923)),f319(f319(f8(f932(f932(x46891,a923),a923),f932(f932(x46892,f932(x46891,a923)),f932(x46892,a923)),f932(x46891,a923)),f8(f932(x46891,a923),a923,x46892)),a316)),x46894))))),f319(f319(f34(x46892,f932(x46891,a923)),x46893),x46894))
% 28.73/28.51 [4696]E(f319(f319(f143(f926(x46961)),f319(f319(f143(x46961),x46962),f319(f134(f926(x46961),f926(x46961),f126(x46961),f105(x46961)),f319(f319(f146(f926(x46961),f926(x46961)),f148(f926(x46961),x46961,f105(x46961),f319(f319(f8(f926(x46961),f932(f926(x46961),f926(x46961)),x46961),f16(f926(x46961),f926(x46961))),f319(f319(f7(x46961,f926(x46961),f926(x46961)),f143(x46961)),f105(x46961))))),x46963)))),f171(x46961,f319(f319(f143(f926(x46961)),x46964),f319(f134(f926(f926(x46961)),f926(f926(x46961)),f126(f926(x46961)),f105(f926(x46961))),f319(f319(f146(f926(x46961),f926(f926(x46961))),f148(f926(f926(x46961)),x46961,f105(f926(x46961)),f319(f16(f932(f926(x46961),f926(f926(x46961))),x46961),f319(f319(f7(f926(x46961),f926(f926(x46961)),f926(f926(x46961))),f143(f926(x46961))),f105(f926(x46961)))))),x46963))))),f171(x46961,f319(f319(f143(f926(x46961)),f319(f319(f143(x46961),x46962),x46964)),x46963)))
% 28.73/28.51 [4703]E(f319(f254(f931(x47031,x47031)),f319(f249(x47031,x47031,a923),f319(f319(f7(x47031,f932(f931(x47032,x47032),a923),f932(x47031,a923)),f319(f319(f8(f932(x47031,f932(f932(f931(x47032,x47032),a923),a923)),f932(f932(f931(x47032,x47032),a923),f932(x47031,a923)),x47031),f7(x47031,f932(f931(x47032,x47032),a923),a923)),f319(f319(f8(f932(x47031,f931(x47032,x47032)),f932(x47031,f932(f932(f931(x47032,x47032),a923),a923)),x47031),f319(f8(f931(x47032,x47032),f932(f932(f931(x47032,x47032),a923),a923),x47031),f321(f931(x47032,x47032)))),f319(f319(f7(x47031,f932(x47031,x47032),f932(x47031,f931(x47032,x47032))),f319(f319(f8(f932(x47032,f931(x47032,x47032)),f932(f932(x47031,x47032),f932(x47031,f931(x47032,x47032))),x47031),f8(x47032,f931(x47032,x47032),x47031)),f319(f319(f8(x47032,f932(x47032,f931(x47032,x47032)),x47031),f244(x47032,x47032)),x47033))),x47033)))),x47034))),f319(f319(f280(x47032,x47031),x47034),x47033))
% 28.73/28.51 [3842]E(f319(f319(f146(x38421,x38422),x38423),f161(x38421,x38424,x38425)),f161(x38422,x38424,f319(x38423,x38425)))
% 28.73/28.51 [4174]E(f122(x41741,x41742,x41743,f118(x41741,x41744,x41745)),f118(x41742,f319(x41743,x41744),f122(x41741,x41742,x41743,x41745)))
% 28.73/28.51 [4405]E(f319(f68(x44051,x44052,x44053,x44054,x44055),x44054),x44055)
% 28.73/28.51 [4457]E(f245(x44571,x44572,x44573,f235(x44572,x44571,x44574),f235(x44573,x44572,x44575)),f235(x44573,x44571,f245(x44573,x44572,x44571,x44575,x44574)))
% 28.73/28.51 [4033]E(f319(f319(f249(x40331,x40332,x40333),x40334),x40335),f319(f319(x40334,f319(f243(x40331,x40332),x40335)),f319(f248(x40331,x40332),x40335)))
% 28.73/28.51 [4034]E(f319(f319(f249(x40341,x40342,x40343),x40344),x40345),f319(f319(x40344,f319(f243(x40341,x40342),x40345)),f319(f248(x40341,x40342),x40345)))
% 28.73/28.51 [4035]E(f319(f319(f249(x40351,x40352,x40353),x40354),x40355),f319(f319(x40354,f319(f243(x40351,x40352),x40355)),f319(f248(x40351,x40352),x40355)))
% 28.73/28.51 [4069]E(f319(f319(f319(f59(x40691,x40692,x40693),x40694),x40695),f180(f932(x40692,a923))),x40695)
% 28.73/28.51 [4344]E(f319(f66(f926(x43441),f926(x43442),f926(x43443),f319(f146(x43441,x43442),x43444)),f319(f146(x43443,x43441),x43445)),f319(f146(x43443,x43442),f319(f66(x43441,x43442,x43443,x43444),x43445)))
% 28.73/28.51 [4345]E(f319(f66(f926(x43451),f926(x43452),f926(x43453),f319(f146(x43451,x43452),x43454)),f319(f146(x43453,x43451),x43455)),f319(f146(x43453,x43452),f319(f66(x43451,x43452,x43453,x43454),x43455)))
% 28.73/28.51 [4419]E(f79(x44191,f60(x44192,x44191,x44193,x44194,x44195)),f319(f319(f58(x44192,x44191,x44193),x44194),x44195))
% 28.73/28.51 [4453]E(f319(f319(f74(a925),f319(f319(f74(a925),f319(x44531,f319(f243(x44532,x44533),x44534))),f319(x44535,f319(f248(x44532,x44533),x44534)))),f319(a104,f2(a925))),f253(x44532,x44533,x44531,x44535,x44534))
% 28.73/28.51 [3972]E(f319(f319(f167(x39721),x39722),f319(f319(f146(x39723,x39721),x39724),x39725)),f319(f319(f146(x39723,x39721),x39724),f319(f319(f167(x39723),x39722),x39725)))
% 28.73/28.51 [3973]E(f319(f319(f130(x39731),x39732),f319(f319(f146(x39733,x39731),x39734),x39735)),f319(f319(f146(x39733,x39731),x39734),f319(f319(f130(x39733),x39732),x39735)))
% 28.73/28.51 [4004]E(f319(f319(f146(x40041,x40042),x40043),f319(f319(f143(x40041),x40044),x40045)),f319(f319(f143(x40042),f319(x40043,x40044)),f319(f319(f146(x40041,x40042),x40043),x40045)))
% 28.73/28.51 [4065]E(f319(f302(x40651,x40652,x40653),f319(f319(f301(x40651),x40654),x40655)),f319(f319(f301(x40652),f319(x40653,x40654)),f319(f302(x40651,x40652,x40653),x40655)))
% 28.73/28.51 [4093]E(f165(x40931,f319(f319(f143(x40931),x40932),x40933),f319(f319(f143(x40931),x40934),x40935)),f319(f319(f143(x40931),x40932),f319(f319(f143(x40931),x40934),f165(x40931,x40933,x40935))))
% 28.73/28.51 [4129]E(f319(f319(f173(x41291,x41292),f319(f319(f167(x41291),x41293),x41294)),f319(f319(f167(x41292),x41293),x41295)),f319(f319(f167(f931(x41291,x41292)),x41293),f319(f319(f173(x41291,x41292),x41294),x41295)))
% 28.73/28.51 [4130]E(f319(f319(f173(x41301,x41302),f319(f319(f130(x41301),x41303),x41304)),f319(f319(f130(x41302),x41303),x41305)),f319(f319(f130(f931(x41301,x41302)),x41303),f319(f319(f173(x41301,x41302),x41304),x41305)))
% 28.73/28.51 [4139]E(f319(f319(f151(x41391,f319(f319(f143(x41391),x41392),x41393)),f319(a104,x41394)),x41395),f319(f319(f143(x41391),x41392),f319(f319(f151(x41391,x41393),x41394),x41395)))
% 28.73/28.51 [4142]E(f319(f319(f126(x41421),f319(f319(f146(x41422,x41421),x41423),x41424)),f319(f319(f146(x41422,x41421),x41423),x41425)),f319(f319(f146(x41422,x41421),x41423),f319(f319(f126(x41422),x41424),x41425)))
% 28.73/28.51 [4146]E(f319(f319(x41461,x41462),f319(f319(f237(x41463,x41464,x41461),x41462),x41465)),f319(f319(f237(x41463,x41464,x41461),x41462),f319(a104,x41465)))
% 28.73/28.51 [4178]E(f155(x41781,x41782,x41783,f319(f319(f143(x41781),x41784),x41785)),f319(f319(f126(x41782),f319(x41783,x41784)),f155(x41781,x41782,x41783,x41785)))
% 28.73/28.51 [4190]E(f319(f319(f281(x41901,x41902,x41903),f319(f278(x41902,x41901),x41904)),f319(f278(x41903,x41902),x41905)),f319(f278(x41903,x41901),f319(f319(f281(x41903,x41902,x41901),x41905),x41904)))
% 28.73/28.51 [4222]E(f319(f319(f319(f175(f926(x42221),f926(x42221)),x42222),f159(x42221)),f319(f319(f146(x42223,x42221),x42224),x42225)),f319(f319(f146(x42223,x42221),x42224),f319(f319(f319(f175(f926(x42223),f926(x42223)),x42222),f159(x42223)),x42225)))
% 28.73/28.51 [4223]E(f319(f319(f251(x42231,x42232,x42231,x42233),f319(f244(x42232,x42231),x42234)),x42235),f319(x42235,x42234))
% 28.73/28.51 [4247]E(f147(x42471,x42472,f319(f319(f146(x42473,x42471),x42474),x42475)),f147(x42473,f319(f66(x42471,a925,x42473,x42472),x42474),x42475))
% 28.73/28.51 [4310]E(f169(f931(x43101,x43102),f319(f66(x43102,a923,f931(x43101,x43102),x43103),f248(x43101,x43102)),f319(f319(f173(x43101,x43102),x43104),x43105)),f319(f319(f173(x43101,x43102),x43104),f169(x43102,x43103,x43105)))
% 28.73/28.51 [4315]E(f319(f302(x43151,x43152,f319(f319(f8(x43153,x43152,x43151),x43154),x43155)),f234(f932(x43151,a923))),f319(f302(x43153,x43152,x43154),f319(f302(x43151,x43153,x43155),f234(f932(x43151,a923)))))
% 28.73/28.51 [4328]E(f169(f931(x43281,x43282),f319(f66(x43281,a923,f931(x43281,x43282),x43283),f243(x43281,x43282)),f319(f319(f173(x43281,x43282),x43284),x43285)),f319(f319(f173(x43281,x43282),f169(x43281,x43283,x43284)),x43285))
% 28.73/28.51 [4349]E(f319(f319(f102(f932(x43491,a923)),f319(f303(x43491,x43492,x43493),f319(f319(f301(x43492),x43494),f180(f932(x43492,a923))))),f319(f303(x43491,x43492,x43493),x43495)),f319(f303(x43491,x43492,x43493),f319(f319(f301(x43492),x43494),x43495)))
% 28.73/28.51 [4404]E(f319(f319(f126(f931(x44041,x44042)),f319(f319(f146(x44042,f931(x44041,x44042)),f319(f244(x44041,x44042),x44043)),x44044)),f53(x44041,x44042,x44045,x44044)),f53(x44041,x44042,f319(f319(f143(x44041),x44043),x44045),x44044))
% 28.73/28.51 [4406]E(f319(f319(f146(x44061,x44062),x44063),f169(x44061,f319(f66(x44062,a923,x44061,x44064),x44063),x44065)),f169(x44062,x44064,f319(f319(f146(x44061,x44062),x44063),x44065)))
% 28.73/28.51 [4411]E(f319(f134(x44111,x44112,f319(f7(x44112,x44111,x44111),f319(f7(x44111,x44112,x44111),x44113)),x44114),f319(f160(x44112),f319(f160(x44112),x44115))),f319(f134(x44111,x44112,x44113,x44114),x44115))
% 28.73/28.51 [4514]P1(f319(f319(f226(f932(x45141,a923)),f319(f302(x45142,x45141,x45143),f319(f319(f93(f932(x45142,a923)),x45144),x45145))),f319(f319(f93(f932(x45141,a923)),f319(f302(x45142,x45141,x45143),x45144)),f319(f302(x45142,x45141,x45143),x45145))))
% 28.73/28.51 [4515]P1(f319(f319(f226(f932(x45151,a923)),f319(f277(x45152,x45151,x45153),f319(f319(f93(f932(x45152,a923)),x45154),x45155))),f319(f319(f93(f932(x45151,a923)),f319(f277(x45152,x45151,x45153),x45154)),f319(f277(x45152,x45151,x45153),x45155))))
% 28.73/28.51 [4614]E(f319(f248(x46141,x46142),f319(f250(x46143,x46141,x46142,x46142,x46144,f25(x46142)),x46145)),f319(f248(x46143,x46142),x46145))
% 28.73/28.51 [4615]E(f319(f243(x46151,x46152),f319(f250(x46151,x46151,x46153,x46152,f25(x46151),x46154),x46155)),f319(f243(x46151,x46153),x46155))
% 28.73/28.51 [4618]E(f319(f243(x46181,x46182),f319(f250(x46183,x46181,x46182,x46182,x46184,f25(x46182)),x46185)),f319(x46184,f319(f243(x46183,x46182),x46185)))
% 28.73/28.51 [4619]E(f319(f248(x46191,x46192),f319(f250(x46191,x46191,x46193,x46192,f25(x46191),x46194),x46195)),f319(x46194,f319(f248(x46191,x46193),x46195)))
% 28.73/28.51 [3814]E(f319(f319(f319(f319(f196(x38141),x38142),x38143),x38144),x38145),f184(x38141,x38142))
% 28.73/28.51 [3815]E(f319(f319(f319(f319(f200(x38151),x38152),x38153),x38154),x38155),f191(x38151,x38152))
% 28.73/28.51 [4179]E(f319(f319(f33(x41791,f932(x41792,a923)),f319(f319(f301(x41791),x41793),x41794)),x41795),f319(f319(f102(f932(x41792,a923)),f319(x41795,x41793)),f319(f319(f33(x41791,f932(x41792,a923)),x41794),x41795)))
% 28.73/28.51 [4180]E(f319(f319(f34(x41801,f932(x41802,a923)),f319(f319(f301(x41801),x41803),x41804)),x41805),f319(f319(f93(f932(x41802,a923)),f319(x41805,x41803)),f319(f319(f34(x41801,f932(x41802,a923)),x41804),x41805)))
% 28.73/28.51 [4230]E(f319(f110(x42301,x42302,f319(x42303,x42304)),f319(f319(f7(x42301,a91,f927(x42302)),x42305),x42304)),f319(f189(x42301,x42302,x42303,x42305),x42304))
% 28.73/28.51 [4241]E(f319(f319(f102(f932(x42411,a923)),f319(f302(x42412,x42411,x42413),x42414)),f319(f302(x42412,x42411,x42413),x42415)),f319(f302(x42412,x42411,x42413),f319(f319(f102(f932(x42412,a923)),x42414),x42415)))
% 28.73/28.51 [4242]E(f319(f319(f102(f932(x42421,a923)),f319(f303(x42421,x42422,x42423),x42424)),f319(f303(x42421,x42422,x42423),x42425)),f319(f303(x42421,x42422,x42423),f319(f319(f102(f932(x42422,a923)),x42424),x42425)))
% 28.73/28.51 [4243]E(f319(f319(f93(f932(x42431,a923)),f319(f303(x42431,x42432,x42433),x42434)),f319(f303(x42431,x42432,x42433),x42435)),f319(f303(x42431,x42432,x42433),f319(f319(f93(f932(x42432,a923)),x42434),x42435)))
% 28.73/28.51 [4244]E(f319(f319(f23(f932(x42441,a923)),f319(f303(x42441,x42442,x42443),x42444)),f319(f303(x42441,x42442,x42443),x42445)),f319(f303(x42441,x42442,x42443),f319(f319(f23(f932(x42442,a923)),x42444),x42445)))
% 28.73/28.51 [4245]E(f319(f319(f102(f932(x42451,a923)),f319(f277(x42452,x42451,x42453),x42454)),f319(f277(x42452,x42451,x42453),x42455)),f319(f277(x42452,x42451,x42453),f319(f319(f102(f932(x42452,a923)),x42454),x42455)))
% 28.73/28.51 [4306]E(f319(f319(f151(x43061,f319(f319(f126(x43061),x43062),f319(f319(f143(x43061),x43063),x43064))),f319(f181(f926(x43061)),x43062)),x43065),f319(f319(f126(x43061),x43062),f319(f319(f143(x43061),x43065),x43064)))
% 28.73/28.51 [4312]E(f319(f319(f34(x43121,f932(x43122,a923)),x43123),f319(f319(f8(f932(x43122,a923),f932(x43122,a923),x43121),f319(f301(x43122),x43124)),x43125)),f319(f319(f301(x43122),x43124),f319(f319(f34(x43121,f932(x43122,a923)),x43123),x43125)))
% 28.73/28.51 [4313]E(f319(f319(f34(x43131,f932(x43132,a923)),x43133),f319(f319(f8(f932(x43132,a923),f932(x43132,a923),x43131),f319(f301(x43132),x43134)),x43135)),f319(f319(f301(x43132),x43134),f319(f319(f34(x43131,f932(x43132,a923)),x43133),x43135)))
% 28.73/28.51 [4421]E(f319(f319(f102(f932(f931(x44211,x44212),a923)),f319(f319(f246(x44211,x44212),x44213),f319(f16(f932(x44212,a923),x44211),x44214))),f319(f319(f246(x44211,x44212),x44215),f319(f16(f932(x44212,a923),x44211),x44214))),f319(f319(f246(x44211,x44212),f319(f319(f102(f932(x44211,a923)),x44213),x44215)),f319(f16(f932(x44212,a923),x44211),x44214)))
% 28.73/28.51 [4422]E(f319(f319(f93(f932(f931(x44221,x44222),a923)),f319(f319(f246(x44221,x44222),x44223),f319(f16(f932(x44222,a923),x44221),x44224))),f319(f319(f246(x44221,x44222),x44225),f319(f16(f932(x44222,a923),x44221),x44224))),f319(f319(f246(x44221,x44222),f319(f319(f93(f932(x44221,a923)),x44223),x44225)),f319(f16(f932(x44222,a923),x44221),x44224)))
% 28.73/28.51 [4423]E(f319(f319(f23(f932(f931(x44231,x44232),a923)),f319(f319(f246(x44231,x44232),x44233),f319(f16(f932(x44232,a923),x44231),x44234))),f319(f319(f246(x44231,x44232),x44235),f319(f16(f932(x44232,a923),x44231),x44234))),f319(f319(f246(x44231,x44232),f319(f319(f23(f932(x44231,a923)),x44233),x44235)),f319(f16(f932(x44232,a923),x44231),x44234)))
% 28.73/28.51 [4466]E(f319(f319(f146(x44661,x44662),x44663),f319(f128(x44661,f319(f66(x44662,a923,x44661,x44664),x44663)),x44665)),f319(f128(x44662,x44664),f319(f319(f146(x44661,x44662),x44663),x44665)))
% 28.73/28.51 [4472]E(f319(f181(f926(x44721)),f319(f128(x44721,x44722),f319(f319(f146(x44723,x44721),x44724),x44725))),f319(f181(f926(x44723)),f319(f128(x44723,f319(f66(x44721,a923,x44723,x44722),x44724)),x44725)))
% 28.73/28.51 [4679]E(f319(f148(f926(f931(x46791,x46792)),x46792,f105(f931(x46791,x46792)),f319(f319(f7(x46792,f932(f926(x46792),f926(f931(x46791,x46792))),f932(f926(x46792),f926(f931(x46791,x46792)))),f319(f319(f8(f932(f926(f931(x46791,x46792)),f926(f931(x46791,x46792))),f932(f932(f926(x46792),f926(f931(x46791,x46792))),f932(f926(x46792),f926(f931(x46791,x46792)))),x46792),f8(f926(f931(x46791,x46792)),f926(f931(x46791,x46792)),f926(x46792))),f319(f319(f8(f931(x46791,x46792),f932(f926(f931(x46791,x46792)),f926(f931(x46791,x46792))),x46792),f143(f931(x46791,x46792))),f319(f244(x46791,x46792),x46793)))),f319(f173(x46791,x46792),x46794))),x46795),f319(f319(f173(x46791,x46792),f319(f319(f143(x46791),x46793),x46794)),x46795))
% 28.73/28.51 [4171]E(f319(f319(f151(x41711,f319(f319(f151(x41711,x41712),x41713),x41714)),x41713),x41715),f319(f319(f151(x41711,x41712),x41713),x41715))
% 28.73/28.51 [4224]E(f319(f276(x42241,x42242),f319(f319(f301(f931(x42241,x42242)),f319(f319(f244(x42241,x42242),x42243),x42244)),x42245)),f319(f319(f301(x42242),x42244),f319(f276(x42241,x42242),x42245)))
% 28.73/28.51 [4225]E(f319(f256(x42251,x42252),f319(f319(f301(f931(x42251,x42252)),f319(f319(f244(x42251,x42252),x42253),x42254)),x42255)),f319(f319(f301(x42251),x42253),f319(f256(x42251,x42252),x42255)))
% 28.73/28.51 [4271]E(f114(x42711,x42712,f319(x42713,x42714),f319(f319(f7(x42711,a91,f927(f929(x42712))),x42715),x42714)),f319(f187(x42711,x42712,x42713,x42715),x42714))
% 28.73/28.51 [4299]E(f319(f319(f102(f932(f931(x42991,x42992),a923)),f319(f319(f246(x42991,x42992),x42993),x42994)),f319(f319(f246(x42991,x42992),x42995),x42994)),f319(f319(f246(x42991,x42992),f319(f319(f102(f932(x42991,a923)),x42993),x42995)),x42994))
% 28.73/28.51 [4300]E(f319(f319(f93(f932(f931(x43001,x43002),a923)),f319(f319(f246(x43001,x43002),x43003),x43004)),f319(f319(f246(x43001,x43002),x43005),x43004)),f319(f319(f246(x43001,x43002),f319(f319(f93(f932(x43001,a923)),x43003),x43005)),x43004))
% 28.73/28.51 [4301]E(f319(f319(f23(f932(f931(x43011,x43012),a923)),f319(f319(f246(x43011,x43012),x43013),x43014)),f319(f319(f246(x43011,x43012),x43015),x43014)),f319(f319(f246(x43011,x43012),f319(f319(f23(f932(x43011,a923)),x43013),x43015)),x43014))
% 28.73/28.51 [4360]E(f319(f319(f102(f932(x43601,a923)),f319(f319(f33(x43602,f932(x43601,a923)),x43603),x43604)),f319(f319(f33(x43602,f932(x43601,a923)),x43605),x43604)),f319(f319(f33(x43602,f932(x43601,a923)),f319(f319(f102(f932(x43602,a923)),x43603),x43605)),x43604))
% 28.73/28.51 [4361]E(f319(f319(f93(f932(x43611,a923)),f319(f319(f34(x43612,f932(x43611,a923)),x43613),x43614)),f319(f319(f34(x43612,f932(x43611,a923)),x43615),x43614)),f319(f319(f34(x43612,f932(x43611,a923)),f319(f319(f102(f932(x43612,a923)),x43613),x43615)),x43614))
% 28.73/28.51 [4370]E(f319(f319(f34(x43701,f932(x43702,a923)),x43703),f319(f319(f8(f932(x43702,a923),f932(x43702,a923),x43701),f319(f102(f932(x43702,a923)),x43704)),x43705)),f319(f319(f102(f932(x43702,a923)),x43704),f319(f319(f34(x43701,f932(x43702,a923)),x43703),x43705)))
% 28.73/28.51 [4371]E(f319(f319(f34(x43711,f932(x43712,a923)),x43713),f319(f319(f8(f932(x43712,a923),f932(x43712,a923),x43711),f319(f102(f932(x43712,a923)),x43714)),x43715)),f319(f319(f102(f932(x43712,a923)),x43714),f319(f319(f34(x43711,f932(x43712,a923)),x43713),x43715)))
% 28.73/28.51 [4372]E(f319(f319(f33(x43721,f932(x43722,a923)),x43723),f319(f319(f8(f932(x43722,a923),f932(x43722,a923),x43721),f319(f93(f932(x43722,a923)),x43724)),x43725)),f319(f319(f93(f932(x43722,a923)),x43724),f319(f319(f33(x43721,f932(x43722,a923)),x43723),x43725)))
% 28.73/28.51 [4373]E(f319(f319(f33(x43731,f932(x43732,a923)),x43733),f319(f319(f8(f932(x43732,a923),f932(x43732,a923),x43731),f319(f93(f932(x43732,a923)),x43734)),x43735)),f319(f319(f93(f932(x43732,a923)),x43734),f319(f319(f33(x43731,f932(x43732,a923)),x43733),x43735)))
% 28.73/28.51 [4374]E(f319(f319(f33(x43741,f932(x43742,a923)),x43743),f319(f319(f8(f932(x43742,a923),f932(x43742,a923),x43741),f319(f23(f932(x43742,a923)),x43744)),x43745)),f319(f319(f23(f932(x43742,a923)),x43744),f319(f319(f34(x43741,f932(x43742,a923)),x43743),x43745)))
% 28.73/28.51 [4375]E(f319(f319(f33(x43751,f932(x43752,a923)),x43753),f319(f319(f8(f932(x43752,a923),f932(x43752,a923),x43751),f319(f93(f932(x43752,a923)),x43754)),x43755)),f319(f319(f93(f932(x43752,a923)),x43754),f319(f319(f33(x43751,f932(x43752,a923)),x43753),x43755)))
% 28.73/28.51 [4376]E(f319(f319(f33(x43761,f932(x43762,a923)),x43763),f319(f319(f8(f932(x43762,a923),f932(x43762,a923),x43761),f319(f23(f932(x43762,a923)),x43764)),x43765)),f319(f319(f23(f932(x43762,a923)),x43764),f319(f319(f34(x43761,f932(x43762,a923)),x43763),x43765)))
% 28.73/28.51 [4377]E(f319(f319(f34(x43771,f932(x43772,a923)),x43773),f319(f319(f8(f932(x43772,a923),f932(x43772,a923),x43771),f319(f102(f932(x43772,a923)),x43774)),x43775)),f319(f319(f102(f932(x43772,a923)),x43774),f319(f319(f34(x43771,f932(x43772,a923)),x43773),x43775)))
% 28.73/28.51 [4431]E(f177(f926(x44311),f319(f319(f143(x44311),x44312),x44313),f319(f319(f8(f926(x44311),f926(x44311),a925),f319(f143(x44311),x44314)),f319(f319(f7(a925,x44311,f926(x44311)),f151(x44311,x44313)),x44312)),x44315),f319(f319(f151(x44311,f319(f319(f143(x44311),x44314),x44313)),x44315),x44312))
% 28.73/28.51 [4435]E(f319(f319(f33(x44351,f932(f931(x44352,x44353),a923)),x44354),f319(f319(f8(f932(f931(x44353,x44352),a923),f932(f931(x44352,x44353),a923),x44351),f278(x44353,x44352)),x44355)),f319(f278(x44353,x44352),f319(f319(f33(x44351,f932(f931(x44353,x44352),a923)),x44354),x44355)))
% 28.73/28.51 [4436]E(f319(f319(f34(x44361,f932(f931(x44362,x44363),a923)),x44364),f319(f319(f8(f932(f931(x44363,x44362),a923),f932(f931(x44362,x44363),a923),x44361),f278(x44363,x44362)),x44365)),f319(f278(x44363,x44362),f319(f319(f34(x44361,f932(f931(x44363,x44362),a923)),x44364),x44365)))
% 28.73/28.51 [4537]P1(f319(f319(f226(f932(x45371,a923)),f319(f319(f23(f932(x45371,a923)),f319(f302(x45372,x45371,x45373),x45374)),f319(f302(x45372,x45371,x45373),x45375))),f319(f302(x45372,x45371,x45373),f319(f319(f23(f932(x45372,a923)),x45374),x45375))))
% 28.73/28.51 [4682]E(f319(f148(f926(f931(x46821,x46822)),x46821,f105(f931(x46821,x46822)),f319(f319(f7(x46821,f932(f926(x46821),f926(f931(x46821,x46822))),f932(f926(x46821),f926(f931(x46821,x46822)))),f319(f319(f8(f932(f926(f931(x46821,x46822)),f926(f931(x46821,x46822))),f932(f932(f926(x46821),f926(f931(x46821,x46822))),f932(f926(x46821),f926(f931(x46821,x46822)))),x46821),f8(f926(f931(x46821,x46822)),f926(f931(x46821,x46822)),f926(x46821))),f319(f319(f8(f931(x46821,x46822),f932(f926(f931(x46821,x46822)),f926(f931(x46821,x46822))),x46821),f143(f931(x46821,x46822))),f319(f319(f7(x46821,x46822,f931(x46821,x46822)),f244(x46821,x46822)),x46823)))),f319(f319(f7(f926(x46821),f926(x46822),f926(f931(x46821,x46822))),f173(x46821,x46822)),x46824))),x46825),f319(f319(f173(x46821,x46822),x46825),f319(f319(f143(x46822),x46823),x46824)))
% 28.73/28.51 [4400]E(f319(f319(f102(f932(x44001,a923)),f319(f277(x44002,x44001,x44003),x44004)),f319(f277(x44002,x44001,x44005),x44004)),f319(f277(x44002,x44001,f319(f319(f102(f932(f931(x44002,x44001),a923)),x44003),x44005)),x44004))
% 28.73/28.51 [4437]E(f319(f319(f126(f931(x44371,x44372)),f319(f319(f173(x44371,x44372),x44373),f319(f319(f167(x44372),f319(f181(f926(x44371)),x44373)),x44374))),f319(f319(f173(x44371,x44372),x44375),f319(f319(f130(x44372),f319(f181(f926(x44371)),x44373)),x44374))),f319(f319(f173(x44371,x44372),f319(f319(f126(x44371),x44373),x44375)),x44374))
% 28.73/28.51 [4540]E(f319(f319(f246(x45401,x45402),x45403),f319(f319(f18(x45401,f932(x45402,a923),f932(x45402,a923)),f319(f319(f8(f932(x45402,a923),f932(f932(x45402,a923),f932(x45402,a923)),x45401),f102(f932(x45402,a923))),x45404)),x45405)),f319(f319(f102(f932(f931(x45401,x45402),a923)),f319(f319(f246(x45401,x45402),x45403),x45404)),f319(f319(f246(x45401,x45402),x45403),x45405)))
% 28.73/28.51 [4541]E(f319(f319(f246(x45411,x45412),x45413),f319(f319(f18(x45411,f932(x45412,a923),f932(x45412,a923)),f319(f319(f8(f932(x45412,a923),f932(f932(x45412,a923),f932(x45412,a923)),x45411),f93(f932(x45412,a923))),x45414)),x45415)),f319(f319(f93(f932(f931(x45411,x45412),a923)),f319(f319(f246(x45411,x45412),x45413),x45414)),f319(f319(f246(x45411,x45412),x45413),x45415)))
% 28.73/28.51 [4542]E(f319(f319(f246(x45421,x45422),x45423),f319(f319(f18(x45421,f932(x45422,a923),f932(x45422,a923)),f319(f319(f8(f932(x45422,a923),f932(f932(x45422,a923),f932(x45422,a923)),x45421),f23(f932(x45422,a923))),x45424)),x45425)),f319(f319(f23(f932(f931(x45421,x45422),a923)),f319(f319(f246(x45421,x45422),x45423),x45424)),f319(f319(f246(x45421,x45422),x45423),x45425)))
% 28.73/28.51 [4543]E(f319(f319(f34(x45431,f932(x45432,a923)),x45433),f319(f319(f7(x45431,f932(x45432,a923),f932(x45432,a923)),f319(f319(f8(f932(x45432,a923),f932(f932(x45432,a923),f932(x45432,a923)),x45431),f102(f932(x45432,a923))),x45434)),x45435)),f319(f319(f102(f932(x45432,a923)),f319(f319(f34(x45431,f932(x45432,a923)),x45433),x45434)),x45435))
% 28.73/28.51 [4544]E(f319(f319(f33(x45441,f932(x45442,a923)),x45443),f319(f319(f7(x45441,f932(x45442,a923),f932(x45442,a923)),f319(f319(f8(f932(x45442,a923),f932(f932(x45442,a923),f932(x45442,a923)),x45441),f93(f932(x45442,a923))),x45444)),x45445)),f319(f319(f93(f932(x45442,a923)),f319(f319(f33(x45441,f932(x45442,a923)),x45443),x45444)),x45445))
% 28.73/28.51 [4545]E(f319(f319(f33(x45451,f932(x45452,a923)),x45453),f319(f319(f7(x45451,f932(x45452,a923),f932(x45452,a923)),f319(f319(f8(f932(x45452,a923),f932(f932(x45452,a923),f932(x45452,a923)),x45451),f23(f932(x45452,a923))),x45454)),x45455)),f319(f319(f23(f932(x45452,a923)),f319(f319(f33(x45451,f932(x45452,a923)),x45453),x45454)),x45455))
% 28.73/28.51 [4546]E(f319(f319(f33(x45461,f932(x45462,a923)),x45463),f319(f319(f7(x45461,f932(x45462,a923),f932(x45462,a923)),f319(f319(f8(f932(x45462,a923),f932(f932(x45462,a923),f932(x45462,a923)),x45461),f93(f932(x45462,a923))),x45464)),x45465)),f319(f319(f93(f932(x45462,a923)),f319(f319(f33(x45461,f932(x45462,a923)),x45463),x45464)),x45465))
% 28.73/28.51 [4547]E(f319(f319(f33(x45471,f932(x45472,a923)),x45473),f319(f319(f7(x45471,f932(x45472,a923),f932(x45472,a923)),f319(f319(f8(f932(x45472,a923),f932(f932(x45472,a923),f932(x45472,a923)),x45471),f23(f932(x45472,a923))),x45474)),x45475)),f319(f319(f23(f932(x45472,a923)),f319(f319(f33(x45471,f932(x45472,a923)),x45473),x45474)),x45475))
% 28.73/28.51 [4548]E(f319(f319(f34(x45481,f932(x45482,a923)),x45483),f319(f319(f7(x45481,f932(x45482,a923),f932(x45482,a923)),f319(f319(f8(f932(x45482,a923),f932(f932(x45482,a923),f932(x45482,a923)),x45481),f102(f932(x45482,a923))),x45484)),x45485)),f319(f319(f102(f932(x45482,a923)),f319(f319(f34(x45481,f932(x45482,a923)),x45483),x45484)),x45485))
% 28.73/28.51 [4552]E(f319(f319(f33(x45521,f932(x45522,a923)),x45523),f319(f319(f18(x45521,f932(x45522,a923),f932(x45522,a923)),f319(f319(f8(f932(x45522,a923),f932(f932(x45522,a923),f932(x45522,a923)),x45521),f102(f932(x45522,a923))),x45524)),x45525)),f319(f319(f102(f932(x45522,a923)),f319(f319(f33(x45521,f932(x45522,a923)),x45523),x45524)),f319(f319(f33(x45521,f932(x45522,a923)),x45523),x45525)))
% 28.73/28.51 [4553]E(f319(f319(f34(x45531,f932(x45532,a923)),x45533),f319(f319(f18(x45531,f932(x45532,a923),f932(x45532,a923)),f319(f319(f8(f932(x45532,a923),f932(f932(x45532,a923),f932(x45532,a923)),x45531),f93(f932(x45532,a923))),x45534)),x45535)),f319(f319(f93(f932(x45532,a923)),f319(f319(f34(x45531,f932(x45532,a923)),x45533),x45534)),f319(f319(f34(x45531,f932(x45532,a923)),x45533),x45535)))
% 28.73/28.51 [4566]E(f319(f319(f33(x45661,f932(x45662,a923)),x45663),f319(f319(f18(x45661,f932(x45662,a923),f932(x45662,a923)),f319(f319(f8(f932(x45662,a923),f932(f932(x45662,a923),f932(x45662,a923)),x45661),f102(f932(x45662,a923))),x45664)),x45665)),f319(f319(f102(f932(x45662,a923)),f31(f932(x45662,a923),f319(f302(x45661,f932(x45662,a923),x45664),x45663))),f31(f932(x45662,a923),f319(f302(x45661,f932(x45662,a923),x45665),x45663))))
% 28.73/28.51 [4567]E(f319(f319(f34(x45671,f932(x45672,a923)),x45673),f319(f319(f18(x45671,f932(x45672,a923),f932(x45672,a923)),f319(f319(f8(f932(x45672,a923),f932(f932(x45672,a923),f932(x45672,a923)),x45671),f93(f932(x45672,a923))),x45674)),x45675)),f319(f319(f93(f932(x45672,a923)),f32(f932(x45672,a923),f319(f302(x45671,f932(x45672,a923),x45674),x45673))),f32(f932(x45672,a923),f319(f302(x45671,f932(x45672,a923),x45675),x45673))))
% 28.73/28.51 [4603]E(f319(f319(f130(x46031),f319(f181(f926(x46031)),f169(x46031,x46032,f319(f319(f146(x46033,x46031),x46034),x46035)))),f319(f319(f146(x46033,x46031),x46034),x46035)),f319(f319(f146(x46033,x46031),x46034),f319(f319(f130(x46033),f319(f181(f926(x46033)),f169(x46033,f319(f66(x46031,a923,x46033,x46032),x46034),x46035))),x46035)))
% 28.73/28.51 [4479]E(f319(f319(f126(f931(x44791,x44792)),f319(f319(f173(x44791,x44792),f319(f319(f167(x44791),f319(f181(f926(x44792)),x44793)),x44794)),x44793)),f319(f319(f173(x44791,x44792),f319(f319(f130(x44791),f319(f181(f926(x44792)),x44793)),x44794)),x44795)),f319(f319(f173(x44791,x44792),x44794),f319(f319(f126(x44792),x44793),x44795)))
% 28.73/28.51 [4594]E(f79(x45941,f319(f319(f18(x45941,a923,a923),f319(f319(f8(a923,f932(a923,a923),x45941),a317),f319(f319(f7(x45941,f932(x45941,a923),a923),f321(x45941)),x45942))),f319(f319(f7(x45941,x45943,a923),f319(f319(f8(x45943,f932(x45943,a923),x45941),a316),x45944)),x45945))),f319(f71(x45941,x45943,x45942,x45944),x45945))
% 28.73/28.51 [4595]E(f84(x45951,f319(f319(f18(x45951,a923,a923),f319(f319(f8(a923,f932(a923,a923),x45951),a317),f319(f319(f7(x45951,f932(x45951,a923),a923),f321(x45951)),x45952))),f319(f319(f7(x45951,x45953,a923),f319(f319(f8(x45953,f932(x45953,a923),x45951),a316),x45954)),x45955))),f319(f85(x45951,x45953,x45952,x45954),x45955))
% 28.73/28.51 [4643]E(f319(f319(f80(a1,x46431),f319(f95(a1),f319(f319(f74(a1),x46432),a89))),f319(f319(f18(a1,x46431,x46431),f319(f319(f7(a1,x46431,f932(x46431,x46431)),f319(f319(f8(a923,f932(x46431,f932(x46431,x46431)),a1),f86(x46431)),a185)),f177(x46431,x46433,x46434,x46435))),f319(f319(f8(a925,x46431,a1),x46434),f319(f319(f7(a1,a925,a925),f319(f319(f8(a925,f932(a925,a925),a1),f74(a925)),a96)),x46435)))),f177(x46431,x46433,x46434,f319(f319(f74(a925),f319(f95(a925),x46432)),x46435)))
% 28.73/28.51 [4678]E(f319(f319(f80(a1,x46781),f319(f95(a1),f319(f319(f74(a1),x46782),a89))),f319(f319(f18(a1,x46781,x46781),f319(f319(f7(a1,x46781,f932(x46781,x46781)),f319(f319(f8(a923,f932(x46781,f932(x46781,x46781)),a1),f86(x46781)),a185)),f319(f176(x46781,x46783,x46784),x46785))),f319(f319(f18(a1,x46781,x46781),f319(f319(f8(a925,f932(x46781,x46781),a1),x46784),f319(f319(f7(a1,a925,a925),f319(f319(f8(a925,f932(a925,a925),a1),f74(a925)),a96)),x46785))),f319(f319(f8(a925,x46781,a1),f176(x46781,x46783,x46784)),f319(f319(f7(a1,a925,a925),f319(f319(f8(a925,f932(a925,a925),a1),f74(a925)),a96)),x46785))))),f319(f176(x46781,x46783,x46784),f319(f319(f74(a925),f319(f95(a925),x46782)),x46785)))
% 28.73/28.51 [4711]E(f319(f254(f931(x47111,x47112)),f319(f249(x47111,x47112,a923),f319(f319(f8(f932(x47112,f932(x47113,a923)),f932(x47112,a923),x47111),f319(f8(f932(x47113,a923),a923,x47112),f81(x47113))),f319(f319(f7(x47111,f932(x47112,f932(x47113,a923)),f932(x47112,f932(x47113,a923))),f319(f319(f8(f932(f932(x47113,a923),f932(x47113,a923)),f932(f932(x47112,f932(x47113,a923)),f932(x47112,f932(x47113,a923))),x47111),f8(f932(x47113,a923),f932(x47113,a923),x47112)),f319(f319(f8(f932(x47113,f932(a923,a923)),f932(f932(x47113,a923),f932(x47113,a923)),x47111),f18(x47113,a923,a923)),f319(f319(f8(f932(x47113,a923),f932(x47113,f932(a923,a923)),x47111),f319(f8(a923,f932(a923,a923),x47113),a317)),f319(f319(f7(x47111,f932(f931(x47111,x47113),a923),f932(x47113,a923)),f319(f319(f8(f932(x47113,f932(f932(f931(x47111,x47113),a923),a923)),f932(f932(f931(x47111,x47113),a923),f932(x47113,a923)),x47111),f7(x47113,f932(f931(x47111,x47113),a923),a923)),f319(f319(f8(f932(x47113,f931(x47111,x47113)),f932(x47113,f932(f932(f931(x47111,x47113),a923),a923)),x47111),f319(f8(f931(x47111,x47113),f932(f932(f931(x47111,x47113),a923),a923),x47113),f321(f931(x47111,x47113)))),f244(x47111,x47113)))),x47114))))),f319(f319(f7(x47112,f932(f931(x47113,x47112),a923),f932(x47113,a923)),f319(f319(f8(f932(x47113,f932(f932(f931(x47113,x47112),a923),a923)),f932(f932(f931(x47113,x47112),a923),f932(x47113,a923)),x47112),f7(x47113,f932(f931(x47113,x47112),a923),a923)),f319(f319(f8(f932(x47113,f931(x47113,x47112)),f932(x47113,f932(f932(f931(x47113,x47112),a923),a923)),x47112),f319(f8(f931(x47113,x47112),f932(f932(f931(x47113,x47112),a923),a923),x47113),f321(f931(x47113,x47112)))),f319(f7(x47113,x47112,f931(x47113,x47112)),f244(x47113,x47112))))),x47115))))),f319(f319(f281(x47111,x47113,x47112),x47114),x47115))
% 28.73/28.51 [4329]E(f216(x43291,x43292,x43293,x43294,f212(x43291,x43292,x43295,x43296)),f319(f319(x43294,x43295),x43296))
% 28.73/28.51 [4330]E(f217(x43301,x43302,x43303,x43304,f212(x43301,x43302,x43305,x43306)),f319(f319(x43304,x43305),x43306))
% 28.73/28.51 [4455]E(f119(x44551,x44552,x44553,x44554,f118(x44552,x44555,x44556)),f319(f319(f319(x44554,x44555),x44556),f119(x44551,x44552,x44553,x44554,x44556)))
% 28.73/28.51 [4474]E(f68(x44741,x44742,f68(x44741,x44742,x44743,x44744,x44745),x44744,x44746),f68(x44741,x44742,x44743,x44744,x44746))
% 28.73/28.51 [4582]E(f319(f66(f931(x45821,x45822),x45822,f931(x45823,x45824),f248(x45821,x45822)),f250(x45823,x45821,x45824,x45822,x45825,x45826)),f319(f66(x45824,x45822,f931(x45823,x45824),x45826),f248(x45823,x45824)))
% 28.73/28.51 [4583]E(f319(f66(f931(x45831,x45832),x45831,f931(x45833,x45834),f243(x45831,x45832)),f250(x45833,x45831,x45834,x45832,x45835,x45836)),f319(f66(x45833,x45831,f931(x45833,x45834),x45835),f243(x45833,x45834)))
% 28.73/28.51 [4199]E(f319(f319(f66(x41991,x41992,x41993,x41994),x41995),x41996),f319(x41994,f319(x41995,x41996)))
% 28.73/28.51 [4200]E(f319(f319(f66(x42001,x42002,x42003,x42004),x42005),x42006),f319(x42004,f319(x42005,x42006)))
% 28.73/28.51 [4339]E(f215(x43391,f931(x43392,f927(x43392)),x43393,f319(f249(x43392,f927(x43392),x43391),x43394),f319(f127(x43392),f118(x43392,x43395,x43396))),f319(f319(x43394,x43395),x43396))
% 28.73/28.51 [4389]E(f218(x43891,x43892,x43893,x43894,f212(x43891,x43892,x43895,x43896)),f319(f319(f74(a925),f319(f319(f74(a925),f319(x43893,x43895)),f319(x43894,x43896))),f319(a104,f2(a925))))
% 28.73/28.51 [4000]E(f319(f319(f249(x40001,x40002,x40003),x40004),f319(f319(f244(x40001,x40002),x40005),x40006)),f319(f319(x40004,x40005),x40006))
% 28.73/28.51 [4001]E(f319(f319(f249(x40011,x40012,x40013),x40014),f319(f319(f244(x40011,x40012),x40015),x40016)),f319(f319(x40014,x40015),x40016))
% 28.73/28.51 [4002]E(f319(f319(f249(x40021,x40022,x40023),x40024),f319(f319(f244(x40021,x40022),x40025),x40026)),f319(f319(x40024,x40025),x40026))
% 28.73/28.51 [4062]E(f319(f319(f319(f8(x40621,x40622,x40623),x40624),x40625),x40626),f319(x40624,f319(x40625,x40626)))
% 28.73/28.51 [4063]E(f319(f319(f319(f7(x40631,x40632,x40633),x40634),x40635),x40636),f319(f319(x40634,x40636),x40635))
% 28.73/28.51 [4079]E(f319(f319(f319(f18(x40791,x40792,x40793),x40794),x40795),x40796),f319(f319(x40794,x40796),f319(x40795,x40796)))
% 28.73/28.51 [4102]E(f319(f148(x41021,x41022,x41023,x41024),f319(f319(f143(x41022),x41025),x41026)),f319(f319(x41024,x41025),x41026))
% 28.73/28.51 [4138]E(f161(f931(x41381,x41382),f319(f319(f224(a925),x41383),x41384),f319(f319(f244(x41381,x41382),x41385),x41386)),f319(f319(f173(x41381,x41382),f161(x41381,x41383,x41385)),f161(x41382,x41384,x41386)))
% 28.73/28.51 [4204]E(f319(f319(f143(f931(x42041,x42042)),f319(f319(f244(x42041,x42042),x42043),x42044)),f319(f319(f173(x42041,x42042),x42045),x42046)),f319(f319(f173(x42041,x42042),f319(f319(f143(x42041),x42043),x42045)),f319(f319(f143(x42042),x42044),x42046)))
% 28.73/28.51 [4205]E(f319(f319(f146(x42051,x42052),x42053),f319(f319(f151(x42051,x42054),x42055),x42056)),f319(f319(f151(x42052,f319(f319(f146(x42051,x42052),x42053),x42054)),x42055),f319(x42053,x42056)))
% 28.73/28.51 [4228]E(f319(f319(f247(x42281,x42282,x42283,x42284),x42285),x42286),f319(x42284,f319(f319(f244(x42281,x42282),x42285),x42286)))
% 28.73/28.51 [4229]E(f319(f319(f247(x42291,x42292,x42293,x42294),x42295),x42296),f319(x42294,f319(f319(f244(x42291,x42292),x42295),x42296)))
% 28.73/28.51 [4246]E(f319(f134(x42461,x42462,x42463,x42464),f319(f319(f143(x42462),x42465),x42466)),f319(f134(x42461,x42462,x42463,f319(f319(x42463,x42464),x42465)),x42466))
% 28.73/28.51 [4272]E(f252(x42721,x42722,x42723,x42724,f319(f319(f244(x42721,x42722),x42725),x42726)),f319(f319(x42724,x42725),x42726))
% 28.73/28.51 [4353]E(f319(f319(f33(x43531,f932(x43532,a923)),x43533),f319(f66(x43534,f932(x43532,a923),x43531,x43535),x43536)),f319(f319(f33(x43534,f932(x43532,a923)),f319(f302(x43531,x43534,x43536),x43533)),x43535))
% 28.73/28.51 [4402]E(f319(f319(f146(x44021,x44022),x44023),f319(f319(f146(x44024,x44021),x44025),x44026)),f319(f319(f146(x44024,x44022),f319(f66(x44021,x44022,x44024,x44023),x44025)),x44026))
% 28.73/28.51 [4403]E(f319(f319(f146(x44031,x44032),x44033),f319(f319(f146(x44034,x44031),x44035),x44036)),f319(f319(f146(x44034,x44032),f319(f66(x44031,x44032,x44034,x44033),x44035)),x44036))
% 28.73/28.51 [4409]E(f319(f302(x44091,x44092,f319(f66(x44093,x44092,x44091,x44094),x44095)),x44096),f319(f302(x44093,x44092,x44094),f319(f302(x44091,x44093,x44095),x44096)))
% 28.73/28.51 [4410]E(f319(f303(x44101,x44102,f319(f66(x44103,x44102,x44101,x44104),x44105)),x44106),f319(f303(x44101,x44103,x44105),f319(f303(x44103,x44102,x44104),x44106)))
% 28.73/28.51 [4438]E(f319(f134(x44381,x44382,x44383,f319(f134(x44381,x44382,x44383,x44384),x44385)),x44386),f319(f134(x44381,x44382,x44383,x44384),f319(f319(f126(x44382),x44385),x44386)))
% 28.73/28.51 [4572]E(f319(f250(x45721,x45721,x45722,x45723,f25(x45721),x45724),f319(f319(f244(x45721,x45722),x45725),x45726)),f319(f319(f244(x45721,x45723),x45725),f319(x45724,x45726)))
% 28.73/28.51 [4573]E(f319(f250(x45731,x45732,x45733,x45733,x45734,f25(x45733)),f319(f319(f244(x45731,x45733),x45735),x45736)),f319(f319(f244(x45732,x45733),f319(x45734,x45735)),x45736))
% 28.73/28.51 [4661]E(f319(f319(f146(f931(x46611,x46612),f931(x46611,x46613)),f319(f249(x46611,x46612,f931(x46611,x46613)),f319(f319(f7(x46611,f932(x46612,x46613),f932(x46612,f931(x46611,x46613))),f319(f319(f8(f932(x46613,f931(x46611,x46613)),f932(f932(x46612,x46613),f932(x46612,f931(x46611,x46613))),x46611),f8(x46613,f931(x46611,x46613),x46612)),f244(x46611,x46613))),x46614))),f319(f319(f173(x46611,x46612),x46615),x46616)),f319(f319(f173(x46611,x46613),x46615),f319(f319(f146(x46612,x46613),x46614),x46616)))
% 28.73/28.51 [4256]E(f319(f319(f66(x42561,x42562,x42563,f319(f16(x42562,x42561),x42564)),x42565),x42566),x42564)
% 28.73/28.51 [4288]E(f319(f302(x42881,x42882,x42883),f319(f302(x42884,x42881,x42885),x42886)),f319(f302(x42884,x42882,f319(f319(f8(x42881,x42882,x42884),x42883),x42885)),x42886))
% 28.73/28.51 [4294]E(f319(f319(f33(x42941,f932(x42942,a923)),f319(f302(x42943,x42941,x42944),x42945)),x42946),f319(f319(f33(x42943,f932(x42942,a923)),x42945),f319(f319(f8(x42941,f932(x42942,a923),x42943),x42946),x42944)))
% 28.73/28.51 [4295]E(f319(f319(f34(x42951,f932(x42952,a923)),f319(f302(x42953,x42951,x42954),x42955)),x42956),f319(f319(f34(x42953,f932(x42952,a923)),x42955),f319(f319(f8(x42951,f932(x42952,a923),x42953),x42956),x42954)))
% 28.73/28.51 [4296]E(f319(f319(f33(x42961,f932(x42962,a923)),x42963),f319(f319(f8(x42964,f932(x42962,a923),x42961),x42965),x42966)),f319(f319(f33(x42964,f932(x42962,a923)),f319(f302(x42961,x42964,x42966),x42963)),x42965))
% 28.73/28.51 [4297]E(f319(f319(f34(x42971,f932(x42972,a923)),x42973),f319(f319(f8(x42974,f932(x42972,a923),x42971),x42975),x42976)),f319(f319(f34(x42974,f932(x42972,a923)),f319(f302(x42971,x42974,x42976),x42973)),x42975))
% 28.73/28.51 [4355]E(f319(f319(f33(x43551,f932(x43552,a923)),x43553),f319(f319(f8(f932(x43554,a923),f932(x43552,a923),x43551),f302(x43554,x43552,x43555)),x43556)),f319(f302(x43554,x43552,x43555),f319(f319(f33(x43551,f932(x43554,a923)),x43553),x43556)))
% 28.73/28.51 [4356]E(f319(f319(f33(x43561,f932(x43562,a923)),x43563),f319(f319(f8(f932(x43564,a923),f932(x43562,a923),x43561),f303(x43562,x43564,x43565)),x43566)),f319(f303(x43562,x43564,x43565),f319(f319(f33(x43561,f932(x43564,a923)),x43563),x43566)))
% 28.73/28.51 [4357]E(f319(f319(f34(x43571,f932(x43572,a923)),x43573),f319(f319(f8(f932(x43574,a923),f932(x43572,a923),x43571),f303(x43572,x43574,x43575)),x43576)),f319(f303(x43572,x43574,x43575),f319(f319(f34(x43571,f932(x43574,a923)),x43573),x43576)))
% 28.73/28.51 [4358]E(f319(f319(f33(x43581,f932(x43582,a923)),x43583),f319(f319(f8(f932(x43584,a923),f932(x43582,a923),x43581),f277(x43584,x43582,x43585)),x43586)),f319(f277(x43584,x43582,x43585),f319(f319(f33(x43581,f932(x43584,a923)),x43583),x43586)))
% 28.73/28.51 [4443]E(f319(f134(x44431,x44432,f319(f7(x44432,x44431,x44431),x44433),x44434),f319(f160(x44432),f319(f319(f143(x44432),x44435),x44436))),f319(f319(x44433,x44435),f319(f134(x44431,x44432,f319(f7(x44432,x44431,x44431),x44433),x44434),f319(f160(x44432),x44436))))
% 28.73/28.51 [4501]E(f319(f319(f18(f931(x45011,x45012),x45012,x45013),f319(f319(f8(x45014,f932(x45012,x45013),f931(x45011,x45012)),x45015),f319(f319(f8(x45011,x45014,f931(x45011,x45012)),x45016),f243(x45011,x45012)))),f248(x45011,x45012)),f319(f249(x45011,x45012,x45013),f319(f319(f8(x45014,f932(x45012,x45013),x45011),x45015),x45016)))
% 28.73/28.51 [4508]E(f319(f134(x45081,x45082,f319(f7(x45082,x45081,x45081),x45083),f319(f134(x45081,x45082,f319(f7(x45082,x45081,x45081),x45083),x45084),f319(f160(x45082),x45085))),f319(f160(x45082),x45086)),f319(f134(x45081,x45082,f319(f7(x45082,x45081,x45081),x45083),x45084),f319(f160(x45082),f319(f319(f126(x45082),x45086),x45085))))
% 28.73/28.51 [4510]E(f319(f319(f146(f931(x45101,x45102),f931(x45103,x45102)),f319(f249(x45101,x45102,f931(x45103,x45102)),f319(f319(f8(x45103,f932(x45102,f931(x45103,x45102)),x45101),f244(x45103,x45102)),x45104))),f319(f319(f173(x45101,x45102),x45105),x45106)),f319(f319(f173(x45103,x45102),f319(f319(f146(x45101,x45103),x45104),x45105)),x45106))
% 28.73/28.51 [4555]P1(f319(f319(f226(f932(x45551,a923)),f319(f277(x45552,x45551,x45553),f319(f319(f34(x45554,f932(x45552,a923)),x45555),x45556))),f319(f319(f34(x45554,f932(x45551,a923)),x45555),f319(f319(f8(f932(x45552,a923),f932(x45551,a923),x45554),f277(x45552,x45551,x45553)),x45556))))
% 28.73/28.51 [4368]E(f319(f319(f173(x43681,x43682),f319(f319(f151(x43681,x43683),x43684),f319(f243(x43681,x43682),x43685))),f319(f319(f151(x43682,x43686),x43684),f319(f248(x43681,x43682),x43685))),f319(f319(f151(f931(x43681,x43682),f319(f319(f173(x43681,x43682),x43683),x43686)),x43684),x43685))
% 28.73/28.51 [4426]E(f319(f319(f102(f932(f931(x44261,x44262),a923)),f319(f319(f281(x44261,x44263,x44262),x44264),x44265)),f319(f319(f281(x44261,x44263,x44262),x44264),x44266)),f319(f319(f281(x44261,x44263,x44262),x44264),f319(f319(f102(f932(f931(x44263,x44262),a923)),x44265),x44266)))
% 28.73/28.51 [4520]E(f319(f319(f301(f931(x45201,x45202)),f319(f319(f244(x45201,x45202),x45203),x45204)),f319(f319(f102(f932(f931(x45201,x45202),a923)),f319(f319(f246(x45201,x45202),x45205),f319(f16(f932(x45202,a923),x45201),f319(f319(f301(x45202),x45204),x45206)))),f319(f319(f246(x45201,x45202),f319(f319(f301(x45201),x45203),x45205)),f319(f16(f932(x45202,a923),x45201),x45206)))),f319(f319(f246(x45201,x45202),f319(f319(f301(x45201),x45203),x45205)),f319(f16(f932(x45202,a923),x45201),f319(f319(f301(x45202),x45204),x45206))))
% 28.73/28.51 [4599]E(f319(f319(f93(f932(x45991,a923)),f319(f303(x45991,x45992,f319(f66(f931(x45992,x45993),x45992,x45991,f243(x45992,x45993)),x45994)),x45995)),f319(f303(x45991,x45993,f319(f66(f931(x45992,x45993),x45993,x45991,f248(x45992,x45993)),x45994)),x45996)),f319(f303(x45991,f931(x45992,x45993),x45994),f319(f319(f246(x45992,x45993),x45995),f319(f16(f932(x45993,a923),x45992),x45996))))
% 28.73/28.51 [4449]E(f319(f319(f102(f932(f931(x44491,x44492),a923)),f319(f319(f281(x44491,x44493,x44492),x44494),x44495)),f319(f319(f281(x44491,x44493,x44492),x44496),x44495)),f319(f319(f281(x44491,x44493,x44492),f319(f319(f102(f932(f931(x44491,x44493),a923)),x44494),x44496)),x44495))
% 28.73/28.51 [4577]E(f319(f319(f33(x45771,f932(x45772,a923)),x45773),f319(f319(f7(x45771,f932(x45774,f932(x45772,a923)),f932(x45772,a923)),f319(f319(f8(f932(x45774,a923),f932(f932(x45774,f932(x45772,a923)),f932(x45772,a923)),x45771),f33(x45774,f932(x45772,a923))),x45775)),x45776)),f319(f319(f33(x45774,f932(x45772,a923)),f319(f319(f33(x45771,f932(x45774,a923)),x45773),x45775)),x45776))
% 28.73/28.51 [4578]E(f319(f319(f33(x45781,f932(x45782,a923)),x45783),f319(f319(f7(x45781,f932(x45784,f932(x45782,a923)),f932(x45782,a923)),f319(f319(f8(f932(x45784,a923),f932(f932(x45784,f932(x45782,a923)),f932(x45782,a923)),x45781),f33(x45784,f932(x45782,a923))),x45785)),x45786)),f319(f319(f33(x45784,f932(x45782,a923)),f319(f319(f33(x45781,f932(x45784,a923)),x45783),x45785)),x45786))
% 28.73/28.51 [4579]E(f319(f319(f34(x45791,f932(x45792,a923)),x45793),f319(f319(f7(x45791,f932(x45794,f932(x45792,a923)),f932(x45792,a923)),f319(f319(f8(f932(x45794,a923),f932(f932(x45794,f932(x45792,a923)),f932(x45792,a923)),x45791),f34(x45794,f932(x45792,a923))),x45795)),x45796)),f319(f319(f34(x45794,f932(x45792,a923)),f319(f319(f33(x45791,f932(x45794,a923)),x45793),x45795)),x45796))
% 28.73/28.51 [4580]E(f319(f319(f33(x45801,f932(x45802,a923)),x45803),f319(f319(f7(x45801,f932(x45804,f932(x45802,a923)),f932(x45802,a923)),f319(f319(f8(f932(x45804,a923),f932(f932(x45804,f932(x45802,a923)),f932(x45802,a923)),x45801),f33(x45804,f932(x45802,a923))),x45805)),x45806)),f319(f319(f33(x45804,f932(x45802,a923)),f319(f319(f33(x45801,f932(x45804,a923)),x45803),x45805)),x45806))
% 28.73/28.51 [4581]E(f319(f319(f34(x45811,f932(x45812,a923)),x45813),f319(f319(f7(x45811,f932(x45814,f932(x45812,a923)),f932(x45812,a923)),f319(f319(f8(f932(x45814,a923),f932(f932(x45814,f932(x45812,a923)),f932(x45812,a923)),x45811),f34(x45814,f932(x45812,a923))),x45815)),x45816)),f319(f319(f34(x45814,f932(x45812,a923)),f319(f319(f33(x45811,f932(x45814,a923)),x45813),x45815)),x45816))
% 28.73/28.51 [4633]E(f319(f249(x46331,x46332,f931(x46333,x46334)),f319(f319(f7(x46331,f932(x46332,x46334),f932(x46332,f931(x46333,x46334))),f319(f319(f8(f932(x46334,f931(x46333,x46334)),f932(f932(x46332,x46334),f932(x46332,f931(x46333,x46334))),x46331),f8(x46334,f931(x46333,x46334),x46332)),f319(f319(f8(x46333,f932(x46334,f931(x46333,x46334)),x46331),f244(x46333,x46334)),x46335))),x46336)),f250(x46331,x46333,x46332,x46334,x46335,x46336))
% 28.73/28.51 [4656]E(f319(f302(x46561,x46562,f319(f319(f18(x46561,x46562,x46562),f319(f319(f18(x46561,x46562,f932(x46562,x46562)),f319(f319(f8(a923,f932(x46562,f932(x46562,x46562)),x46561),f86(x46562)),x46563)),x46564)),x46565)),x46566),f319(f319(f102(f932(x46562,a923)),f319(f302(x46561,x46562,x46564),f319(f319(f93(f932(x46561,a923)),x46566),f319(f254(x46561),x46563)))),f319(f302(x46561,x46562,x46565),f319(f319(f93(f932(x46561,a923)),x46566),f319(f254(x46561),f319(f319(f8(a923,a923,x46561),a314),x46563))))))
% 28.73/28.51 [4668]E(f319(f302(x46681,f931(x46682,x46683),f319(f319(f18(x46681,x46683,f931(x46682,x46683)),f319(f319(f8(x46682,f932(x46683,f931(x46682,x46683)),x46681),f244(x46682,x46683)),x46684)),x46685)),x46686),f319(f319(f246(x46682,x46683),f319(f302(x46681,x46682,x46684),x46686)),f319(f319(f8(f932(x46681,a923),f932(x46683,a923),x46682),f302(x46681,x46683,x46685)),f319(f319(f7(x46682,f932(x46681,a923),f932(x46681,a923)),f319(f319(f8(f932(x46681,a923),f932(f932(x46681,a923),f932(x46681,a923)),x46682),f93(f932(x46681,a923))),f319(f319(f8(f932(x46682,a923),f932(x46681,a923),x46682),f303(x46681,x46682,x46684)),f319(f319(f7(x46682,f932(x46682,a923),f932(x46682,a923)),f301(x46682)),f180(f932(x46682,a923)))))),x46686))))
% 28.73/28.51 [4693]E(f238(x46931,x46932,x46933,x46934,x46935,x46936),f319(x46934,f319(f254(x46931),f319(f319(f8(f932(f932(x46933,x46931),a923),a923,x46931),f81(f932(x46933,x46931))),f319(f319(f8(f932(f932(x46933,x46931),a923),f932(f932(x46933,x46931),a923),x46931),f319(f18(f932(x46933,x46931),a923,a923),f319(f319(f8(a923,f932(a923,a923),f932(x46933,x46931)),a317),f319(f319(f7(f932(x46933,x46931),f932(f932(x46933,x46931),a923),a923),f321(f932(x46933,x46931))),x46935)))),f319(f319(f7(x46931,f932(f932(x46933,x46931),x46931),f932(f932(x46933,x46931),a923)),f319(f319(f8(f932(x46931,a923),f932(f932(f932(x46933,x46931),x46931),f932(f932(x46933,x46931),a923)),x46931),f8(x46931,a923,f932(x46933,x46931))),a316)),f319(f319(f7(f932(x46933,x46931),x46933,x46931),f5(f932(x46933,x46931))),x46936)))))))
% 28.73/28.51 [4482]E(f319(f66(x44821,x44822,x44823,x44824),f68(x44823,x44821,x44825,x44826,x44827)),f68(x44823,x44822,f319(f66(x44821,x44822,x44823,x44824),x44825),x44826,f319(x44824,x44827)))
% 28.73/28.51 [4616]E(f319(f248(x46161,x46162),f319(f250(x46163,x46161,x46164,x46162,x46165,x46166),x46167)),f319(x46166,f319(f248(x46163,x46164),x46167)))
% 28.73/28.51 [4617]E(f319(f243(x46171,x46172),f319(f250(x46173,x46171,x46174,x46172,x46175,x46176),x46177)),f319(x46175,f319(f243(x46173,x46174),x46177)))
% 28.73/28.51 [4331]E(f319(f319(f173(x43311,x43312),f319(f319(f151(x43311,x43313),x43314),x43315)),f319(f319(f151(x43312,x43316),x43314),x43317)),f319(f319(f151(f931(x43311,x43312),f319(f319(f173(x43311,x43312),x43313),x43316)),x43314),f319(f319(f244(x43311,x43312),x43315),x43317)))
% 28.73/28.51 [4397]E(f319(f319(f319(f251(x43971,x43972,x43973,x43974),x43975),x43976),x43977),f319(f319(f249(x43972,x43973,x43974),x43976),f319(x43975,x43977)))
% 28.73/28.51 [4398]E(f319(f319(f319(f251(x43981,x43982,x43983,x43984),x43985),x43986),x43987),f319(f319(f249(x43982,x43983,x43984),x43986),f319(x43985,x43987)))
% 28.73/28.51 [4408]E(f319(f319(f319(f251(x44081,x44082,x44083,x44084),x44085),x44086),x44087),f319(f319(x44086,f319(f243(x44082,x44083),f319(x44085,x44087))),f319(f248(x44082,x44083),f319(x44085,x44087))))
% 28.73/28.51 [4460]E(f319(f66(x44601,x44602,x44603,x44604),f319(f66(x44605,x44601,x44603,x44606),x44607)),f319(f66(x44605,x44602,x44603,f319(f66(x44601,x44602,x44605,x44604),x44606)),x44607))
% 28.73/28.51 [4637]E(f319(f250(x46371,x46372,x46373,x46373,x46374,f25(x46373)),f319(f250(x46371,x46371,x46375,x46373,f25(x46371),x46376),x46377)),f319(f319(f244(x46372,x46373),f319(x46374,f319(f243(x46371,x46375),x46377))),f319(x46376,f319(f248(x46371,x46375),x46377))))
% 28.73/28.51 [4638]E(f319(f250(x46381,x46381,x46382,x46383,f25(x46381),x46384),f319(f250(x46385,x46381,x46382,x46382,x46386,f25(x46382)),x46387)),f319(f319(f244(x46381,x46383),f319(x46386,f319(f243(x46385,x46382),x46387))),f319(x46384,f319(f248(x46385,x46382),x46387))))
% 28.73/28.51 [4654]E(f319(f250(x46541,x46542,x46543,x46543,x46544,f25(x46543)),f319(f250(x46545,x46541,x46543,x46543,x46546,f25(x46543)),x46547)),f319(f250(x46545,x46542,x46543,x46543,f319(f66(x46541,x46542,x46545,x46544),x46546),f25(x46543)),x46547))
% 28.73/28.51 [4655]E(f319(f250(x46551,x46551,x46552,x46553,f25(x46551),x46554),f319(f250(x46551,x46551,x46555,x46552,f25(x46551),x46556),x46557)),f319(f250(x46551,x46551,x46555,x46553,f25(x46551),f319(f66(x46552,x46553,x46555,x46554),x46556)),x46557))
% 28.73/28.51 [4665]E(f319(f250(x46651,x46652,x46653,x46653,x46654,f25(x46653)),f319(f250(x46651,x46651,x46655,x46653,f25(x46651),x46656),x46657)),f319(f250(x46652,x46652,x46655,x46653,f25(x46652),x46656),f319(f250(x46651,x46652,x46655,x46655,x46654,f25(x46655)),x46657)))
% 28.73/28.51 [4365]E(f319(f319(f281(x43651,x43652,x43653),f319(f319(f281(x43651,x43654,x43652),x43655),x43656)),x43657),f319(f319(f281(x43651,x43654,x43653),x43655),f319(f319(f281(x43654,x43652,x43653),x43656),x43657)))
% 28.73/28.51 [4432]E(f319(f319(f249(x44321,x44322,x44323),f319(f66(x44324,f932(x44322,x44323),x44321,x44325),x44326)),x44327),f319(f319(x44325,f319(x44326,f319(f243(x44321,x44322),x44327))),f319(f248(x44321,x44322),x44327)))
% 28.73/28.51 [4513]E(f319(f134(x45131,x45132,f319(f7(x45132,x45131,x45131),x45133),x45134),f319(f160(x45132),f319(f319(f146(x45135,x45132),x45136),x45137))),f319(f134(x45131,x45135,f319(f7(x45135,x45131,x45131),f319(f66(x45132,f932(x45131,x45131),x45135,x45133),x45136)),x45134),f319(f160(x45135),x45137)))
% 28.73/28.51 [4461]E(f319(f319(f33(x44611,f932(f931(x44612,x44613),a923)),x44614),f319(f319(f8(f932(f931(x44615,x44613),a923),f932(f931(x44612,x44613),a923),x44611),f319(f281(x44612,x44615,x44613),x44616)),x44617)),f319(f319(f281(x44612,x44615,x44613),x44616),f319(f319(f33(x44611,f932(f931(x44615,x44613),a923)),x44614),x44617)))
% 28.73/28.51 [4604]E(f319(f319(f33(x46041,f932(f931(x46042,x46043),a923)),x46044),f319(f319(f7(x46041,f932(f931(x46045,x46043),a923),f932(f931(x46042,x46043),a923)),f319(f319(f8(f932(f931(x46042,x46045),a923),f932(f932(f931(x46045,x46043),a923),f932(f931(x46042,x46043),a923)),x46041),f281(x46042,x46045,x46043)),x46046)),x46047)),f319(f319(f281(x46042,x46045,x46043),f319(f319(f33(x46041,f932(f931(x46042,x46045),a923)),x46044),x46046)),x46047))
% 28.73/28.51 [4605]E(f319(f134(x46051,x46052,f319(f319(f7(x46051,f932(x46052,x46053),f932(x46052,x46051)),f319(f319(f8(f932(x46053,x46051),f932(f932(x46052,x46053),f932(x46052,x46051)),x46051),f8(x46053,x46051,x46052)),x46054)),x46055),x46056),x46057),f319(f134(x46051,x46053,x46054,x46056),f319(f319(f146(x46052,x46053),x46055),x46057)))
% 28.73/28.51 [4666]E(f319(f319(f34(x46661,f932(x46662,a923)),x46663),f319(f319(f8(f932(x46664,f932(x46662,a923)),f932(x46662,a923),x46661),f319(f34(x46664,f932(x46662,a923)),x46665)),f319(f319(f7(x46661,f932(x46664,f932(x46662,a923)),f932(x46664,f932(x46662,a923))),f319(f319(f8(f932(f932(x46662,a923),f932(x46662,a923)),f932(f932(x46664,f932(x46662,a923)),f932(x46664,f932(x46662,a923))),x46661),f8(f932(x46662,a923),f932(x46662,a923),x46664)),f319(f319(f8(f932(x46662,a923),f932(f932(x46662,a923),f932(x46662,a923)),x46661),f102(f932(x46662,a923))),x46666))),x46667))),f319(f319(f102(f932(x46662,a923)),f319(f319(f34(x46661,f932(x46662,a923)),x46663),x46666)),f319(f319(f34(x46664,f932(x46662,a923)),x46665),x46667)))
% 28.73/28.51 [4667]E(f319(f319(f33(x46671,f932(x46672,a923)),x46673),f319(f319(f8(f932(x46674,f932(x46672,a923)),f932(x46672,a923),x46671),f319(f33(x46674,f932(x46672,a923)),x46675)),f319(f319(f7(x46671,f932(x46674,f932(x46672,a923)),f932(x46674,f932(x46672,a923))),f319(f319(f8(f932(f932(x46672,a923),f932(x46672,a923)),f932(f932(x46674,f932(x46672,a923)),f932(x46674,f932(x46672,a923))),x46671),f8(f932(x46672,a923),f932(x46672,a923),x46674)),f319(f319(f8(f932(x46672,a923),f932(f932(x46672,a923),f932(x46672,a923)),x46671),f93(f932(x46672,a923))),x46676))),x46677))),f319(f319(f93(f932(x46672,a923)),f319(f319(f33(x46671,f932(x46672,a923)),x46673),x46676)),f319(f319(f33(x46674,f932(x46672,a923)),x46675),x46677)))
% 28.73/28.51 [4659]E(f189(x46591,x46592,f319(f319(f319(x46593,x46594),x46595),x46596),f319(f319(f7(x46591,f931(a91,a91),f932(a91,f927(x46592))),f319(f319(f7(x46591,a91,f932(f931(a91,a91),f932(a91,f927(x46592)))),f319(f319(f7(x46591,a91,f932(a91,f932(f931(a91,a91),f932(a91,f927(x46592))))),x46597),x46594)),x46595)),x46596)),f319(f319(f319(f201(x46591,x46592,x46593,x46597),x46594),x46595),x46596))
% 28.73/28.51 [4673]E(f190(x46731,x46732,f319(f319(f319(x46733,x46734),x46735),x46736),f319(f319(f7(x46731,f931(a91,a91),f932(a91,f927(x46732))),f319(f319(f7(x46731,a91,f932(f931(a91,a91),f932(a91,f927(x46732)))),f319(f319(f7(x46731,a91,f932(a91,f932(f931(a91,a91),f932(a91,f927(x46732))))),x46737),x46734)),x46735)),x46736)),f203(x46731,x46732,x46733,x46737,x46734,x46735,x46736))
% 28.73/28.51 [4664]E(f187(x46641,x46642,f319(f319(f319(x46643,x46644),x46645),x46646),f319(f319(f7(x46641,f931(a91,a91),f932(a91,f927(f929(x46642)))),f319(f319(f7(x46641,a91,f932(f931(a91,a91),f932(a91,f927(f929(x46642))))),f319(f319(f7(x46641,a91,f932(a91,f932(f931(a91,a91),f932(a91,f927(f929(x46642)))))),x46647),x46644)),x46645)),x46646)),f319(f319(f319(f197(x46641,x46642,x46643,x46647),x46644),x46645),x46646))
% 28.73/28.51 [4675]E(f188(x46751,x46752,f319(f319(f319(x46753,x46754),x46755),x46756),f319(f319(f7(x46751,f931(a91,a91),f932(a91,f927(f929(x46752)))),f319(f319(f7(x46751,a91,f932(f931(a91,a91),f932(a91,f927(f929(x46752))))),f319(f319(f7(x46751,a91,f932(a91,f932(f931(a91,a91),f932(a91,f927(f929(x46752)))))),x46757),x46754)),x46755)),x46756)),f199(x46751,x46752,x46753,x46757,x46754,x46755,x46756))
% 28.73/28.51 [4574]E(f319(f250(x45741,x45742,x45743,x45744,x45745,x45746),f319(f319(f244(x45741,x45743),x45747),x45748)),f319(f319(f244(x45742,x45744),f319(x45745,x45747)),f319(x45746,x45748)))
% 28.73/28.51 [4677]E(f319(f319(f146(f931(x46771,x46772),f931(x46773,x46774)),f319(f249(x46771,x46772,f931(x46773,x46774)),f319(f319(f7(x46771,f932(x46772,x46774),f932(x46772,f931(x46773,x46774))),f319(f319(f8(f932(x46774,f931(x46773,x46774)),f932(f932(x46772,x46774),f932(x46772,f931(x46773,x46774))),x46771),f8(x46774,f931(x46773,x46774),x46772)),f319(f319(f8(x46773,f932(x46774,f931(x46773,x46774)),x46771),f244(x46773,x46774)),x46775))),x46776))),f319(f319(f173(x46771,x46772),x46777),x46778)),f319(f319(f173(x46773,x46774),f319(f319(f146(x46771,x46773),x46775),x46777)),f319(f319(f146(x46772,x46774),x46776),x46778)))
% 28.73/28.51 [4680]E(f319(f319(f146(f931(x46801,x46802),x46803),f319(f249(x46801,x46802,x46803),f319(f319(f8(f932(x46802,f931(x46801,x46804)),f932(x46802,x46803),x46801),f319(f8(f931(x46801,x46804),x46803,x46802),x46805)),f319(f319(f7(x46801,f932(x46802,x46804),f932(x46802,f931(x46801,x46804))),f319(f319(f8(f932(x46804,f931(x46801,x46804)),f932(f932(x46802,x46804),f932(x46802,f931(x46801,x46804))),x46801),f8(x46804,f931(x46801,x46804),x46802)),f244(x46801,x46804))),x46806)))),f319(f319(f173(x46801,x46802),x46807),x46808)),f319(f319(f146(f931(x46801,x46804),x46803),x46805),f319(f319(f173(x46801,x46804),x46807),f319(f319(f146(x46802,x46804),x46806),x46808))))
% 28.73/28.51 [4608]E(f319(f319(f146(f931(x46081,x46082),x46083),f319(f249(x46081,x46082,x46083),f319(f319(f8(f932(x46082,f931(x46084,x46082)),f932(x46082,x46083),x46081),f319(f8(f931(x46084,x46082),x46083,x46082),x46085)),f319(f319(f8(x46084,f932(x46082,f931(x46084,x46082)),x46081),f244(x46084,x46082)),x46086)))),f319(f319(f173(x46081,x46082),x46087),x46088)),f319(f319(f146(f931(x46084,x46082),x46083),x46085),f319(f319(f173(x46084,x46082),f319(f319(f146(x46081,x46084),x46086),x46087)),x46088)))
% 28.73/28.51 [4565]E(f319(f319(f249(x45651,x45652,x45653),f319(f319(f8(f932(x45652,f931(x45654,x45655)),f932(x45652,x45653),x45651),f319(f8(f931(x45654,x45655),x45653,x45652),f319(f249(x45654,x45655,x45653),x45656))),x45657)),x45658),f319(f319(f249(x45654,x45655,x45653),x45656),f319(f319(f249(x45651,x45652,f931(x45654,x45655)),x45657),x45658)))
% 28.73/28.51 [4681]E(f319(f319(f33(f931(x46811,x46812),f932(f931(x46813,x46814),a923)),f319(f319(f246(x46811,x46812),x46815),f319(f16(f932(x46812,a923),x46811),x46816))),f319(f249(x46811,x46812,f932(f931(x46813,x46814),a923)),f319(f319(f7(x46811,f932(x46812,f932(x46813,f932(x46814,a923))),f932(x46812,f932(f931(x46813,x46814),a923))),f319(f319(f8(f932(f932(x46813,f932(x46814,a923)),f932(f931(x46813,x46814),a923)),f932(f932(x46812,f932(x46813,f932(x46814,a923))),f932(x46812,f932(f931(x46813,x46814),a923))),x46811),f8(f932(x46813,f932(x46814,a923)),f932(f931(x46813,x46814),a923),x46812)),f319(f319(f8(f932(x46813,a923),f932(f932(x46813,f932(x46814,a923)),f932(f931(x46813,x46814),a923)),x46811),f246(x46813,x46814)),x46817))),f319(f319(f8(f932(x46814,a923),f932(x46813,f932(x46814,a923)),x46812),f16(f932(x46814,a923),x46813)),x46818)))),f319(f319(f246(x46813,x46814),f319(f319(f33(x46811,f932(x46813,a923)),x46815),x46817)),f319(f16(f932(x46814,a923),x46813),f319(f319(f33(x46812,f932(x46814,a923)),x46816),x46818))))
% 28.73/28.51 [4622]E(f319(f319(f251(x46221,x46222,x46223,x46224),f319(f319(f251(x46221,x46225,x46226,f931(x46222,x46223)),x46227),x46228)),x46229),f319(f319(f251(x46221,x46225,x46226,x46224),x46227),f319(f319(f7(x46225,f932(x46222,f932(x46223,x46224)),f932(x46226,x46224)),f319(f319(f8(f932(x46226,f931(x46222,x46223)),f932(f932(x46222,f932(x46223,x46224)),f932(x46226,x46224)),x46225),f251(x46226,x46222,x46223,x46224)),x46228)),x46229)))
% 28.73/28.51 [4650]E(f319(f66(f931(x46501,x46502),f931(x46503,x46504),f931(x46505,x46506),f250(x46501,x46503,x46502,x46504,x46507,x46508)),f250(x46505,x46501,x46506,x46502,x46509,x465010)),f250(x46505,x46503,x46506,x46504,f319(f66(x46501,x46503,x46505,x46507),x46509),f319(f66(x46502,x46504,x46506,x46508),x465010)))
% 28.73/28.51 [4651]E(f319(f66(f931(x46511,x46512),f931(x46513,x46514),f931(x46515,x46516),f250(x46511,x46513,x46512,x46514,x46517,x46518)),f250(x46515,x46511,x46516,x46512,x46519,x465110)),f250(x46515,x46513,x46516,x46514,f319(f66(x46511,x46513,x46515,x46517),x46519),f319(f66(x46512,x46514,x46516,x46518),x465110)))
% 28.73/28.51 [4657]E(f319(f250(x46571,x46572,x46573,x46574,x46575,x46576),f319(f250(x46577,x46571,x46578,x46573,x46579,x465710),x465711)),f319(f250(x46577,x46572,x46578,x46574,f319(f66(x46571,x46572,x46577,x46575),x46579),f319(f66(x46573,x46574,x46578,x46576),x465710)),x465711))
% 28.73/28.51 [4784]~P5(x47841)+P5(f929(x47841))
% 28.73/28.51 [4785]~P71(x47851)+P71(f929(x47851))
% 28.73/28.51 [4786]~P111(x47861)+P111(f926(x47861))
% 28.73/28.51 [4788]~P150(x47881)+~E(f72(x47881),f2(x47881))
% 28.73/28.51 [4789]~P150(x47891)+~E(f72(x47891),f2(x47891))
% 28.73/28.51 [4791]~E(x47911,f2(a91))+E(f319(a22,x47911),f2(a1))
% 28.73/28.51 [4792]~E(x47921,f2(a1))+E(f76(a1,x47921),f2(a1))
% 28.73/28.51 [4798]~P149(x47981)+P29(x47981,f2(x47981))
% 28.73/28.51 [4799]~P4(x47991)+P14(x47991,f105(x47991))
% 28.73/28.51 [4800]~P4(x48001)+P14(x48001,f105(x48001))
% 28.73/28.51 [4809]P1(x48091)+P1(f319(a314,x48091))
% 28.73/28.51 [4863]~P149(x48631)+~P29(x48631,f72(x48631))
% 28.73/28.51 [4900]~P1(x49001)+~P1(f319(a314,x49001))
% 28.73/28.51 [4921]E(f319(a96,x49211),f2(a925))+~P1(f319(a185,x49211))
% 28.73/28.51 [4987]~P107(x49871)+P16(x49871,x49871,f102(x49871))
% 28.73/28.51 [4988]~P108(x49881)+P16(x49881,x49881,f93(x49881))
% 28.73/28.51 [4989]~P101(x49891)+P16(x49891,x49891,f75(x49891))
% 28.73/28.51 [4990]~P4(x49901)+P16(x49901,x49901,f224(x49901))
% 28.73/28.51 [4991]~P4(x49911)+P16(x49911,x49911,f225(x49911))
% 28.73/28.51 [4992]~P76(x49921)+P18(x49921,x49921,f75(x49921))
% 28.73/28.51 [4795]~E(x47951,f2(a925))+E(f319(f92(a1),x47951),f2(a1))
% 28.73/28.51 [4801]~P99(x48011)+E(f319(f95(x48011),a77),f2(x48011))
% 28.73/28.51 [4802]~P99(x48021)+E(f319(f95(x48021),a77),f2(x48021))
% 28.73/28.51 [4805]~E(f596(x48051),f2(a925))+E(f319(f157(a925),x48051),f2(a925))
% 28.73/28.51 [4806]~P3(x48061)+E(f228(x48061,f226(x48061)),f224(x48061))
% 28.73/28.51 [4807]~P3(x48071)+E(f229(x48071,f226(x48071)),f225(x48071))
% 28.73/28.51 [4808]~P94(x48081)+E(f76(x48081,f2(x48081)),f2(x48081))
% 28.73/28.51 [4817]~P149(x48171)+E(f319(f92(x48171),f72(a925)),f72(x48171))
% 28.73/28.51 [4818]~P149(x48181)+E(f319(f92(x48181),f2(a925)),f2(x48181))
% 28.73/28.51 [4819]~P145(x48191)+E(f319(f94(x48191),f72(a1)),f72(x48191))
% 28.73/28.51 [4820]~P145(x48201)+E(f319(f94(x48201),f2(a1)),f2(x48201))
% 28.73/28.51 [4821]E(x48211,f2(a925))+~E(f319(f92(a1),x48211),f2(a1))
% 28.73/28.51 [4857]~P96(x48571)+E(f319(f73(x48571),f234(x48571)),f180(x48571))
% 28.73/28.51 [4858]~P96(x48581)+E(f319(f73(x48581),f180(x48581)),f234(x48581))
% 28.73/28.51 [4859]~P69(x48591)+E(f319(f73(x48591),f2(x48591)),f2(x48591))
% 28.73/28.51 [4860]~P126(x48601)+E(f319(f69(x48601),f72(x48601)),f72(x48601))
% 28.73/28.51 [4861]~P92(x48611)+E(f319(f69(x48611),f2(x48611)),f2(x48611))
% 28.73/28.51 [4862]~P88(x48621)+E(f319(f157(x48621),f105(x48621)),f2(x48621))
% 28.73/28.51 [4880]~P37(x48801)+P42(f319(f164(a1),x48801))
% 28.73/28.51 [4904]~P99(x49041)+E(f319(f73(x49041),f72(x49041)),f319(f95(x49041),a89))
% 28.73/28.51 [4905]~P99(x49051)+E(f319(f73(x49051),f72(x49051)),f319(f95(x49051),a89))
% 28.73/28.51 [4920]~P99(x49201)+P29(x49201,f319(f95(x49201),a77))
% 28.73/28.51 [4946]P37(x49461)+~P42(f319(f164(a1),x49461))
% 28.73/28.51 [4993]E(f319(f92(a1),f319(a96,x49931)),x49931)+P1(f319(a185,x49931))
% 28.73/28.51 [5063]~P119(x50631)+E(f237(x50631,f72(x50631),f75(x50631)),f236(x50631))
% 28.73/28.51 [5096]~P99(x50961)+~P29(x50961,f319(f95(x50961),a89))
% 28.73/28.51 [5188]~E(x51881,f2(a925))+P1(f319(f319(f226(a925),x51881),f2(a925)))
% 28.73/28.51 [5244]E(f319(f69(a1),x52441),x52441)+P1(f319(f319(f227(a1),x52441),f2(a1)))
% 28.73/28.51 [5262]~E(f319(a96,x52621),f2(a925))+P1(f319(f319(f226(a1),x52621),f2(a1)))
% 28.73/28.51 [5331]~P1(f319(a185,x53311))+P1(f319(f319(f227(a1),x53311),f2(a1)))
% 28.73/28.51 [5374]~P129(x53741)+P1(f319(f319(f226(x53741),f2(x53741)),f72(x53741)))
% 28.73/28.51 [5375]~P145(x53751)+P1(f319(f319(f321(x53751),f72(x53751)),f101(x53751)))
% 28.73/28.51 [5376]~P149(x53761)+P1(f319(f319(f321(x53761),f72(x53761)),f178(x53761)))
% 28.73/28.51 [5377]~P145(x53771)+P1(f319(f319(f321(x53771),f2(x53771)),f101(x53771)))
% 28.73/28.51 [5378]~P149(x53781)+P1(f319(f319(f321(x53781),f2(x53781)),f178(x53781)))
% 28.73/28.51 [5379]~P129(x53791)+P1(f319(f319(f227(x53791),f2(x53791)),f72(x53791)))
% 28.73/28.51 [5432]E(x54321,f2(a925))+~P1(f319(f319(f226(a925),x54321),f2(a925)))
% 28.73/28.51 [5473]E(f319(a96,x54731),f2(a925))+~P1(f319(f319(f226(a1),x54731),f2(a1)))
% 28.73/28.51 [5474]E(f319(a96,x54741),f2(a925))+~P1(f319(f319(f226(a1),x54741),f2(a1)))
% 28.73/28.51 [5529]P1(f319(a185,x55291))+~P1(f319(f319(f227(a1),x55291),f2(a1)))
% 28.73/28.51 [5536]~P4(x55361)+P18(x55361,f926(x55361),f140(x55361,x55361,f5(x55361)))
% 28.73/28.51 [5554]P42(x55541)+~P1(f319(f319(f226(a1),f2(a1)),f327(x55541)))
% 28.73/28.51 [5559]E(f319(f69(a1),x55591),f319(f73(a1),x55591))+~P1(f319(f319(f227(a1),x55591),f2(a1)))
% 28.73/28.51 [5730]~P129(x57301)+~P1(f319(f319(f226(x57301),f72(x57301)),f2(x57301)))
% 28.73/28.51 [5731]~P129(x57311)+~P1(f319(f319(f227(x57311),f72(x57311)),f2(x57311)))
% 28.73/28.51 [5745]~E(x57451,f2(a925))+P1(f319(f319(f226(a1),f319(f92(a1),x57451)),f2(a1)))
% 28.73/28.51 [5746]~E(x57461,f2(a1))+P1(f319(f319(f227(a1),f319(f69(a1),x57461)),f72(a1)))
% 28.73/28.51 [5868]~P88(x58681)+E(f134(x58681,x58681,f74(x58681),f2(x58681)),f157(x58681))
% 28.73/28.51 [6043]~P110(x60431)+P26(a925,x60431,f92(x60431),f234(f932(a925,a923)))
% 28.73/28.51 [6251]E(x62511,f2(a925))+~P1(f319(f319(f226(a1),f319(f92(a1),x62511)),f2(a1)))
% 28.73/28.51 [6252]E(x62521,f2(a1))+~P1(f319(f319(f227(a1),f319(f69(a1),x62521)),f72(a1)))
% 28.73/28.51 [7056]~P1(f319(f319(f227(a1),x70561),f2(a1)))+P1(f319(f319(f227(a1),f319(f319(f74(a1),x70561),x70561)),f2(a1)))
% 28.73/28.51 [7612]P1(f319(f319(f227(a1),x76121),f2(a1)))+~P1(f319(f319(f227(a1),f319(f319(f74(a1),x76121),x76121)),f2(a1)))
% 28.73/28.51 [8159]E(x81591,f319(a3,f2(a925)))+P1(f319(f319(f227(a925),f319(f319(f23(a925),f319(a20,x81591)),f319(a104,f2(a925)))),f319(a20,x81591)))
% 28.73/28.51 [8934]~P1(f319(f319(f227(a1),x89341),f2(a1)))+P1(f319(f319(f227(a1),f319(f319(f23(a1),f319(f319(f74(a1),x89341),x89341)),a89)),f2(a1)))
% 28.73/28.51 [9032]~P1(f319(f319(f227(a1),x90321),f2(a1)))+P1(f319(f319(f227(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x90321)),x90321)),f2(a1)))
% 28.73/28.51 [9358]P1(f319(f319(f227(a1),x93581),f2(a1)))+~P1(f319(f319(f227(a1),f319(f319(f23(a1),f319(f319(f74(a1),x93581),x93581)),a89)),f2(a1)))
% 28.73/28.51 [9421]P1(f319(f319(f227(a1),x94211),f2(a1)))+~P1(f319(f319(f227(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x94211)),x94211)),f2(a1)))
% 28.73/28.51 [4894]~E(a77,x48941)+E(f319(f319(f74(a1),x48941),x48941),a77)
% 28.73/28.51 [4895]~E(x48951,a77)+E(f319(f319(f74(a1),x48951),x48951),a77)
% 28.73/28.51 [4906]E(x49061,f2(a1))+E(f319(f319(f30(a1),x49061),x49061),f72(a1))
% 28.73/28.51 [5040]E(x50401,a77)+~E(f319(f319(f74(a1),x50401),x50401),a77)
% 28.73/28.51 [5041]E(a77,x50411)+~E(f319(f319(f74(a1),x50411),x50411),a77)
% 28.73/28.51 [5043]~P99(x50431)+E(f319(f94(x50431),f319(f95(a1),a89)),f319(f95(x50431),a89))
% 28.73/28.51 [5053]~P6(x50531)+E(f32(x50531,f234(f932(x50531,a923))),f180(x50531))
% 28.73/28.51 [5054]~P6(x50541)+E(f32(x50541,f180(f932(x50541,a923))),f234(x50541))
% 28.73/28.51 [5055]~P6(x50551)+E(f31(x50551,f234(f932(x50551,a923))),f234(x50551))
% 28.73/28.51 [5056]~P6(x50561)+E(f31(x50561,f180(f932(x50561,a923))),f180(x50561))
% 28.73/28.51 [5057]~P4(x50571)+E(f131(x50571,f180(f932(x50571,a923))),f105(x50571))
% 28.73/28.51 [5199]E(x51991,f2(a925))+P1(f319(f319(f227(a925),f2(a925)),x51991))
% 28.73/28.51 [5200]E(x52001,f2(a925))+P1(f319(f319(f227(a925),f2(a925)),x52001))
% 28.73/28.51 [5219]~P7(x52191)+P1(f319(f319(f226(a1),f2(a1)),x52191))
% 28.73/28.51 [5252]~E(f319(f95(a925),x52521),f2(a925))+P1(f319(f319(f226(a1),x52521),a77))
% 28.73/28.51 [5253]~E(f319(f95(a925),x52531),f2(a925))+P1(f319(f319(f226(a1),x52531),a77))
% 28.73/28.51 [5258]P42(x52581)+P1(f319(f319(f321(a1),f327(x52581)),x52581))
% 28.73/28.51 [5259]E(x52591,f319(a3,f2(a925)))+P1(f319(f319(f226(a91),f72(a91)),x52591))
% 28.73/28.51 [5302]P1(f319(a185,x53021))+P1(f319(f319(f226(a1),f2(a1)),x53021))
% 28.73/28.51 [5356]E(f319(f92(a1),f319(a96,x53561)),f2(a1))+P1(f319(f319(f226(a1),f2(a1)),x53561))
% 28.73/28.51 [5399]~P71(x53991)+P1(f319(f55(x53991),f234(f932(x53991,a923))))
% 28.73/28.51 [5414]E(f319(f92(a1),f319(f95(a925),x54141)),f319(f95(a1),x54141))+P1(f319(a185,f319(f95(a1),x54141)))
% 28.73/28.51 [5417]~E(x54171,f2(a925))+P1(f319(f319(f227(a925),x54171),f319(a104,f2(a925))))
% 28.73/28.51 [5437]E(f319(f95(a925),x54371),f2(a925))+~P1(f319(f319(f226(a1),x54371),a77))
% 28.73/28.51 [5438]E(f319(f95(a925),x54381),f2(a925))+~P1(f319(a185,f319(f95(a1),x54381)))
% 28.73/28.51 [5439]E(f319(f95(a925),x54391),f2(a925))+~P1(f319(f319(f226(a1),x54391),a77))
% 28.73/28.51 [5471]P7(x54711)+~P1(f319(f319(f226(a1),f2(a1)),x54711))
% 28.73/28.51 [5484]~E(x54841,f2(a925))+~P1(f319(f319(f227(a925),f2(a925)),x54841))
% 28.73/28.51 [5539]E(f319(a104,f371(x55391)),x55391)+~P1(f319(f319(f227(a925),f2(a925)),x55391))
% 28.73/28.51 [5548]E(f319(a104,f319(f95(a925),x55481)),f72(a925))+~P1(f319(a185,f319(f95(a1),x55481)))
% 28.73/28.51 [5555]E(f319(f92(a1),f438(x55551)),x55551)+~P1(f319(f319(f227(a1),f2(a1)),x55551))
% 28.73/28.51 [5562]~E(x55621,f319(a3,f2(a925)))+~P1(f319(f319(f226(a91),f72(a91)),x55621))
% 28.73/28.51 [5569]E(f319(f92(a1),f319(f95(a925),x55691)),f2(a1))+~P1(f319(a185,f319(f95(a1),x55691)))
% 28.73/28.51 [5595]E(f319(f157(a925),x55951),f2(a925))+P1(f319(f319(f321(a925),f596(x55951)),f319(f164(a925),x55951)))
% 28.73/28.51 [5614]E(f319(f92(a1),f319(a96,x56141)),x56141)+~P1(f319(f319(f226(a1),f2(a1)),x56141))
% 28.73/28.51 [5615]E(f319(f92(a1),f319(a96,x56151)),x56151)+~P1(f319(f319(f226(a1),f2(a1)),x56151))
% 28.73/28.51 [5623]~P1(f319(a185,x56231))+~P1(f319(f319(f226(a1),f2(a1)),x56231))
% 28.73/28.51 [5723]E(f319(f319(f74(a925),f72(a925)),f319(f95(a925),x57231)),f72(a925))+~P1(f319(f319(f227(a1),x57231),a77))
% 28.73/28.51 [5787]E(x57871,f2(a925))+~P1(f319(f319(f227(a925),x57871),f319(a104,f2(a925))))
% 28.73/28.51 [5826]E(f319(f319(f23(a925),f319(f95(a925),x58261)),f72(a925)),f2(a925))+~P1(f319(f319(f226(a1),x58261),a77))
% 28.73/28.51 [5827]E(f319(f319(f74(a925),f319(f95(a925),x58271)),f72(a925)),f72(a925))+~P1(f319(f319(f227(a1),x58271),a77))
% 28.73/28.51 [5839]~P42(x58391)+E(f319(f29(a925),f319(f302(a1,a925,a96),x58391)),f319(f29(a1),x58391))
% 28.73/28.51 [5869]~P4(x58691)+E(f228(x58691,f319(f7(x58691,x58691,a923),f226(x58691))),f225(x58691))
% 28.73/28.51 [5870]~P4(x58701)+E(f229(x58701,f319(f7(x58701,x58701,a923),f226(x58701))),f224(x58701))
% 28.73/28.51 [5880]E(f39(a925,f319(a104,f2(a925)),f319(f95(a925),x58801)),f319(a104,f2(a925)))+~P1(f319(a185,f319(f95(a1),x58801)))
% 28.73/28.51 [5889]~P1(f319(f319(f227(a1),f2(a1)),x58891))+P1(f319(f319(f226(a1),f72(a1)),x58891))
% 28.73/28.51 [5890]P1(f319(f319(f227(a1),f2(a1)),x58901))+~P1(f319(f319(f226(a1),f72(a1)),x58901))
% 28.73/28.51 [5900]E(f319(a104,f319(f319(f23(a925),x59001),f72(a925))),x59001)+~P1(f319(f319(f227(a925),f2(a925)),x59001))
% 28.73/28.51 [5901]E(f319(a104,f319(f319(f23(a925),x59011),f72(a925))),x59011)+~P1(f319(f319(f227(a925),f2(a925)),x59011))
% 28.73/28.51 [5957]P1(f319(f319(f227(a925),f2(a925)),f438(x59571)))+~P1(f319(f319(f227(a1),f2(a1)),x59571))
% 28.73/28.51 [6018]E(f39(a1,f319(f95(a1),a89),x60181),f319(f319(f23(a1),x60181),f72(a1)))+~P1(f319(f319(f227(a1),f2(a1)),x60181))
% 28.73/28.51 [6056]~P1(f319(f319(f227(a1),a77),x60561))+P1(f319(f319(f227(a925),f2(a925)),f319(f95(a925),x60561)))
% 28.73/28.51 [6061]E(f319(a20,f833(x60611)),x60611)+~P1(f319(f319(f321(a925),x60611),f234(f932(a925,a923))))
% 28.73/28.51 [6115]P1(f319(f319(f227(a925),f2(a925)),f319(a96,x61151)))+~P1(f319(f319(f227(a1),f2(a1)),x61151))
% 28.73/28.51 [6134]E(f319(a20,f319(a3,x61341)),x61341)+~P1(f319(f319(f321(a925),x61341),f234(f932(a925,a923))))
% 28.73/28.51 [6165]~P1(f319(f319(f227(a925),f2(a925)),x61651))+P1(f319(f319(f227(a1),f2(a1)),f319(f92(a1),x61651)))
% 28.73/28.51 [6201]~P1(f319(f319(f227(a925),f2(a925)),f319(a96,x62011)))+P1(f319(f319(f227(a1),f2(a1)),x62011))
% 28.73/28.51 [6219]~P42(x62191)+E(f319(f302(a925,a1,f92(a1)),f319(f302(a1,a925,a96),x62191)),x62191)
% 28.73/28.51 [6232]P1(f319(f319(f227(a1),a77),x62321))+~P1(f319(f319(f227(a925),f2(a925)),f319(f95(a925),x62321)))
% 28.73/28.51 [6287]P1(f319(f319(f227(a925),f2(a925)),x62871))+~P1(f319(f319(f227(a1),f2(a1)),f319(f92(a1),x62871)))
% 28.73/28.51 [6322]E(f171(x63221,f105(f926(x63221))),f105(f926(x63221)))+~P1(f319(f307(f926(f926(x63221)),f172(x63221)),f105(f926(x63221))))
% 28.73/28.51 [6400]E(f319(f302(a925,a1,f92(a1)),f319(f274(a925),f319(a96,x64001))),f319(f294(a1,f2(a1)),x64001))+~P1(f319(f319(f226(a1),f2(a1)),x64001))
% 28.73/28.51 [6417]~P129(x64171)+P1(f319(f319(f227(x64171),f2(x64171)),f319(f319(f74(x64171),f72(x64171)),f72(x64171))))
% 28.73/28.51 [6466]P1(f319(f319(f227(a925),f319(a104,f2(a925))),f319(a96,x64661)))+~P1(f319(f319(f227(a1),f72(a1)),x64661))
% 28.73/28.51 [6565]E(x65651,f2(a1))+P1(f319(f43(f2(a1),x65651),f319(f319(f244(a1,a1),f2(a1)),f2(a1))))
% 28.73/28.51 [6736]~P1(f319(f319(f227(a925),f319(a104,f2(a925))),f319(a96,x67361)))+P1(f319(f319(f227(a1),f72(a1)),x67361))
% 28.73/28.51 [6784]E(f319(a104,f319(f319(f23(a925),f319(f95(a925),x67841)),f72(a925))),f319(f95(a925),x67841))+~P1(f319(f319(f227(a925),f2(a925)),f319(f95(a925),x67841)))
% 28.73/28.51 [7170]~P114(x71701)+P38(x71701,f319(f254(f931(x71701,x71701)),f319(f249(x71701,x71701,a923),f227(x71701))))
% 28.73/28.51 [5774]E(f319(f95(a925),f319(f319(f23(a1),x57741),a89)),f319(a104,f319(f95(a925),x57741)))+P1(f319(a185,f319(f95(a1),x57741)))
% 28.73/28.51 [5790]~P37(x57901)+E(f319(f319(f146(a925,a1),f92(a1)),f319(f319(f146(a1,a925),a96),x57901)),x57901)
% 28.73/28.51 [5907]E(f319(f73(a1),f319(f92(a1),f319(a104,f439(x59071)))),x59071)+~P1(f319(f319(f227(a1),x59071),f2(a1)))
% 28.73/28.51 [5917]E(f319(f319(f74(a925),f72(a925)),f319(f95(a925),x59171)),f319(f95(a925),f319(f319(f23(a1),x59171),a89)))+P1(f319(f319(f227(a1),x59171),a77))
% 28.73/28.51 [5959]E(f319(f319(f30(a1),f319(f95(a1),a89)),x59591),f319(f95(a1),a89))+~P1(f319(f319(f227(a1),f2(a1)),x59591))
% 28.73/28.51 [6052]E(f319(f319(f23(a925),f319(f95(a925),x60521)),f72(a925)),f319(f95(a925),f319(f319(f74(a1),x60521),a89)))+P1(f319(f319(f226(a1),x60521),a77))
% 28.73/28.51 [6053]E(f319(f319(f74(a925),f319(f95(a925),x60531)),f72(a925)),f319(f95(a925),f319(f319(f23(a1),x60531),a89)))+P1(f319(f319(f227(a1),x60531),a77))
% 28.73/28.51 [6100]E(f319(a96,f319(f319(f74(a1),f72(a1)),x61001)),f319(a104,f319(a96,x61001)))+~P1(f319(f319(f226(a1),f2(a1)),x61001))
% 28.73/28.51 [6136]E(f319(a104,f319(f319(f23(a925),x61361),f319(a104,f2(a925)))),x61361)+~P1(f319(f319(f227(a925),f2(a925)),x61361))
% 28.73/28.51 [6351]E(f39(a925,f319(a104,f2(a925)),f319(f95(a925),x63511)),f319(a96,f39(a1,f72(a1),f319(f95(a1),x63511))))+P1(f319(a185,f319(f95(a1),x63511)))
% 28.73/28.51 [6393]~P1(f319(f319(f226(a1),a77),x63931))+P1(f319(f319(f226(a1),a77),f319(f319(f74(a1),x63931),x63931)))
% 28.73/28.51 [6394]~P1(f319(f319(f227(a1),a89),x63941))+P1(f319(f319(f226(a1),a89),f319(f319(f74(a1),x63941),x63941)))
% 28.73/28.51 [6395]~P1(f319(f319(f227(a1),a77),x63951))+P1(f319(f319(f227(a1),a77),f319(f319(f74(a1),x63951),x63951)))
% 28.73/28.51 [6396]~P1(f319(f319(f227(a1),a89),x63961))+P1(f319(f319(f227(a1),a89),f319(f319(f74(a1),x63961),x63961)))
% 28.73/28.51 [6578]~P1(f319(f55(x65781),f234(f932(x65781,a923))))+P1(f319(f55(f929(x65781)),f234(f932(f929(x65781),a923))))
% 28.73/28.51 [6666]~P1(f319(f319(f226(a1),f2(a1)),x66661))+P1(f319(f319(f227(a1),f2(a1)),f319(f319(f74(a1),f72(a1)),x66661)))
% 28.73/28.51 [6673]E(f319(f243(a1,a1),f41(f72(a1),f319(f95(a1),x66731))),f319(f319(f30(a1),f72(a1)),f319(f95(a1),x66731)))+~P1(f319(f319(f226(a1),f2(a1)),f319(f95(a1),x66731)))
% 28.73/28.51 [6695]E(f319(f248(a1,a1),f41(f72(a1),f319(f95(a1),x66951))),f39(a1,f72(a1),f319(f95(a1),x66951)))+~P1(f319(f319(f226(a1),f2(a1)),f319(f95(a1),x66951)))
% 28.73/28.51 [6707]P1(f319(f55(x67071),f234(f932(x67071,a923))))+~P1(f319(f55(f929(x67071)),f234(f932(f929(x67071),a923))))
% 28.73/28.51 [6737]P1(f319(f319(f226(a1),a77),x67371))+~P1(f319(f319(f226(a1),a77),f319(f319(f74(a1),x67371),x67371)))
% 28.73/28.51 [6738]P1(f319(f319(f227(a1),a77),x67381))+~P1(f319(f319(f227(a1),a77),f319(f319(f74(a1),x67381),x67381)))
% 28.73/28.51 [6739]P1(f319(f319(f227(a1),a89),x67391))+~P1(f319(f319(f226(a1),a89),f319(f319(f74(a1),x67391),x67391)))
% 28.73/28.51 [6740]P1(f319(f319(f227(a1),a89),x67401))+~P1(f319(f319(f227(a1),a89),f319(f319(f74(a1),x67401),x67401)))
% 28.73/28.51 [6936]~P1(f319(f55(a925),x69361))+P1(f319(f55(a1),f319(f302(a925,a1,f92(a1)),x69361)))
% 28.73/28.51 [7062]~P1(f319(f55(x70621),f234(f932(x70621,a923))))+P1(f319(f319(f227(a925),f2(a925)),f319(f29(x70621),f234(f932(x70621,a923)))))
% 28.73/28.51 [7650]P1(f319(f55(a925),x76501))+~P1(f319(f55(a1),f319(f302(a925,a1,f92(a1)),x76501)))
% 28.73/28.51 [5698]~E(a89,x56981)+E(f319(f319(f23(a1),f319(f319(f74(a1),x56981),x56981)),a89),a89)
% 28.73/28.51 [5699]~E(x56991,a89)+E(f319(f319(f23(a1),f319(f319(f74(a1),x56991),x56991)),a89),a89)
% 28.73/28.51 [6227]E(x62271,a89)+~E(f319(f319(f23(a1),f319(f319(f74(a1),x62271),x62271)),a89),a89)
% 28.73/28.51 [6228]E(a89,x62281)+~E(f319(f319(f23(a1),f319(f319(f74(a1),x62281),x62281)),a89),a89)
% 28.73/28.51 [6634]~E(f319(f95(a925),x66341),f2(a925))+P1(f319(a185,f319(f95(a1),f319(f319(f74(a1),x66341),a89))))
% 28.73/28.51 [6990]~P1(f319(a185,f319(f95(a1),x69901)))+P1(f319(a185,f319(f95(a1),f319(f319(f74(a1),x69901),x69901))))
% 28.73/28.51 [6991]~P1(f319(f319(f226(a1),x69911),a77))+P1(f319(f319(f226(a1),f319(f319(f74(a1),x69911),x69911)),a77))
% 28.73/28.51 [6992]~P1(f319(f319(f226(a1),x69921),a89))+P1(f319(f319(f226(a1),f319(f319(f74(a1),x69921),x69921)),a89))
% 28.73/28.51 [6993]~P1(f319(f319(f227(a1),x69931),a77))+P1(f319(f319(f227(a1),f319(f319(f74(a1),x69931),x69931)),a77))
% 28.73/28.51 [6994]~P1(f319(f319(f226(a1),x69941),a89))+P1(f319(f319(f227(a1),f319(f319(f74(a1),x69941),x69941)),a89))
% 28.73/28.51 [7316]E(f319(f95(a925),x73161),f2(a925))+~P1(f319(a185,f319(f95(a1),f319(f319(f74(a1),x73161),a89))))
% 28.73/28.51 [7567]~P1(f319(f319(f226(a1),f2(a1)),f319(f95(a1),x75671)))+P1(f319(f319(f226(a1),f2(a1)),f319(f95(a1),f319(f319(f74(a1),x75671),x75671))))
% 28.73/28.51 [7568]P1(f319(a185,f319(f95(a1),x75681)))+~P1(f319(a185,f319(f95(a1),f319(f319(f74(a1),x75681),x75681))))
% 28.73/28.51 [7569]P1(f319(f319(f226(a1),x75691),a77))+~P1(f319(f319(f226(a1),f319(f319(f74(a1),x75691),x75691)),a77))
% 28.73/28.51 [7570]P1(f319(f319(f226(a1),x75701),a89))+~P1(f319(f319(f226(a1),f319(f319(f74(a1),x75701),x75701)),a89))
% 28.73/28.51 [7571]P1(f319(f319(f226(a1),x75711),a89))+~P1(f319(f319(f227(a1),f319(f319(f74(a1),x75711),x75711)),a89))
% 28.73/28.51 [7572]P1(f319(f319(f227(a1),x75721),a77))+~P1(f319(f319(f227(a1),f319(f319(f74(a1),x75721),x75721)),a77))
% 28.73/28.51 [7928]E(f319(a99,f589(x79281)),x79281)+~P1(f319(f319(f321(f932(f931(a925,a925),a923)),x79281),a90))
% 28.73/28.51 [6550]~P99(x65501)+E(f319(f95(x65501),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f72(x65501))
% 28.73/28.51 [6551]~P99(x65511)+E(f319(f95(x65511),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f72(x65511))
% 28.73/28.51 [7040]~P1(f319(a185,f319(f95(a1),x70401)))+E(f319(f95(a925),f319(f319(f23(a1),f319(f319(f74(a1),x70401),x70401)),a89)),f2(a925))
% 28.73/28.51 [8104]~P1(f319(f319(f227(a1),f319(f95(a1),x81041)),f2(a1)))+E(f319(f243(a1,a1),f319(a45,f44(f319(f73(a1),f72(a1)),f319(f73(a1),f319(f95(a1),x81041))))),f319(f319(f30(a1),f72(a1)),f319(f95(a1),x81041)))
% 28.73/28.51 [8117]~P1(f319(f319(f227(a1),f319(f95(a1),x81171)),f2(a1)))+E(f319(f248(a1,a1),f319(a45,f44(f319(f73(a1),f72(a1)),f319(f73(a1),f319(f95(a1),x81171))))),f39(a1,f72(a1),f319(f95(a1),x81171)))
% 28.73/28.51 [8167]~P1(f319(f319(f226(a1),a77),x81671))+P1(f319(f319(f226(a1),a77),f319(f319(f23(a1),f319(f319(f74(a1),x81671),x81671)),a89)))
% 28.73/28.51 [8168]~P1(f319(f319(f226(a1),a89),x81681))+P1(f319(f319(f226(a1),a89),f319(f319(f23(a1),f319(f319(f74(a1),x81681),x81681)),a89)))
% 28.73/28.51 [8169]~P1(f319(f319(f226(a1),a77),x81691))+P1(f319(f319(f227(a1),a77),f319(f319(f23(a1),f319(f319(f74(a1),x81691),x81691)),a89)))
% 28.73/28.51 [8170]~P1(f319(f319(f227(a1),a89),x81701))+P1(f319(f319(f227(a1),a89),f319(f319(f23(a1),f319(f319(f74(a1),x81701),x81701)),a89)))
% 28.73/28.51 [8470]~P99(x84701)+~P29(x84701,f319(f95(x84701),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))
% 28.73/28.51 [8654]P1(f319(f319(f226(a1),a77),x86541))+~P1(f319(f319(f226(a1),a77),f319(f319(f23(a1),f319(f319(f74(a1),x86541),x86541)),a89)))
% 28.73/28.51 [8655]P1(f319(f319(f226(a1),a77),x86551))+~P1(f319(f319(f227(a1),a77),f319(f319(f23(a1),f319(f319(f74(a1),x86551),x86551)),a89)))
% 28.73/28.51 [8656]P1(f319(f319(f226(a1),a89),x86561))+~P1(f319(f319(f226(a1),a89),f319(f319(f23(a1),f319(f319(f74(a1),x86561),x86561)),a89)))
% 28.73/28.51 [8657]P1(f319(f319(f227(a1),a89),x86571))+~P1(f319(f319(f227(a1),a89),f319(f319(f23(a1),f319(f319(f74(a1),x86571),x86571)),a89)))
% 28.73/28.51 [8981]E(f319(f95(a925),f319(f319(f23(a1),f319(f319(f74(a1),x89811),x89811)),a89)),f319(f319(f80(a925,a925),f319(f95(a925),x89811)),f319(f319(f8(a925,a925,a925),a104),f319(f319(f18(a925,a925,a925),f74(a925)),f5(a925)))))+P1(f319(a185,f319(f95(a1),x89811)))
% 28.73/28.52 [9853]E(x98531,f180(f932(f931(a925,a925),a923)))+P1(f319(f319(f321(f931(f932(f931(a925,a925),a923),f932(f931(a925,a925),a923))),f319(f319(f244(f932(f931(a925,a925),a923),f932(f931(a925,a925),a923)),x98531),f180(f932(f931(a925,a925),a923)))),a27))
% 28.73/28.52 [8908]~P1(f319(a185,f319(f95(a1),x89081)))+P1(f319(a185,f319(f95(a1),f319(f319(f23(a1),f319(f319(f74(a1),x89081),x89081)),a89))))
% 28.73/28.52 [8909]~P1(f319(f319(f227(a1),x89091),a77))+P1(f319(f319(f226(a1),f319(f319(f23(a1),f319(f319(f74(a1),x89091),x89091)),a89)),a77))
% 28.73/28.52 [8910]~P1(f319(f319(f226(a1),x89101),a89))+P1(f319(f319(f226(a1),f319(f319(f23(a1),f319(f319(f74(a1),x89101),x89101)),a89)),a89))
% 28.73/28.52 [8911]~P1(f319(f319(f227(a1),x89111),a77))+P1(f319(f319(f227(a1),f319(f319(f23(a1),f319(f319(f74(a1),x89111),x89111)),a89)),a77))
% 28.73/28.52 [8912]~P1(f319(f319(f227(a1),x89121),a89))+P1(f319(f319(f227(a1),f319(f319(f23(a1),f319(f319(f74(a1),x89121),x89121)),a89)),a89))
% 28.73/28.52 [9023]~P1(f319(f319(f226(a1),f2(a1)),f319(f95(a1),x90231)))+P1(f319(f319(f226(a1),f2(a1)),f319(f95(a1),f319(f319(f23(a1),f319(f319(f74(a1),x90231),x90231)),a89))))
% 28.73/28.52 [9186]~P99(x91861)+E(f319(f319(f74(x91861),f72(x91861)),f72(x91861)),f319(f95(x91861),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))))
% 28.73/28.52 [9342]P1(f319(a185,f319(f95(a1),x93421)))+~P1(f319(a185,f319(f95(a1),f319(f319(f23(a1),f319(f319(f74(a1),x93421),x93421)),a89))))
% 28.73/28.52 [9343]P1(f319(f319(f226(a1),x93431),a89))+~P1(f319(f319(f226(a1),f319(f319(f23(a1),f319(f319(f74(a1),x93431),x93431)),a89)),a89))
% 28.73/28.52 [9344]P1(f319(f319(f227(a1),x93441),a77))+~P1(f319(f319(f226(a1),f319(f319(f23(a1),f319(f319(f74(a1),x93441),x93441)),a89)),a77))
% 28.73/28.52 [9345]P1(f319(f319(f227(a1),x93451),a77))+~P1(f319(f319(f227(a1),f319(f319(f23(a1),f319(f319(f74(a1),x93451),x93451)),a89)),a77))
% 28.73/28.52 [9346]P1(f319(f319(f227(a1),x93461),a89))+~P1(f319(f319(f227(a1),f319(f319(f23(a1),f319(f319(f74(a1),x93461),x93461)),a89)),a89))
% 28.73/28.52 [9898]~P1(f319(f55(f931(a925,a925)),x98981))+P1(f319(f319(f321(f931(f932(f931(a925,a925),a923),f932(f931(a925,a925),a923))),f319(f319(f244(f932(f931(a925,a925),a923),f932(f931(a925,a925),a923)),f180(f932(f931(a925,a925),a923))),x98981)),a63))
% 28.73/28.52 [9679]~P149(x96791)+E(f319(f319(f236(x96791),f72(x96791)),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),f72(x96791))
% 28.73/28.52 [9680]~P149(x96801)+E(f319(f319(f236(x96801),f2(x96801)),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),f2(x96801))
% 28.73/28.52 [10142]~P1(f319(f319(f227(a925),f72(a925)),x101421))+P1(f319(f319(f227(a925),f2(a925)),f319(f319(f30(a925),x101421),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))))))
% 28.73/28.52 [10148]~P1(f319(f319(f227(a925),f2(a925)),x101481))+P1(f319(f319(f227(a925),f2(a925)),f319(f319(f30(a925),f319(f319(f74(a925),x101481),f72(a925))),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))))))
% 28.73/28.52 [10186]~E(f39(a925,x101861,f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),f72(a925))+P1(f319(f319(f227(a925),f2(a925)),f39(a925,x101861,f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))))))
% 28.73/28.52 [10218]E(f39(a925,x102181,f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),f72(a925))+~P1(f319(f319(f227(a925),f2(a925)),f39(a925,x102181,f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))))))
% 28.73/28.52 [4825]~P8(x48251,x48252)+P50(x48251,x48252)
% 28.73/28.52 [4826]~P8(x48261,x48262)+P50(x48261,x48262)
% 28.73/28.52 [4827]~P38(x48271,x48272)+P62(x48271,x48272)
% 28.73/28.52 [4828]~P45(x48281,x48282)+P62(x48281,x48282)
% 28.73/28.52 [4829]~P8(x48291,x48292)+P54(x48291,x48292)
% 28.73/28.52 [4830]~P8(x48301,x48302)+P54(x48301,x48302)
% 28.73/28.52 [4831]~P17(x48311,x48312)+P54(x48311,x48312)
% 28.73/28.52 [4832]~P17(x48321,x48322)+P54(x48321,x48322)
% 28.73/28.52 [4833]~P8(x48331,x48332)+P55(x48331,x48332)
% 28.73/28.52 [4834]~P8(x48341,x48342)+P55(x48341,x48342)
% 28.73/28.52 [4835]~P17(x48351,x48352)+P55(x48351,x48352)
% 28.73/28.52 [4836]~P17(x48361,x48362)+P55(x48361,x48362)
% 28.73/28.52 [4837]~P8(x48371,x48372)+P17(x48371,x48372)
% 28.73/28.52 [4787]~E(x47871,x47872)+E(f261(x47871,x47872),f72(a91))
% 28.73/28.52 [4790]E(f208(x47901,x47902),x47901)+~E(x47902,f2(a925))
% 28.73/28.52 [4796]~E(x47962,f105(x47961))+E(f144(x47961,x47962),f105(x47961))
% 28.73/28.52 [4797]~E(x47972,f105(x47971))+E(f144(x47971,x47972),f105(x47971))
% 28.73/28.52 [4815]~E(f144(x48152,x48151),f105(x48152))+E(x48151,f105(x48152))
% 28.73/28.52 [4816]~E(f144(x48162,x48161),f105(x48162))+E(x48161,f105(x48162))
% 28.73/28.52 [4841]~P2(x48412)+P2(f932(x48411,x48412))
% 28.73/28.52 [4842]~P3(x48422)+P3(f932(x48421,x48422))
% 28.73/28.52 [4843]~P113(x48432)+P113(f932(x48431,x48432))
% 28.73/28.52 [4844]~P6(x48442)+P6(f932(x48441,x48442))
% 28.73/28.52 [4845]~P67(x48452)+P67(f932(x48451,x48452))
% 28.73/28.52 [4846]~P96(x48462)+P96(f932(x48461,x48462))
% 28.73/28.52 [4847]~P102(x48472)+P102(f932(x48471,x48472))
% 28.73/28.52 [4848]~P102(x48482)+P107(f932(x48481,x48482))
% 28.73/28.52 [4849]~P102(x48492)+P108(f932(x48491,x48492))
% 28.73/28.52 [4850]~P105(x48502)+P103(f932(x48501,x48502))
% 28.73/28.52 [4851]~P115(x48512)+P115(f932(x48511,x48512))
% 28.73/28.52 [4852]~P106(x48522)+P106(f932(x48521,x48522))
% 28.73/28.52 [4853]~P109(x48532)+P109(f932(x48531,x48532))
% 28.73/28.52 [4854]~P105(x48542)+P104(f932(x48541,x48542))
% 28.73/28.52 [4855]~P83(x48552)+P83(f932(x48551,x48552))
% 28.73/28.52 [4856]~P105(x48562)+P105(f932(x48561,x48562))
% 28.73/28.52 [4868]E(x48681,x48682)+~E(f319(a104,x48681),f319(a104,x48682))
% 28.73/28.52 [4869]E(x48691,x48692)+~E(f319(a104,x48691),f319(a104,x48692))
% 28.73/28.52 [4870]E(x48701,x48702)+~E(f319(a99,x48701),f319(a99,x48702))
% 28.73/28.52 [4871]E(x48711,x48712)+~E(f319(a3,x48711),f319(a3,x48712))
% 28.73/28.52 [4872]E(x48721,x48722)+~E(f319(a20,x48721),f319(a20,x48722))
% 28.73/28.52 [4873]E(x48731,x48732)+~E(f319(a20,x48731),f319(a20,x48732))
% 28.73/28.52 [4922]P40(x49221,x49222)+~E(f727(x49222,x49221),f728(x49222,x49221))
% 28.73/28.52 [4952]~P62(x49521,x49522)+P40(x49521,f299(x49521,x49522))
% 28.73/28.52 [4953]~P56(x49531,x49532)+P56(x49531,f299(x49531,x49532))
% 28.73/28.52 [4966]~P65(x49661)+E(f39(x49661,x49662,x49662),f2(x49661))
% 28.73/28.52 [5000]~P38(x50001,x50002)+P38(f926(x50001),f138(x50001,x50002))
% 28.73/28.52 [5001]~P38(x50011,x50012)+P38(f926(x50011),f137(x50011,x50012))
% 28.73/28.52 [5002]~P39(x50021,x50022)+P39(f926(x50021),f139(x50021,x50022))
% 28.73/28.52 [5003]~P39(x50031,x50032)+P39(f926(x50031),f150(x50031,x50032))
% 28.73/28.52 [5004]~P56(x50041,x50042)+P56(f926(x50041),f150(x50041,x50042))
% 28.73/28.52 [5101]~P38(x51011,x51012)+P38(f932(x51011,a923),f310(x51011,x51012))
% 28.73/28.52 [5102]~P38(x51021,x51022)+P38(f932(x51021,a923),f311(x51021,x51022))
% 28.73/28.52 [5228]~P7(x52281)+P42(f295(a1,x52281,x52282))
% 28.73/28.52 [5334]~P38(x53341,x53342)+P64(x53341,f61(x53341,x53341,x53342))
% 28.73/28.52 [5833]~P68(x58331)+P26(x58331,x58331,f73(x58331),x58332)
% 28.73/28.52 [4810]~E(x48102,f105(x48101))+E(f319(f160(x48101),x48102),f105(x48101))
% 28.73/28.52 [4811]~E(x48112,f105(x48111))+E(f319(f159(x48111),x48112),f105(x48111))
% 28.73/28.52 [4812]~E(x48122,f105(x48121))+E(f319(f160(x48121),x48122),f105(x48121))
% 28.73/28.52 [4875]E(x48751,f319(a96,x48752))+~E(f319(f92(a1),x48751),x48752)
% 28.73/28.52 [4877]E(x48771,f105(x48772))+~E(f319(f160(x48772),x48771),f105(x48772))
% 28.73/28.52 [4878]E(x48781,f105(x48782))+~E(f319(f159(x48782),x48781),f105(x48782))
% 28.73/28.52 [4879]E(x48791,f105(x48792))+~E(f319(f160(x48792),x48791),f105(x48792))
% 28.73/28.52 [4891]~P99(x48911)+E(f319(f95(x48911),x48912),f319(f94(x48911),x48912))
% 28.73/28.52 [4898]~P71(x48981)+P1(f319(f55(x48981),x48982))
% 28.73/28.52 [4899]~P71(x48991)+P1(f319(f55(x48991),x48992))
% 28.73/28.52 [4907]~E(f687(x49072,x49071),f105(x49071))+E(f171(x49071,x49072),f105(f926(x49071)))
% 28.73/28.52 [4916]~E(x49162,f105(x49161))+E(f319(f164(x49161),x49162),f180(f932(x49161,a923)))
% 28.73/28.52 [4917]~E(x49172,f105(x49171))+E(f180(f932(x49171,a923)),f319(f164(x49171),x49172))
% 28.73/28.52 [4918]E(x49181,x49182)+~E(f319(f92(a1),x49181),f319(f92(a1),x49182))
% 28.73/28.52 [4919]E(x49191,x49192)+~E(f319(f92(a1),x49191),f319(f92(a1),x49192))
% 28.73/28.52 [4923]E(f206(x49231,x49232),f2(a925))+P1(f319(f55(x49231),x49232))
% 28.73/28.52 [4941]~P126(x49411)+E(f76(x49411,f76(x49411,x49412)),f76(x49411,x49412))
% 28.73/28.52 [4955]~P87(x49551)+E(f319(f319(f236(x49551),x49552),f72(a925)),x49552)
% 28.73/28.52 [4956]~P121(x49561)+E(f319(f319(f236(x49561),x49562),f72(a925)),x49562)
% 28.73/28.52 [4957]~P56(x49571,x49572)+E(f319(f278(x49571,x49571),x49572),x49572)
% 28.73/28.52 [4961]E(x49611,x49612)+E(f261(x49611,x49612),f319(f319(f74(a91),x49612),f72(a91)))
% 28.73/28.52 [4962]E(f319(f29(x49621),x49622),f2(a925))+P1(f319(f55(x49621),x49622))
% 28.73/28.52 [4963]E(f319(f29(x49631),x49632),f2(a925))+P1(f319(f55(x49631),x49632))
% 28.73/28.52 [4964]E(f319(f29(x49641),x49642),f2(a925))+P1(f319(f55(x49641),x49642))
% 28.73/28.52 [4967]~E(f144(x49671,x49672),x49672)+P1(f319(f129(x49671),x49672))
% 28.73/28.52 [4970]~P104(x49701)+E(f319(f319(f102(x49701),x49702),f180(x49701)),x49702)
% 28.73/28.52 [4971]~P103(x49711)+E(f319(f319(f93(x49711),x49712),f234(x49711)),x49712)
% 28.73/28.52 [4972]~P69(x49721)+E(f319(f319(f23(x49721),x49722),f2(x49721)),x49722)
% 28.73/28.52 [4973]~P78(x49731)+E(f319(f319(f75(x49731),x49732),f72(x49731)),x49732)
% 28.73/28.52 [4974]~P87(x49741)+E(f319(f319(f75(x49741),x49742),f72(x49741)),x49742)
% 28.73/28.52 [4975]~P121(x49751)+E(f319(f319(f75(x49751),x49752),f72(x49751)),x49752)
% 28.73/28.52 [4976]~P79(x49761)+E(f319(f319(f74(x49761),x49762),f2(x49761)),x49762)
% 28.73/28.52 [4977]~P121(x49771)+E(f319(f319(f74(x49771),x49772),f2(x49771)),x49772)
% 28.73/28.52 [4978]~P88(x49781)+E(f319(f319(f74(x49781),x49782),f2(x49781)),x49782)
% 28.73/28.52 [4979]~P124(x49791)+E(f319(f319(f283(x49791),x49792),f72(x49791)),x49792)
% 28.73/28.52 [4980]~P65(x49801)+E(f319(f319(f30(x49801),x49802),f72(x49801)),x49802)
% 28.73/28.52 [4981]~P121(x49811)+E(f319(f319(f236(x49811),x49812),f2(a925)),f72(x49811))
% 28.73/28.52 [4982]~P119(x49821)+E(f319(f319(f236(x49821),x49822),f2(a925)),f72(x49821))
% 28.73/28.52 [4983]~E(x49832,f180(f932(x49831,a923)))+E(f319(f29(x49831),x49832),f2(a925))
% 28.73/28.52 [4994]~P65(x49941)+E(f39(x49941,x49942,f2(x49941)),x49942)
% 28.73/28.52 [5005]~P103(x50051)+E(f319(f319(f102(x50051),x50052),f234(x50051)),f234(x50051))
% 28.73/28.52 [5006]~P104(x50061)+E(f319(f319(f93(x50061),x50062),f180(x50061)),f180(x50061))
% 28.73/28.52 [5007]~P121(x50071)+E(f319(f319(f75(x50071),x50072),f2(x50071)),f2(x50071))
% 28.73/28.52 [5008]~P133(x50081)+E(f319(f319(f75(x50081),x50082),f2(x50081)),f2(x50081))
% 28.73/28.52 [5009]~P125(x50091)+E(f319(f319(f283(x50091),x50092),f2(x50091)),f2(x50091))
% 28.73/28.52 [5010]~P65(x50101)+E(f319(f319(f30(x50101),x50102),f2(x50101)),f2(x50101))
% 28.73/28.52 [5012]~P65(x50121)+E(f39(x50121,x50122,f72(x50121)),f2(x50121))
% 28.73/28.52 [5013]~P65(x50131)+E(f39(x50131,f2(x50131),x50132),f2(x50131))
% 28.73/28.52 [5042]E(x50421,f2(a925))+E(f49(x50422,x50421,f105(x50422)),f105(f926(x50422)))
% 28.73/28.52 [5065]P56(x50651,x50652)+~E(f319(f278(x50651,x50651),x50652),x50652)
% 28.73/28.52 [5066]P38(x50661,x50662)+~E(f597(x50662,x50661),f180(f932(x50661,a923)))
% 28.73/28.52 [5067]E(x50671,f105(x50672))+~E(f319(f164(x50672),x50671),f180(f932(x50672,a923)))
% 28.73/28.52 [5068]E(x50681,f105(x50682))+~E(f180(f932(x50682,a923)),f319(f164(x50682),x50681))
% 28.73/28.52 [5071]~E(x50711,x50712)+P1(f319(f319(a316,x50711),x50712))
% 28.73/28.52 [5081]P1(x50811)+P1(f319(f319(a322,x50811),x50812))
% 28.73/28.52 [5082]E(x50821,f105(x50822))+E(f319(f319(f156(x50822),x50821),f2(a925)),f319(f133(x50822),x50821))
% 28.73/28.52 [5084]E(f144(x50841,x50842),x50842)+~P1(f319(f129(x50841),x50842))
% 28.73/28.52 [5085]E(f144(x50851,x50852),x50852)+~P1(f319(f129(x50851),x50852))
% 28.73/28.52 [5092]~P1(x50922)+P1(f319(f319(a318,x50921),x50922))
% 28.73/28.52 [5093]~P1(x50931)+P1(f319(f319(a318,x50931),x50932))
% 28.73/28.52 [5094]~P1(x50942)+P1(f319(f319(a322,x50941),x50942))
% 28.73/28.52 [5104]~E(f688(x51042,x51041),f694(x51042,x51041))+P1(f319(f129(x51041),x51042))
% 28.73/28.52 [5111]E(f319(f254(x51111),x51112),f180(f932(x51111,a923)))+P1(f319(x51112,f325(x51112)))
% 28.73/28.52 [5112]E(f180(f932(x51121,a923)),f319(f254(x51121),x51122))+P1(f319(x51122,f326(x51122)))
% 28.73/28.52 [5182]~P126(x51821)+E(f319(f319(f75(x51821),x51822),f76(x51821,x51822)),f319(f69(x51821),x51822))
% 28.73/28.52 [5192]~E(x51921,f2(a1))+E(f40(x51921,x51922),f319(f319(f244(a1,a1),f2(a1)),f2(a1)))
% 28.73/28.52 [5193]~E(x51931,f2(a1))+E(f40(x51931,x51932),f319(f319(f244(a1,a1),f2(a1)),f2(a1)))
% 28.73/28.52 [5224]~P62(x52241,x52242)+P62(x52241,f319(f278(x52241,x52241),x52242))
% 28.73/28.52 [5225]~P39(x52251,x52252)+P39(x52251,f319(f278(x52251,x52251),x52252))
% 28.73/28.52 [5226]~P40(x52261,x52262)+P40(x52261,f319(f278(x52261,x52261),x52262))
% 28.73/28.52 [5227]~P56(x52271,x52272)+P56(x52271,f319(f278(x52271,x52271),x52272))
% 28.73/28.52 [5249]E(x52491,x52492)+~P1(f319(f319(a316,x52491),x52492))
% 28.73/28.52 [5260]P1(x52601)+~P1(f319(f319(a317,x52602),x52601))
% 28.73/28.52 [5261]P1(x52611)+~P1(f319(f319(a317,x52611),x52612))
% 28.73/28.52 [5266]~P115(x52661)+P1(f319(f319(f226(x52661),x52662),f234(x52661)))
% 28.73/28.52 [5267]~P121(x52671)+P1(f319(f319(f279(x52671),x52672),f2(x52671)))
% 28.73/28.52 [5271]E(x52711,x52712)+~E(f319(x52711,f433(x52712,x52711)),f319(x52712,f433(x52712,x52711)))
% 28.73/28.52 [5304]E(x53041,f2(a925))+E(f208(x53041,f39(a925,x53042,x53041)),f208(x53042,x53041))
% 28.73/28.52 [5309]~P4(x53091)+P14(x53091,f319(f319(f143(x53091),x53092),f105(x53091)))
% 28.73/28.52 [5313]E(x53131,f2(a1))+P1(f319(f43(x53132,x53131),f40(x53132,x53131)))
% 28.73/28.52 [5329]~P17(x53292,x53291)+P1(f319(f319(x53291,f820(x53291)),f820(x53291)))
% 28.73/28.52 [5332]~E(x53321,x53322)+P1(f319(f319(f227(a925),x53321),f319(a104,x53322)))
% 28.73/28.52 [5342]~E(x53421,f2(a925))+P1(f319(f319(f227(a925),x53421),f319(a104,x53422)))
% 28.73/28.52 [5355]P1(f319(x53551,x53552))+P1(f319(f319(f226(a1),f2(a1)),f426(x53551)))
% 28.73/28.52 [5419]P62(x54191,x54192)+~P62(x54191,f319(f278(x54191,x54191),x54192))
% 28.73/28.52 [5420]P39(x54201,x54202)+~P39(x54201,f319(f278(x54201,x54201),x54202))
% 28.73/28.52 [5421]P40(x54211,x54212)+~P40(x54211,f319(f278(x54211,x54211),x54212))
% 28.73/28.52 [5422]P56(x54221,x54222)+~P56(x54221,f319(f278(x54221,x54221),x54222))
% 28.73/28.52 [5425]~E(f39(a925,x54252,x54251),f2(a925))+E(f319(f319(f75(a925),x54251),f452(x54251,x54252)),x54252)
% 28.73/28.52 [5426]~E(f39(a1,x54262,x54261),f2(a1))+E(f319(f319(f75(a1),x54261),f453(x54261,x54262)),x54262)
% 28.73/28.52 [5431]~E(x54311,f319(a104,x54312))+P1(f319(f319(f226(a925),x54311),f319(a104,x54312)))
% 28.73/28.52 [5452]~P1(f319(x54521,x54522))+P1(f319(f319(f226(a1),f2(a1)),f425(x54521)))
% 28.73/28.52 [5463]E(f319(f319(f23(a925),f319(a96,x54631)),f319(a96,x54632)),f319(a96,x54631))+~P1(f319(a185,x54632))
% 28.73/28.52 [5486]E(f264(x54861,x54862),f72(a91))+~P1(f319(f319(f226(a91),x54861),f72(a91)))
% 28.73/28.52 [5581]E(f319(f319(f156(x55811),x55812),f688(x55812,x55811)),f319(f319(f156(x55811),x55812),f694(x55812,x55811)))+P1(f319(f129(x55811),x55812))
% 28.73/28.52 [5624]~P1(f319(x56241,f84(x56242,x56241)))+P1(f319(x56241,f608(x56242,x56241)))
% 28.73/28.52 [5688]P64(x56881,x56882)+~P1(f319(f307(x56881,x56882),f576(x56882,x56881)))
% 28.73/28.52 [5830]~P17(x58302,x58301)+P1(f319(f319(x58301,f821(x58301,x58302)),f821(x58301,x58302)))
% 28.73/28.52 [5831]~P17(x58312,x58311)+P1(f319(f319(x58311,f826(x58311,x58312)),f826(x58311,x58312)))
% 28.73/28.52 [5840]~E(f319(a104,f39(a925,x58401,x58402)),x58402)+E(f39(a925,f319(a104,x58401),x58402),f2(a925))
% 28.73/28.52 [5896]P38(x58961,x58962)+P1(f319(f319(f321(x58961),f628(x58962,x58961)),f629(x58962,x58961)))
% 28.73/28.52 [5903]~P145(x59031)+P1(f319(f319(f321(x59031),f319(f92(x59031),x59032)),f101(x59031)))
% 28.73/28.52 [5904]~P149(x59041)+P1(f319(f319(f321(x59041),f319(f92(x59041),x59042)),f178(x59041)))
% 28.73/28.52 [5905]~P145(x59051)+P1(f319(f319(f321(x59051),f319(f94(x59051),x59052)),f101(x59051)))
% 28.73/28.52 [5906]~P99(x59061)+P1(f319(f319(f321(x59061),f319(f95(x59061),x59062)),f101(x59061)))
% 28.73/28.52 [6040]~P39(x60401,x60402)+E(f319(f319(f281(x60401,x60401,x60401),x60402),f299(x60401,x60402)),x60402)
% 28.73/28.52 [6055]E(f319(a104,f39(a925,x60551,x60552)),x60552)+E(f39(a925,f319(a104,x60551),x60552),f319(a104,f39(a925,x60551,x60552)))
% 28.73/28.52 [6478]P38(x64781,x64782)+~P1(f319(f319(f321(x64781),f559(x64782,x64781)),f308(x64781,x64782)))
% 28.73/28.52 [6516]~P129(x65161)+~P1(f319(f319(f227(x65161),f319(f92(x65161),x65162)),f2(x65161)))
% 28.73/28.52 [6517]~P92(x65171)+~P1(f319(f319(f227(x65171),f319(f69(x65171),x65172)),f2(x65171)))
% 28.73/28.52 [6607]P1(f319(f319(f227(a1),x66071),f39(a1,x66072,x66071)))+~P1(f319(f319(f227(a1),x66071),f2(a1)))
% 28.73/28.52 [6608]P1(f319(f319(f227(a1),x66081),f39(a1,x66082,x66081)))+~P1(f319(f319(f227(a1),x66081),f2(a1)))
% 28.73/28.52 [6709]E(f319(f319(f301(a925),f319(a104,x67091)),f295(a925,x67092,x67091)),f295(a925,x67092,f319(a104,x67091)))+~P1(f319(f319(f226(a925),x67092),f319(a104,x67091)))
% 28.73/28.52 [6798]~P4(x67981)+P14(x67981,f142(x67981,x67981,f5(x67981),x67982))
% 28.73/28.52 [6934]E(f319(f159(x69341),x69342),x69342)+~P1(f319(f319(f226(a925),f319(f181(f926(x69341)),x69342)),f72(a925)))
% 28.73/28.52 [6954]~P92(x69541)+P1(f319(f319(f226(x69541),f319(f73(x69541),f319(f69(x69541),x69542))),f2(x69541)))
% 28.73/28.52 [6986]~P38(x69861,x69862)+P38(x69861,f319(f319(f281(x69861,x69861,x69861),x69862),f299(x69861,x69862)))
% 28.73/28.52 [6987]~P56(x69871,x69872)+P56(x69871,f319(f319(f281(x69871,x69871,x69871),x69872),f299(x69871,x69872)))
% 28.73/28.52 [7209]~P1(f319(f319(f227(a1),x72092),f2(a1)))+P1(f319(f319(f226(a1),f39(a1,x72091,x72092)),f2(a1)))
% 28.73/28.52 [7210]~P1(f319(f319(f227(a1),x72102),f2(a1)))+P1(f319(f319(f226(a1),f39(a1,x72101,x72102)),f2(a1)))
% 28.73/28.52 [7608]~P149(x76081)+E(f182(x76081,f319(f319(f7(x76081,x76081,x76081),f74(x76081)),f72(x76081)),x76082,f2(x76081)),f319(f92(x76081),x76082))
% 28.73/28.52 [7636]~P131(x76361)+~P1(f319(f319(f227(x76361),f319(f319(f75(x76361),x76362),x76362)),f2(x76361)))
% 28.73/28.52 [10312]~P126(x103121)+~P1(f319(f319(f227(x103121),f319(f319(f236(x103121),x103122),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))))),f2(x103121)))
% 28.73/28.52 [4876]~E(x48762,f105(x48761))+E(f319(f181(f926(x48761)),x48762),f2(a925))
% 28.73/28.52 [4908]~E(x49081,f2(a925))+E(f319(f319(f74(a925),x49081),x49082),x49082)
% 28.73/28.52 [4909]~E(x49092,f2(a925))+E(f319(f319(f75(a925),x49091),x49092),f2(a925))
% 28.73/28.52 [4910]~E(x49101,f2(a925))+E(f319(f319(f75(a925),x49101),x49102),f2(a925))
% 28.73/28.52 [4911]~E(x49111,f2(a925))+E(f319(f319(f75(a925),x49111),x49112),f2(a925))
% 28.73/28.52 [4912]~E(x49122,f2(a925))+E(f319(f319(f236(a925),x49121),x49122),f72(a925))
% 28.73/28.52 [4913]~E(x49132,f2(a1))+E(f319(f319(f30(a1),x49131),x49132),f2(a1))
% 28.73/28.52 [4924]E(x49241,f105(x49242))+~E(f319(f181(f926(x49242)),x49241),f2(a925))
% 28.73/28.52 [4925]~P102(x49251)+E(f319(f319(f102(x49251),x49252),x49252),x49252)
% 28.73/28.52 [4926]~P107(x49261)+E(f319(f319(f102(x49261),x49262),x49262),x49262)
% 28.73/28.52 [4927]~P107(x49271)+E(f319(f319(f102(x49271),x49272),x49272),x49272)
% 28.73/28.52 [4928]~P102(x49281)+E(f319(f319(f93(x49281),x49282),x49282),x49282)
% 28.73/28.52 [4929]~P108(x49291)+E(f319(f319(f93(x49291),x49292),x49292),x49292)
% 28.73/28.52 [4930]~P108(x49301)+E(f319(f319(f93(x49301),x49302),x49302),x49302)
% 28.73/28.52 [4931]~P101(x49311)+E(f319(f319(f75(x49311),x49312),x49312),x49312)
% 28.73/28.52 [4932]~P101(x49321)+E(f319(f319(f75(x49321),x49322),x49322),x49322)
% 28.73/28.52 [4933]~P4(x49331)+E(f319(f319(f224(x49331),x49332),x49332),x49332)
% 28.73/28.52 [4934]~P4(x49341)+E(f319(f319(f224(x49341),x49342),x49342),x49342)
% 28.73/28.52 [4935]~P4(x49351)+E(f319(f319(f225(x49351),x49352),x49352),x49352)
% 28.73/28.52 [4936]~P4(x49361)+E(f319(f319(f225(x49361),x49362),x49362),x49362)
% 28.73/28.52 [4954]~P69(x49541)+E(f319(f319(f23(x49541),x49542),x49542),f2(x49541))
% 28.73/28.52 [4968]~P96(x49681)+E(f319(f73(x49681),f319(f73(x49681),x49682)),x49682)
% 28.73/28.52 [4969]~P69(x49691)+E(f319(f73(x49691),f319(f73(x49691),x49692)),x49692)
% 28.73/28.52 [4986]~E(x49862,f2(a925))+E(f319(f319(f236(a925),x49861),x49862),f319(a104,f2(a925)))
% 28.73/28.52 [5021]~P104(x50211)+E(f319(f319(f102(x50211),f180(x50211)),x50212),x50212)
% 28.73/28.52 [5022]~P103(x50221)+E(f319(f319(f93(x50221),f234(x50221)),x50222),x50222)
% 28.73/28.52 [5023]~P78(x50231)+E(f319(f319(f75(x50231),f72(x50231)),x50232),x50232)
% 28.73/28.52 [5024]~P87(x50241)+E(f319(f319(f75(x50241),f72(x50241)),x50242),x50242)
% 28.73/28.52 [5025]~P121(x50251)+E(f319(f319(f75(x50251),f72(x50251)),x50252),x50252)
% 28.73/28.52 [5026]~P79(x50261)+E(f319(f319(f74(x50261),f2(x50261)),x50262),x50262)
% 28.73/28.52 [5027]~P121(x50271)+E(f319(f319(f74(x50271),f2(x50271)),x50272),x50272)
% 28.73/28.52 [5028]~P88(x50281)+E(f319(f319(f74(x50281),f2(x50281)),x50282),x50282)
% 28.73/28.52 [5046]~P103(x50461)+E(f319(f319(f102(x50461),f234(x50461)),x50462),f234(x50461))
% 28.73/28.52 [5047]~P104(x50471)+E(f319(f319(f93(x50471),f180(x50471)),x50472),f180(x50471))
% 28.73/28.52 [5048]~P121(x50481)+E(f319(f319(f75(x50481),f2(x50481)),x50482),f2(x50481))
% 28.73/28.52 [5049]~P133(x50491)+E(f319(f319(f75(x50491),f2(x50491)),x50492),f2(x50491))
% 28.73/28.52 [5050]~P87(x50501)+E(f319(f319(f236(x50501),f72(x50501)),x50502),f72(x50501))
% 28.73/28.52 [5051]~P124(x50511)+E(f319(f319(f283(x50511),f2(x50511)),x50512),f2(x50511))
% 28.73/28.52 [5052]~P65(x50521)+E(f319(f319(f30(x50521),f2(x50521)),x50522),f2(x50521))
% 28.73/28.52 [5060]E(x50601,f105(x50602))+E(f136(x50602,f319(f160(x50602),x50601)),f319(f133(x50602),x50601))
% 28.73/28.52 [5061]E(x50611,f105(x50612))+E(f319(f133(x50612),f319(f160(x50612),x50611)),f136(x50612,x50611))
% 28.73/28.52 [5062]E(x50621,f2(a925))+~E(f319(f319(f74(a925),x50622),x50621),x50622)
% 28.73/28.52 [5069]~P145(x50691)+E(f319(f94(x50691),f319(f92(a1),x50692)),f319(f92(x50691),x50692))
% 28.73/28.52 [5070]~P99(x50701)+E(f319(f94(x50701),f319(f95(a1),x50702)),f319(f95(x50701),x50702))
% 28.73/28.52 [5075]E(x50751,f72(a925))+~E(f319(f319(f75(a925),x50752),x50751),f72(a925))
% 28.73/28.52 [5076]E(x50761,f72(a925))+~E(f319(f319(f75(a925),x50761),x50762),f72(a925))
% 28.73/28.52 [5077]E(x50771,f72(a925))+~E(f319(f319(f75(a925),x50772),x50771),f72(a925))
% 28.73/28.52 [5078]E(x50781,f72(a925))+~E(f319(f319(f75(a925),x50781),x50782),f72(a925))
% 28.73/28.52 [5079]E(x50791,f2(a925))+~E(f319(f319(f74(a925),x50792),x50791),f2(a925))
% 28.73/28.52 [5080]E(x50801,f2(a925))+~E(f319(f319(f74(a925),x50801),x50802),f2(a925))
% 28.73/28.52 [5097]~P92(x50971)+E(f319(f69(x50971),f319(f73(x50971),x50972)),f319(f69(x50971),x50972))
% 28.73/28.52 [5098]~P126(x50981)+E(f319(f69(x50981),f319(f92(x50981),x50982)),f319(f92(x50981),x50982))
% 28.73/28.52 [5099]~P92(x50991)+E(f319(f69(x50991),f319(f69(x50991),x50992)),f319(f69(x50991),x50992))
% 28.73/28.52 [5100]~P79(x51001)+E(f319(f157(x51001),f319(f160(x51001),x51002)),f319(f157(x51001),x51002))
% 28.73/28.52 [5105]~E(x51051,f319(a104,f2(a925)))+E(f319(f319(f236(a925),x51051),x51052),f319(a104,f2(a925)))
% 28.73/28.52 [5114]~P69(x51141)+E(f319(f319(f23(x51141),f2(x51141)),x51142),f319(f73(x51141),x51142))
% 28.73/28.52 [5115]~E(x51152,f2(a925))+E(f131(a925,f319(f294(a925,x51151),x51152)),f105(a925))
% 28.73/28.52 [5124]~P99(x51241)+E(f319(f319(f74(x51241),x51242),f319(f95(x51241),a77)),x51242)
% 28.73/28.52 [5125]E(x51251,f2(a1))+E(f41(f319(f69(a1),x51252),f319(f69(a1),x51251)),f47(x51252,x51251))
% 28.73/28.52 [5139]~E(x51391,x51392)+P1(f319(f319(f226(a925),x51391),x51392))
% 28.73/28.52 [5140]~E(x51401,x51402)+P1(f319(f319(f226(a925),x51401),x51402))
% 28.73/28.52 [5141]~E(x51411,x51412)+P1(f319(f319(f226(a925),x51411),x51412))
% 28.73/28.52 [5148]~E(x51481,f2(a91))+E(f319(f319(f74(a925),f319(a20,x51481)),x51482),x51482)
% 28.73/28.52 [5149]~E(f319(f95(a1),x51492),f319(f92(a1),x51491))+E(x51491,f319(a96,f319(f95(a1),x51492)))
% 28.73/28.52 [5150]~P6(x51501)+E(f87(x51501,f319(f16(x51501,x51501),x51502)),x51502)
% 28.73/28.52 [5163]~P7(x51631)+P7(f319(f319(f236(a1),x51631),x51632))
% 28.73/28.52 [5164]~P96(x51641)+E(f319(f319(f102(x51641),x51642),f319(f73(x51641),x51642)),f234(x51641))
% 28.73/28.52 [5165]~P96(x51651)+E(f319(f319(f93(x51651),x51652),f319(f73(x51651),x51652)),f180(x51651))
% 28.73/28.52 [5166]~P69(x51661)+E(f319(f319(f74(x51661),x51662),f319(f73(x51661),x51662)),f2(x51661))
% 28.73/28.52 [5190]E(x51901,f2(a925))+~E(f319(f73(a1),f319(f92(a1),x51902)),f319(f92(a1),x51901))
% 28.73/28.52 [5191]E(x51911,f2(a925))+~E(f319(f73(a1),f319(f92(a1),x51911)),f319(f92(a1),x51912))
% 28.73/28.52 [5201]E(f186(x52011,x52012),f2(a1))+P1(f319(f319(f226(a1),x52012),x52011))
% 28.73/28.52 [5202]E(f170(x52021,x52022),f105(a1))+P1(f319(f319(f226(a1),x52021),x52022))
% 28.73/28.52 [5203]E(f233(x52031,x52032),f2(a91))+P1(f319(f319(f227(a91),x52031),x52032))
% 28.73/28.52 [5216]E(x52161,f319(a104,f2(a925)))+~E(f319(f319(f75(a925),x52162),x52161),f319(a104,f2(a925)))
% 28.73/28.52 [5217]E(x52171,f319(a104,f2(a925)))+~E(f319(f319(f75(a925),x52171),x52172),f319(a104,f2(a925)))
% 28.73/28.52 [5218]~P2(x52181)+P1(f319(f319(f226(x52181),x52182),x52182))
% 28.73/28.52 [5221]~P99(x52211)+E(f319(f319(f75(x52211),x52212),f319(f95(x52211),a89)),f319(f73(x52211),x52212))
% 28.73/28.52 [5240]~P99(x52401)+E(f319(f73(x52401),f319(f95(x52401),x52402)),f319(f95(x52401),f319(f73(a1),x52402)))
% 28.73/28.52 [5241]~P145(x52411)+E(f319(f73(x52411),f319(f94(x52411),x52412)),f319(f94(x52411),f319(f73(a1),x52412)))
% 28.73/28.52 [5242]~P99(x52421)+E(f319(f73(x52421),f319(f95(x52421),x52422)),f319(f95(x52421),f319(f73(a1),x52422)))
% 28.73/28.52 [5272]~E(x52721,f319(a104,x52722))+P1(f319(f319(f227(a925),f2(a925)),x52721))
% 28.73/28.52 [5290]~P4(x52901)+E(f319(f73(f932(x52901,a923)),f319(f296(x52901),x52902)),f319(f293(x52901),x52902))
% 28.73/28.52 [5291]~P4(x52911)+E(f319(f73(f932(x52911,a923)),f319(f274(x52911),x52912)),f319(f275(x52911),x52912))
% 28.73/28.52 [5292]~P4(x52921)+E(f319(f73(f932(x52921,a923)),f319(f275(x52921),x52922)),f319(f274(x52921),x52922))
% 28.73/28.52 [5293]~P4(x52931)+E(f319(f73(f932(x52931,a923)),f319(f293(x52931),x52932)),f319(f296(x52931),x52932))
% 28.73/28.52 [5303]~E(f319(f92(a1),x53032),x53031)+P1(f319(f319(f226(a1),f2(a1)),x53031))
% 28.73/28.52 [5312]~E(x53122,f2(a1))+E(f47(x53121,x53122),f319(f319(f244(a1,a1),f2(a1)),f319(f69(a1),x53121)))
% 28.73/28.52 [5314]~P109(x53141)+P1(f319(f319(f226(x53141),f180(x53141)),x53142))
% 28.73/28.52 [5347]E(x53471,x53472)+~E(f319(f319(f74(a1),x53471),x53471),f319(f319(f74(a1),x53472),x53472))
% 28.73/28.52 [5354]~P1(f319(x53541,x53542))+P1(f319(x53541,f319(a96,f425(x53541))))
% 28.73/28.52 [5380]~P126(x53801)+E(f319(f319(f75(x53801),f76(x53801,x53802)),f319(f69(x53801),x53802)),x53802)
% 28.73/28.52 [5387]~E(x53872,f2(a925))+E(f79(f931(a925,a925),f42(x53871,x53872)),f319(f319(f244(a925,a925),f2(a925)),x53871))
% 28.73/28.52 [5388]~E(x53881,x53882)+~P1(f319(f319(f227(a925),x53881),x53882))
% 28.73/28.52 [5389]~E(x53891,x53892)+~P1(f319(f319(f227(a925),x53891),x53892))
% 28.73/28.52 [5390]~E(x53901,x53902)+~P1(f319(f319(f227(a925),x53901),x53902))
% 28.73/28.52 [5391]~E(x53911,x53912)+~P1(f319(f319(f227(a925),x53911),x53912))
% 28.73/28.52 [5392]~E(x53921,x53922)+~P1(f319(f319(f227(a925),x53921),x53922))
% 28.73/28.52 [5393]~E(x53931,x53932)+~P1(f319(f319(f227(a1),x53931),x53932))
% 28.73/28.52 [5396]~P149(x53961)+E(f319(f319(f74(x53961),f72(x53961)),f319(f92(x53961),x53962)),f319(f92(x53961),f319(a104,x53962)))
% 28.73/28.52 [5400]~E(x54001,f2(a925))+~P1(f319(f319(f227(a925),x54002),x54001))
% 28.73/28.52 [5415]E(f144(x54151,x54152),x54152)+~E(f319(f181(f926(x54151)),f144(x54151,x54152)),f319(f181(f926(x54151)),x54152))
% 28.73/28.52 [5416]E(f319(f29(x54161),f319(f164(x54161),x54162)),f319(f181(f926(x54161)),x54162))+~P1(f319(f129(x54161),x54162))
% 28.73/28.52 [5430]~P1(f319(x54301,f329(x54301)))+P1(f319(x54301,f319(f92(a1),x54302)))
% 28.73/28.52 [5440]E(f233(x54401,x54402),x54402)+~P1(f319(f319(f227(a91),x54401),x54402))
% 28.73/28.52 [5442]E(f264(x54421,x54422),f72(a91))+~P1(f319(f319(f227(a91),x54422),x54421))
% 28.73/28.52 [5443]E(f170(x54431,x54432),f105(a1))+~P1(f319(f319(f227(a1),x54432),x54431))
% 28.73/28.52 [5444]E(f120(x54441,x54442),f107(a1))+~P1(f319(f319(f227(a1),x54441),x54442))
% 28.73/28.52 [5446]~P113(x54461)+E(f295(x54461,x54462,x54462),f319(f319(f301(x54461),x54462),f180(f932(x54461,a923))))
% 28.73/28.52 [5466]~E(f319(f319(f23(a925),x54661),x54662),f2(a925))+P1(f319(f319(f226(a925),x54661),x54662))
% 28.73/28.52 [5483]~E(x54832,f2(a925))+E(f49(x54831,x54832,f105(x54831)),f319(f319(f143(f926(x54831)),f105(x54831)),f105(f926(x54831))))
% 28.73/28.52 [5487]~P2(x54871)+~P1(f319(f319(f227(x54871),x54872),x54872))
% 28.73/28.52 [5488]~E(f39(a1,x54881,x54882),f2(a1))+E(f39(a1,x54881,f319(f73(a1),x54882)),f2(a1))
% 28.73/28.52 [5489]~E(f39(a1,x54891,x54892),f2(a1))+E(f39(a1,x54891,f319(f73(a1),x54892)),f2(a1))
% 28.73/28.52 [5490]~E(f39(a1,x54901,x54902),f2(a1))+E(f39(a1,f319(f73(a1),x54901),x54902),f2(a1))
% 28.73/28.52 [5491]~E(f39(a1,x54911,x54912),f2(a1))+E(f39(a1,f319(f73(a1),x54911),x54912),f2(a1))
% 28.73/28.52 [5498]E(f319(f294(a925,x54981),f319(a104,x54982)),f180(f932(a925,a923)))+P1(f319(f319(f226(a925),x54981),x54982))
% 28.73/28.52 [5521]E(f131(a925,f319(f294(a925,x55211),x55212)),f105(a925))+P1(f319(f319(f227(a925),x55211),x55212))
% 28.73/28.52 [5526]~E(f319(f29(x55261),f319(f164(x55261),x55262)),f319(f181(f926(x55261)),x55262))+P1(f319(f129(x55261),x55262))
% 28.73/28.52 [5530]~P1(f319(f129(x55301),x55302))+P1(f319(f129(x55301),f319(f159(x55301),x55302)))
% 28.73/28.52 [5531]~P1(f319(f129(x55311),x55312))+P1(f319(f129(x55311),f319(f163(x55311),x55312)))
% 28.73/28.52 [5532]~P1(f319(f129(x55321),x55322))+P1(f319(f129(x55321),f319(f160(x55321),x55322)))
% 28.73/28.52 [5540]P1(f319(x55401,x55402))+~P1(f319(x55401,f319(a96,f426(x55401))))
% 28.73/28.52 [5541]P1(f319(f319(f226(a925),x55412),x55411))+P1(f319(f319(f226(a925),x55411),x55412))
% 28.73/28.52 [5542]P1(f319(f319(f226(a1),x55422),x55421))+P1(f319(f319(f226(a1),x55421),x55422))
% 28.73/28.52 [5546]~P92(x55461)+P1(f319(f319(f226(x55461),x55462),f319(f69(x55461),x55462)))
% 28.73/28.52 [5549]P1(f319(x55491,f330(x55491)))+~P1(f319(x55491,f319(f92(a1),x55492)))
% 28.73/28.52 [5572]E(f319(f319(f23(a925),x55721),x55722),f2(a925))+~P1(f319(f319(f226(a925),x55721),x55722))
% 28.73/28.52 [5573]E(f319(f319(f23(a925),x55731),x55732),f2(a925))+~P1(f319(f319(f226(a925),x55731),x55732))
% 28.73/28.52 [5574]E(f319(f319(f30(a925),x55741),x55742),f2(a925))+~P1(f319(f319(f227(a925),x55741),x55742))
% 28.73/28.52 [5592]E(f39(a925,x55921,x55922),x55921)+~P1(f319(f319(f227(a925),x55921),x55922))
% 28.73/28.52 [5593]E(f39(a925,x55931,x55932),x55931)+~P1(f319(f319(f227(a925),x55931),x55932))
% 28.73/28.52 [5601]E(f39(a1,x56011,f319(f73(a1),x56012)),f284(x56011,x56012))+P1(f319(f319(f226(a1),f2(a1)),x56012))
% 28.73/28.52 [5612]E(f319(f319(f23(a1),x56121),x56122),f186(x56121,x56122))+~P1(f319(f319(f226(a1),x56122),x56121))
% 28.73/28.52 [5613]E(f319(f319(f23(a1),x56131),x56132),f186(x56131,x56132))+~P1(f319(f319(f226(a1),x56132),x56131))
% 28.73/28.52 [5633]P1(f319(f319(f226(a1),f2(a1)),f329(x56331)))+P1(f319(x56331,f319(f92(a1),x56332)))
% 28.73/28.52 [5645]~P129(x56451)+P1(f319(f319(f226(x56451),f2(x56451)),f319(f92(x56451),x56452)))
% 28.73/28.52 [5646]~P129(x56461)+P1(f319(f319(f226(x56461),f2(x56461)),f319(f92(x56461),x56462)))
% 28.73/28.52 [5647]~P92(x56471)+P1(f319(f319(f226(x56471),f2(x56471)),f319(f69(x56471),x56472)))
% 28.73/28.52 [5674]E(f319(f319(f74(a925),x56741),f331(x56742,x56741)),x56742)+~P1(f319(f319(f226(a925),x56741),x56742))
% 28.73/28.52 [5686]~E(f319(f95(a1),x56861),f319(f92(a1),x56862))+P1(f319(f319(f226(a1),f2(a1)),f319(f95(a1),x56861)))
% 28.73/28.52 [5689]E(f295(a1,x56891,x56892),f180(f932(a1,a923)))+~P1(f319(f319(f227(a1),x56892),x56891))
% 28.73/28.52 [5692]~P126(x56921)+E(f319(f319(f75(x56921),f319(f69(x56921),x56922)),f319(f69(x56921),x56922)),f319(f319(f75(x56921),x56922),x56922))
% 28.73/28.52 [5697]E(f131(a925,f319(f294(a925,x56971),f319(a104,x56972))),f105(a925))+P1(f319(f319(f226(a925),x56971),x56972))
% 28.73/28.52 [5701]E(f319(f319(f30(a1),x57011),x57012),f285(x57011,x57012))+~P1(f319(f319(f226(a1),f2(a1)),x57012))
% 28.73/28.52 [5721]P1(f319(f129(x57211),x57212))+~P1(f319(f129(x57211),f319(f159(x57211),x57212)))
% 28.73/28.52 [5722]P1(f319(f129(x57221),x57222))+~P1(f319(f129(x57221),f319(f160(x57221),x57222)))
% 28.73/28.52 [5747]P1(f319(f55(a925),x57471))+P1(f319(f319(f321(a925),f332(x57471,x57472)),x57471))
% 28.73/28.52 [5748]P1(f319(f55(a925),x57481))+P1(f319(f319(f321(a925),f351(x57481,x57482)),x57481))
% 28.73/28.52 [5751]P1(f319(f319(f227(a925),x57512),f319(a104,x57511)))+P1(f319(f319(f227(a925),x57511),x57512))
% 28.73/28.52 [5752]E(f39(a1,x57521,x57522),f284(x57521,x57522))+~P1(f319(f319(f226(a1),f2(a1)),x57522))
% 28.73/28.52 [5754]E(f131(a925,f319(f294(a925,x57541),x57542)),f105(a925))+~P1(f319(f319(f226(a925),x57542),x57541))
% 28.73/28.52 [5755]E(f131(a925,f319(f294(a925,x57551),x57552)),f105(a925))+~P1(f319(f319(f226(a925),x57552),x57551))
% 28.73/28.52 [5756]~P68(x57561)+E(f319(f302(x57561,x57561,f73(x57561)),f319(f296(x57561),x57562)),f319(f274(x57561),f319(f73(x57561),x57562)))
% 28.73/28.52 [5757]~P68(x57571)+E(f319(f302(x57571,x57571,f73(x57571)),f319(f274(x57571),x57572)),f319(f296(x57571),f319(f73(x57571),x57572)))
% 28.73/28.52 [5758]~P68(x57581)+E(f319(f302(x57581,x57581,f73(x57581)),f319(f275(x57581),x57582)),f319(f293(x57581),f319(f73(x57581),x57582)))
% 28.73/28.52 [5759]~P68(x57591)+E(f319(f302(x57591,x57591,f73(x57591)),f319(f293(x57591),x57592)),f319(f275(x57591),f319(f73(x57591),x57592)))
% 28.73/28.52 [5770]E(x57701,f180(f932(x57702,a923)))+P1(f319(f319(f321(x57702),f825(x57701,x57702)),x57701))
% 28.73/28.52 [5771]E(x57711,f180(f932(x57712,a923)))+P1(f319(f319(f321(x57712),f837(x57711,x57712)),x57711))
% 28.73/28.52 [5778]~P1(f319(f319(f227(a925),x57781),x57782))+P1(f319(f319(f226(a925),x57781),x57782))
% 28.73/28.52 [5779]~P1(f319(f319(f227(a925),x57791),x57792))+P1(f319(f319(f226(a925),x57791),x57792))
% 28.73/28.52 [5780]~P1(f319(f319(f227(a925),x57801),x57802))+P1(f319(f319(f226(a925),x57801),x57802))
% 28.73/28.52 [5781]~P1(f319(f319(f227(a925),x57811),x57812))+P1(f319(f319(f226(a925),x57811),x57812))
% 28.73/28.52 [5782]~P1(f319(f319(f227(a925),x57821),x57822))+P1(f319(f319(f226(a925),x57821),x57822))
% 28.73/28.52 [5783]~P1(f319(f319(f227(a1),x57831),x57832))+P1(f319(f319(f226(a1),x57831),x57832))
% 28.73/28.52 [5799]E(f41(x57991,x57992),f319(f319(f244(a1,a1),f2(a1)),x57991))+~P1(f319(f319(f227(a1),x57991),x57992))
% 28.73/28.52 [5801]E(f207(f319(f73(a1),x58011),f319(f73(a1),x58012)),f207(x58011,x58012))+~P1(f319(f319(f227(a1),x58012),f2(a1)))
% 28.73/28.52 [5812]E(x58121,x58122)+~E(f319(a3,f319(a104,f319(a20,x58121))),f319(a3,f319(a104,f319(a20,x58122))))
% 28.73/28.52 [5817]E(f41(x58171,x58172),f319(f319(f244(a1,a1),f2(a1)),x58171))+~P1(f319(f319(f226(a1),x58172),f2(a1)))
% 28.73/28.52 [5846]E(f39(a925,f319(f95(a925),x58461),f319(f95(a925),x58462)),f2(a925))+~P1(f319(a185,f319(f95(a1),x58461)))
% 28.73/28.52 [5861]P1(f319(f319(f226(a1),f2(a1)),f330(x58611)))+~P1(f319(x58611,f319(f92(a1),x58612)))
% 28.73/28.52 [5894]P42(f295(a1,x58941,x58942))+~P1(f319(f319(f226(a1),f2(a1)),x58941))
% 28.73/28.52 [5899]~P1(f319(f55(x58991),x58992))+P1(f319(f55(f932(x58991,a923)),f319(f300(x58991),x58992)))
% 28.73/28.52 [5912]E(f319(f319(f74(a1),x59121),f319(f92(a1),f365(x59122,x59121))),x59122)+~P1(f319(f319(f226(a1),x59121),x59122))
% 28.73/28.52 [5920]P1(f319(f319(f226(a925),x59201),x59202))+P1(f319(f319(f226(a925),f319(a104,x59202)),x59201))
% 28.73/28.52 [5964]E(f319(f319(f30(a925),f319(f95(a925),x59641)),f319(f95(a925),x59642)),f2(a925))+~P1(f319(a185,f319(f95(a1),x59641)))
% 28.73/28.52 [5965]E(f319(f319(f75(a925),f319(f95(a925),x59651)),f319(f95(a925),x59652)),f2(a925))+~P1(f319(f319(f227(a1),x59651),a77))
% 28.73/28.52 [5966]P1(f319(f319(f226(a925),x59661),f319(a104,x59662)))+~P1(f319(f319(f226(a925),x59661),x59662))
% 28.73/28.52 [5967]P1(f319(f319(f226(a925),x59671),f319(a104,x59672)))+~P1(f319(f319(f226(a925),x59671),x59672))
% 28.73/28.52 [5968]P1(f319(f319(f227(a925),x59681),f319(a104,x59682)))+~P1(f319(f319(f226(a925),x59681),x59682))
% 28.73/28.52 [5969]P1(f319(f319(f227(a925),x59691),f319(a104,x59692)))+~P1(f319(f319(f226(a925),x59691),x59692))
% 28.73/28.52 [5970]P1(f319(f319(f227(a925),x59701),f319(a104,x59702)))+~P1(f319(f319(f227(a925),x59701),x59702))
% 28.73/28.52 [5971]P1(f319(f319(f227(a925),x59711),f319(a104,x59712)))+~P1(f319(f319(f227(a925),x59711),x59712))
% 28.73/28.52 [5974]~E(x59741,x59742)+P1(f319(f319(f227(a1),x59741),f319(f319(f74(a1),x59742),f72(a1))))
% 28.73/28.52 [5977]E(f39(a1,x59771,x59772),f2(a1))+E(f319(f319(f23(a1),x59772),f39(a1,x59771,x59772)),f39(a1,f319(f73(a1),x59771),x59772))
% 28.73/28.52 [5986]E(x59861,f105(x59862))+P1(f319(f319(f321(x59862),f136(x59862,x59861)),f319(f164(x59862),x59861)))
% 28.73/28.52 [5997]E(f79(f931(a925,a925),f42(x59971,x59972)),f319(f319(f244(a925,a925),f2(a925)),x59971))+~P1(f319(f319(f227(a925),x59971),x59972))
% 28.73/28.52 [5998]E(f79(f931(a925,a925),f42(x59981,x59982)),f319(f319(f244(a925,a925),f2(a925)),x59981))+~P1(f319(f319(f227(a925),x59981),x59982))
% 28.73/28.52 [6033]E(f319(f319(f23(a925),f319(f95(a925),x60331)),f319(f95(a925),x60332)),f319(f95(a925),x60331))+~P1(f319(f319(f227(a1),x60332),a77))
% 28.73/28.52 [6034]E(f319(f319(f74(a925),f319(f95(a925),x60341)),f319(f95(a925),x60342)),f319(f95(a925),x60342))+~P1(f319(f319(f227(a1),x60341),a77))
% 28.73/28.52 [6041]E(f319(a104,f319(f319(f74(a925),x60411),f416(x60412,x60411))),x60412)+~P1(f319(f319(f227(a925),x60411),x60412))
% 28.73/28.52 [6066]P1(f319(x60661,x60662))+~P1(f319(x60661,f319(a83,f588(x60662,x60661))))
% 28.73/28.52 [6067]P1(f319(x60671,x60672))+~P1(f319(x60671,f319(a3,f838(x60672,x60671))))
% 28.73/28.52 [6077]~P1(f319(f319(f227(a925),x60771),f319(a104,x60772)))+P1(f319(f319(f226(a925),x60771),x60772))
% 28.73/28.52 [6114]P1(f319(x61141,x61142))+P1(f319(f319(f321(a925),f838(x61142,x61141)),f234(f932(a925,a923))))
% 28.73/28.52 [6127]E(f319(f319(f301(a925),x61271),f319(f294(a925,x61272),x61271)),f319(f294(a925,x61272),f319(a104,x61271)))+~P1(f319(f319(f226(a925),x61272),x61271))
% 28.73/28.52 [6129]E(x61291,f105(x61292))+E(f319(f319(f126(x61292),f106(x61292,x61291)),f319(f319(f143(x61292),f136(x61292,x61291)),f105(x61292))),x61291)
% 28.73/28.52 [6145]P1(f319(f55(x61451),x61452))+~P1(f319(f319(f227(a925),f2(a925)),f319(f29(x61451),x61452)))
% 28.73/28.52 [6146]P1(f319(f55(x61461),x61462))+~P1(f319(f319(f227(a925),f2(a925)),f319(f29(x61461),x61462)))
% 28.73/28.52 [6150]~E(x61501,f180(f932(x61502,a923)))+~P1(f319(f319(f227(a925),f2(a925)),f319(f29(x61502),x61501)))
% 28.73/28.52 [6160]~P1(f319(f319(f227(a925),x61601),x61602))+P1(f319(f319(f226(a925),f319(a104,x61601)),x61602))
% 28.73/28.52 [6161]~P1(f319(f319(f227(a925),x61611),x61612))+P1(f319(f319(f226(a925),f319(a104,x61611)),x61612))
% 28.73/28.52 [6162]~P1(f319(f319(f227(a925),x61621),x61622))+P1(f319(f319(f226(a925),f319(a104,x61621)),x61622))
% 28.73/28.52 [6166]~P4(x61661)+E(f142(x61661,x61661,f5(x61661),f144(x61661,x61662)),f131(x61661,f319(f164(x61661),x61662)))
% 28.73/28.52 [6169]E(x61691,f105(x61692))+P1(f319(f319(f321(x61692),f319(f133(x61692),x61691)),f319(f164(x61692),x61691)))
% 28.73/28.52 [6175]~P129(x61751)+P1(f319(f319(f227(x61751),x61752),f319(f319(f74(x61751),x61752),f72(x61751))))
% 28.73/28.52 [6177]~P92(x61771)+P1(f319(f319(f226(x61771),f319(f73(x61771),x61772)),f319(f69(x61771),x61772)))
% 28.73/28.52 [6191]~E(x61911,x61912)+E(f282(a925,f279(a925),x61911,x61912),f319(f319(f301(a925),x61911),f180(f932(a925,a923))))
% 28.73/28.52 [6211]P1(f319(f55(a925),x62111))+~P1(f319(f319(f226(a925),f332(x62111,x62112)),x62112))
% 28.73/28.52 [6212]P1(f319(f55(a925),x62121))+~P1(f319(f319(f227(a925),f351(x62121,x62122)),x62122))
% 28.73/28.52 [6216]~P1(f319(f55(f931(x62161,x62161)),x62162))+P1(f319(f55(x62161),f319(f273(x62161),x62162)))
% 28.73/28.52 [6269]E(f170(f319(f95(a1),x62691),f319(f95(a1),x62692)),f105(a1))+P1(f319(f319(f226(a1),f319(f95(a1),x62691)),f319(f95(a1),x62692)))
% 28.73/28.52 [6271]~P1(f319(f319(f227(a925),x62712),f319(a104,x62711)))+~P1(f319(f319(f227(a925),x62711),x62712))
% 28.73/28.52 [6272]~P113(x62721)+E(f319(f319(f93(f932(x62721,a923)),f319(f293(x62721),x62722)),f319(f275(x62721),x62722)),f319(f319(f301(x62721),x62722),f180(f932(x62721,a923))))
% 28.73/28.52 [6274]E(f319(f319(f236(a925),f319(f95(a925),x62741)),f319(f95(a925),x62742)),f319(f319(f236(a925),f2(a925)),f319(f95(a925),x62742)))+~P1(f319(a185,f319(f95(a1),x62741)))
% 28.73/28.52 [6284]P1(f319(f55(x62841),x62842))+~P1(f319(f55(f932(x62841,a923)),f319(f300(x62841),x62842)))
% 28.73/28.52 [6306]P1(f319(f319(f226(a925),f319(a104,x63061)),f319(a104,x63062)))+~P1(f319(f319(f226(a925),x63061),x63062))
% 28.73/28.52 [6307]P1(f319(f319(f226(a925),f319(a20,x63071)),f319(a20,x63072)))+~P1(f319(f319(f226(a91),x63071),x63072))
% 28.73/28.52 [6308]P1(f319(f319(f226(a91),f319(a3,x63081)),f319(a3,x63082)))+~P1(f319(f319(f226(a925),x63081),x63082))
% 28.73/28.52 [6309]P1(f319(f319(f227(a925),f319(a104,x63091)),f319(a104,x63092)))+~P1(f319(f319(f227(a925),x63091),x63092))
% 28.73/28.52 [6310]P1(f319(f319(f227(a925),f319(a104,x63101)),f319(a104,x63102)))+~P1(f319(f319(f227(a925),x63101),x63102))
% 28.73/28.52 [6311]P1(f319(f319(f227(a925),f319(a20,x63111)),f319(a20,x63112)))+~P1(f319(f319(f227(a91),x63111),x63112))
% 28.73/28.52 [6312]P1(f319(f319(f227(a91),f319(a3,x63121)),f319(a3,x63122)))+~P1(f319(f319(f227(a925),x63121),x63122))
% 28.73/28.52 [6317]E(x63171,x63172)+~E(f319(f302(a925,a1,f92(a1)),x63171),f319(f302(a925,a1,f92(a1)),x63172))
% 28.73/28.52 [6333]P1(f319(f319(f226(a925),x63331),x63332))+~P1(f319(f319(f226(a925),f319(a104,x63331)),x63332))
% 28.73/28.52 [6334]P1(f319(f319(f227(a925),x63341),x63342))+~P1(f319(f319(f226(a925),f319(a104,x63341)),x63342))
% 28.73/28.52 [6335]P1(f319(f319(f227(a925),x63351),x63352))+~P1(f319(f319(f226(a925),f319(a104,x63351)),x63352))
% 28.73/28.52 [6336]P1(f319(f319(f227(a925),x63361),x63362))+~P1(f319(f319(f226(a925),f319(a104,x63361)),x63362))
% 28.73/28.52 [6337]P1(f319(f319(f227(a925),x63371),x63372))+~P1(f319(f319(f227(a925),f319(a104,x63371)),x63372))
% 28.73/28.52 [6354]E(f39(a1,x63541,x63542),f2(a1))+E(f319(f319(f23(a1),f39(a1,x63541,x63542)),x63542),f39(a1,x63541,f319(f73(a1),x63542)))
% 28.73/28.52 [6420]E(f319(f29(f932(x64201,a923)),f319(f300(x64201),x64202)),f319(f319(f236(a925),f319(a104,f319(a104,f2(a925)))),f319(f29(x64201),x64202)))+~P1(f319(f55(x64201),x64202))
% 28.73/28.52 [6423]E(x64231,f105(x64232))+E(f319(f319(f156(x64232),x64231),f319(f319(f23(a925),f319(f181(f926(x64232)),x64231)),f72(a925))),f136(x64232,x64231))
% 28.73/28.52 [6445]E(x64451,f105(x64452))+E(f319(f319(f126(x64452),f319(f163(x64452),x64451)),f319(f319(f143(x64452),f319(f133(x64452),x64451)),f105(x64452))),f319(f159(x64452),x64451))
% 28.73/28.52 [6446]~P1(f319(f180(f932(x64461,a923)),x64462))+P1(f319(f319(f321(x64461),x64462),f180(f932(x64461,a923))))
% 28.73/28.52 [6475]~P1(f319(f55(x64751),f31(f932(x64751,a923),x64752)))+P1(f319(f55(f932(x64751,a923)),x64752))
% 28.73/28.52 [6497]P1(f319(f319(f226(a925),f319(f95(a925),x64971)),f319(f95(a925),x64972)))+~P1(f319(f319(f226(a1),x64971),a77))
% 28.73/28.52 [6518]~P1(f319(f319(f227(a1),x65181),x65182))+P1(f319(f319(f226(a1),x65181),f319(f319(f23(a1),x65182),f72(a1))))
% 28.73/28.52 [6519]~P1(f319(f319(f226(a1),x65191),x65192))+P1(f319(f319(f227(a1),x65191),f319(f319(f74(a1),x65192),f72(a1))))
% 28.73/28.52 [6520]~P1(f319(f319(f227(a1),x65201),x65202))+P1(f319(f319(f227(a1),x65201),f319(f319(f74(a1),x65202),f72(a1))))
% 28.73/28.52 [6522]~P1(f319(f319(f226(a1),x65221),x65222))+P1(f319(f319(f226(a925),f319(f95(a925),x65221)),f319(f95(a925),x65222)))
% 28.73/28.52 [6523]~P1(f319(f319(f226(a925),x65231),x65232))+P1(f319(f319(f226(a1),f319(f92(a1),x65231)),f319(f92(a1),x65232)))
% 28.73/28.52 [6524]~P1(f319(f319(f226(a925),x65241),x65242))+P1(f319(f319(f226(a1),f319(f92(a1),x65241)),f319(f92(a1),x65242)))
% 28.73/28.52 [6525]~P1(f319(f319(f226(a1),x65251),x65252))+P1(f319(f319(f226(a1),f319(f95(a1),x65251)),f319(f95(a1),x65252)))
% 28.73/28.52 [6526]~P1(f319(f319(f227(a925),x65261),x65262))+P1(f319(f319(f227(a1),f319(f92(a1),x65261)),f319(f92(a1),x65262)))
% 28.73/28.52 [6527]~P1(f319(f319(f227(a925),x65271),x65272))+P1(f319(f319(f227(a1),f319(f92(a1),x65271)),f319(f92(a1),x65272)))
% 28.73/28.52 [6528]~P1(f319(f319(f227(a1),x65281),x65282))+P1(f319(f319(f227(a1),f319(f95(a1),x65281)),f319(f95(a1),x65282)))
% 28.73/28.52 [6535]~E(x65352,f180(f932(x65351,a923)))+P1(f319(f319(f226(f932(x65351,a923)),x65352),f180(f932(x65351,a923))))
% 28.73/28.52 [6548]~P1(f319(f319(f226(a925),x65481),x65482))+~P1(f319(f319(f226(a925),f319(a104,x65482)),x65481))
% 28.73/28.52 [6591]~P1(f319(f319(f226(a925),f319(a104,x65911)),f319(a104,x65912)))+P1(f319(f319(f226(a925),x65911),x65912))
% 28.73/28.52 [6592]~P1(f319(f319(f226(a91),f319(a3,x65921)),f319(a3,x65922)))+P1(f319(f319(f226(a925),x65921),x65922))
% 28.73/28.52 [6593]~P1(f319(f319(f226(a925),f319(a20,x65931)),f319(a20,x65932)))+P1(f319(f319(f226(a91),x65931),x65932))
% 28.73/28.52 [6594]~P1(f319(f319(f227(a925),f319(a104,x65941)),f319(a104,x65942)))+P1(f319(f319(f227(a925),x65941),x65942))
% 28.73/28.52 [6595]~P1(f319(f319(f227(a925),f319(a104,x65951)),f319(a104,x65952)))+P1(f319(f319(f227(a925),x65951),x65952))
% 28.73/28.52 [6596]~P1(f319(f319(f227(a91),f319(a3,x65961)),f319(a3,x65962)))+P1(f319(f319(f227(a925),x65961),x65962))
% 28.73/28.52 [6597]~P1(f319(f319(f227(a925),f319(a96,x65971)),f319(a96,x65972)))+P1(f319(f319(f227(a1),x65971),x65972))
% 28.73/28.52 [6598]~P1(f319(f319(f227(a925),f319(a20,x65981)),f319(a20,x65982)))+P1(f319(f319(f227(a91),x65981),x65982))
% 28.73/28.52 [6620]~P1(f319(f319(f321(x66201),x66202),f180(f932(x66201,a923))))+P1(f319(f180(f932(x66201,a923)),x66202))
% 28.73/28.52 [6640]~P1(f319(f319(f227(a925),f319(a96,x66402)),f319(a96,x66401)))+P1(f319(f319(f227(a1),f2(a1)),x66401))
% 28.73/28.52 [6671]P1(f319(f319(f226(a1),f2(a1)),f39(a1,x66711,x66712)))+~P1(f319(f319(f227(a1),f2(a1)),x66712))
% 28.73/28.52 [6672]P1(f319(f319(f226(a1),f2(a1)),f39(a1,x66721,x66722)))+~P1(f319(f319(f227(a1),f2(a1)),x66722))
% 28.73/28.52 [6836]P38(x68361,x68362)+~E(f319(f319(f281(x68361,x68361,x68361),x68362),x68362),f180(f932(f931(x68361,x68361),a923)))
% 28.73/28.52 [6850]~P38(x68501,x68502)+P38(x68501,f319(f319(f281(x68501,x68501,x68501),x68502),x68502))
% 28.73/28.52 [6861]P1(f319(f319(f226(a1),x68611),x68612))+~P1(f319(f319(f227(a1),x68611),f319(f319(f74(a1),x68612),f72(a1))))
% 28.73/28.52 [6862]P1(f319(f319(f227(a1),x68621),x68622))+~P1(f319(f319(f226(a1),x68621),f319(f319(f23(a1),x68622),f72(a1))))
% 28.73/28.52 [6864]P1(f319(f319(f226(a925),x68641),x68642))+~P1(f319(f319(f226(a1),f319(f92(a1),x68641)),f319(f92(a1),x68642)))
% 28.73/28.52 [6865]P1(f319(f319(f226(a925),x68651),x68652))+~P1(f319(f319(f226(a1),f319(f92(a1),x68651)),f319(f92(a1),x68652)))
% 28.73/28.52 [6866]P1(f319(f319(f226(a1),x68661),x68662))+~P1(f319(f319(f226(a1),f319(f95(a1),x68661)),f319(f95(a1),x68662)))
% 28.73/28.52 [6867]P1(f319(f319(f227(a925),x68671),x68672))+~P1(f319(f319(f227(a1),f319(f92(a1),x68671)),f319(f92(a1),x68672)))
% 28.73/28.52 [6868]P1(f319(f319(f227(a925),x68681),x68682))+~P1(f319(f319(f227(a1),f319(f92(a1),x68681)),f319(f92(a1),x68682)))
% 28.73/28.52 [6869]P1(f319(f319(f227(a1),x68691),x68692))+~P1(f319(f319(f227(a925),f319(f95(a925),x68691)),f319(f95(a925),x68692)))
% 28.73/28.52 [6870]P1(f319(f319(f227(a1),x68701),x68702))+~P1(f319(f319(f227(a1),f319(f95(a1),x68701)),f319(f95(a1),x68702)))
% 28.73/28.52 [6968]~E(f717(x69682,x69681),f105(x69681))+E(f319(f134(f926(x69681),f926(x69681),f126(x69681),f105(x69681)),x69682),f105(x69681))
% 28.73/28.52 [6969]~E(f718(x69692,x69691),f105(x69691))+E(f319(f134(f926(x69691),f926(x69691),f126(x69691),f105(x69691)),x69692),f105(x69691))
% 28.73/28.52 [6973]~P6(x69731)+E(f319(f134(x69731,x69731,f93(x69731),f234(x69731)),x69732),f32(x69731,f319(f164(x69731),x69732)))
% 28.73/28.52 [6974]~P6(x69741)+E(f319(f134(x69741,x69741,f102(x69741),f180(x69741)),x69742),f31(x69741,f319(f164(x69741),x69742)))
% 28.73/28.52 [6988]E(x69881,f2(a91))+E(f319(f319(f74(a925),f319(a20,f319(f319(f23(a91),x69881),f72(a91)))),f319(a104,x69882)),f319(f319(f74(a925),f319(a20,x69881)),x69882))
% 28.73/28.52 [7037]P1(f319(f319(f227(a1),f319(f319(f23(a1),x70371),x70372)),f2(a1)))+~P1(f319(f319(f227(a1),x70371),x70372))
% 28.73/28.52 [7064]~P4(x70641)+E(f319(f319(f102(f932(x70641,a923)),f319(f319(f301(x70641),x70642),f180(f932(x70641,a923)))),f319(f296(x70641),x70642)),f319(f275(x70641),x70642))
% 28.73/28.52 [7140]~P64(x71401,x71402)+P38(x71401,f319(f254(f931(x71401,x71401)),f319(f249(x71401,x71401,a923),x71402)))
% 28.73/28.52 [7141]~P64(x71411,x71412)+P62(x71411,f319(f254(f931(x71411,x71411)),f319(f249(x71411,x71411,a923),x71412)))
% 28.73/28.52 [7142]~P54(x71421,x71422)+P39(x71421,f319(f254(f931(x71421,x71421)),f319(f249(x71421,x71421,a923),x71422)))
% 28.73/28.52 [7143]~P55(x71431,x71432)+P56(x71431,f319(f254(f931(x71431,x71431)),f319(f249(x71431,x71431,a923),x71432)))
% 28.73/28.52 [7144]E(x71441,f180(f932(x71442,a923)))+~P1(f319(f319(f226(f932(x71442,a923)),x71441),f180(f932(x71442,a923))))
% 28.73/28.52 [7225]~P1(f319(f319(f227(a925),f2(a925)),x72252))+P1(f319(f319(f226(a925),f39(a925,x72251,x72252)),x72252))
% 28.73/28.52 [7226]~P1(f319(f319(f226(a1),f2(a1)),x72261))+P1(f319(f319(f226(a1),f39(a1,x72261,x72262)),x72261))
% 28.73/28.52 [7227]~P1(f319(f319(f227(a925),f2(a925)),x72272))+P1(f319(f319(f227(a925),f39(a925,x72271,x72272)),x72272))
% 28.73/28.52 [7228]~P1(f319(f319(f227(a1),f2(a1)),x72282))+P1(f319(f319(f227(a1),f39(a1,x72281,x72282)),x72282))
% 28.73/28.52 [7229]~P1(f319(f319(f227(a1),f2(a1)),x72292))+P1(f319(f319(f227(a1),f39(a1,x72291,x72292)),x72292))
% 28.73/28.52 [7306]~P113(x73061)+E(f319(f319(f23(f932(x73061,a923)),f319(f319(f301(x73061),x73062),f180(f932(x73061,a923)))),f319(f274(x73061),x73062)),f319(f319(f301(x73061),x73062),f180(f932(x73061,a923))))
% 28.73/28.52 [7381]~P50(x73811,x73812)+P57(x73811,f234(f932(x73811,a923)),f319(f254(f931(x73811,x73811)),f319(f249(x73811,x73811,a923),x73812)))
% 28.73/28.52 [7382]P1(f319(x73821,x73822))+P1(f319(f319(f321(f932(f931(a925,a925),a923)),f588(x73822,x73821)),a90))
% 28.73/28.52 [7426]E(f319(f319(f126(a925),f131(a925,f319(f294(a925,x74261),x74262))),f319(f319(f143(a925),x74262),f105(a925))),f131(a925,f319(f294(a925,x74261),f319(a104,x74262))))+~P1(f319(f319(f226(a925),x74261),x74262))
% 28.73/28.52 [7427]E(f319(f319(f126(a925),f131(a925,f319(f294(a925,x74271),x74272))),f319(f319(f143(a925),x74272),f105(a925))),f131(a925,f319(f294(a925,x74271),f319(a104,x74272))))+~P1(f319(f319(f226(a925),x74271),x74272))
% 28.73/28.52 [7576]E(x75761,f2(a925))+~E(f319(f134(a925,a925,f74(a925),x75761),x75762),f2(a925))
% 28.73/28.52 [7600]~P1(f319(f319(f227(a1),f319(f319(f23(a1),x76001),x76002)),f2(a1)))+P1(f319(f319(f227(a1),x76001),x76002))
% 28.73/28.52 [7628]P38(x76281,x76282)+~P38(x76281,f319(f319(f281(x76281,x76281,x76281),x76282),x76282))
% 28.73/28.52 [7653]~P1(f319(f319(f226(a925),f319(a104,x76531)),x76532))+P1(f177(a923,a231,f319(f226(a925),x76531),x76532))
% 28.73/28.52 [7805]P26(a925,a925,f319(f319(f7(a925,a925,a925),f23(a925)),x78051),x78052)+P1(f319(f319(f321(a925),f442(x78051,x78052)),x78052))
% 28.73/28.52 [7862]E(f319(f319(f319(f59(a925,x78621,f74(a925)),f319(f16(a925,x78621),f72(a925))),f2(a925)),x78622),f319(f29(x78621),x78622))+~P1(f319(f55(x78621),x78622))
% 28.73/28.52 [7863]E(f319(f319(f319(f59(a925,x78631,f74(a925)),f319(f16(a925,x78631),f72(a925))),f2(a925)),x78632),f319(f29(x78631),x78632))+~P1(f319(f55(x78631),x78632))
% 28.73/28.52 [7905]P26(a925,a925,f319(f319(f7(a925,a925,a925),f23(a925)),x79051),x79052)+~P1(f319(f319(f226(a925),x79051),f442(x79051,x79052)))
% 28.73/28.52 [7960]P38(x79601,x79602)+P1(f319(f319(f226(f932(x79601,a923)),f597(x79602,x79601)),f319(f277(x79601,x79601,x79602),f597(x79602,x79601))))
% 28.73/28.52 [7965]P64(x79651,x79652)+~P38(x79651,f319(f254(f931(x79651,x79651)),f319(f249(x79651,x79651,a923),x79652)))
% 28.73/28.52 [7966]P54(x79661,x79662)+~P39(x79661,f319(f254(f931(x79661,x79661)),f319(f249(x79661,x79661,a923),x79662)))
% 28.73/28.52 [7967]P55(x79671,x79672)+~P56(x79671,f319(f254(f931(x79671,x79671)),f319(f249(x79671,x79671,a923),x79672)))
% 28.73/28.52 [8034]P1(f319(f319(f226(a925),f319(a104,x80341)),x80342))+~P1(f177(a923,a231,f319(f226(a925),x80341),x80342))
% 28.73/28.52 [8092]P1(f319(f319(f321(f931(a925,a925)),f319(f319(f244(a925,a925),x80921),x80922)),f299(a925,a309)))+~P1(f319(f319(f226(a925),x80921),x80922))
% 28.73/28.52 [8190]P50(x81901,x81902)+~P57(x81901,f234(f932(x81901,a923)),f319(f254(f931(x81901,x81901)),f319(f249(x81901,x81901,a923),x81902)))
% 28.73/28.52 [8246]~P1(f319(f129(x82461),x82462))+P1(f319(f129(f932(x82461,a923)),f319(f319(f146(f926(x82461),f932(x82461,a923)),f164(x82461)),f48(x82461,x82462))))
% 28.73/28.52 [8447]~P38(x84471,f319(f278(x84471,x84471),x84472))+P38(x84471,f319(f278(x84471,x84471),f319(f319(f281(x84471,x84471,x84471),x84472),f299(x84471,x84472))))
% 28.73/28.52 [8547]P27(x85471,a925,f515(x85472,x85471),x85472,f319(f294(a925,f2(a925)),f319(f29(x85471),x85472)))+~P1(f319(f55(x85471),x85472))
% 28.73/28.52 [8548]P27(a925,x85481,f458(x85482,x85481),f319(f294(a925,f2(a925)),f319(f29(x85481),x85482)),x85482)+~P1(f319(f55(x85481),x85482))
% 28.73/28.52 [8566]P27(a925,x85661,f451(x85662,x85661),f295(a925,f72(a925),f319(f29(x85661),x85662)),x85662)+~P1(f319(f55(x85661),x85662))
% 28.73/28.52 [8575]P1(f319(f55(f931(x85751,x85751)),f319(f319(f281(x85751,x85751,x85751),x85752),f299(x85751,x85752))))+~P1(f319(f55(f931(x85751,x85751)),x85752))
% 28.73/28.52 [8602]E(x86021,f2(a1))+P1(f319(f43(x86022,x86021),f319(f319(f244(a1,a1),f319(f319(f30(a1),x86022),x86021)),f39(a1,x86022,x86021))))
% 28.73/28.52 [8616]~P1(f319(f319(f321(f931(a925,a925)),f319(f319(f244(a925,a925),x86161),x86162)),f299(a925,a309)))+P1(f319(f319(f226(a925),x86161),x86162))
% 28.73/28.52 [8632]~P88(x86321)+E(f319(f134(x86321,x86321,f319(f7(x86321,x86321,x86321),f74(x86321)),f2(x86321)),f319(f160(x86321),x86322)),f319(f134(x86321,x86321,f74(x86321),f2(x86321)),x86322))
% 28.73/28.52 [8808]~P4(x88081)+E(f319(f134(f926(x88081),x88081,f319(f7(x88081,f926(x88081),f926(x88081)),f140(x88081,x88081,f5(x88081))),f105(x88081)),x88082),f142(x88081,x88081,f5(x88081),x88082))
% 28.73/28.52 [8919]~P62(x89191,f319(f254(f931(x89191,x89191)),f319(f249(x89191,x89191,a923),x89192)))+P62(x89191,f319(f254(f931(x89191,x89191)),f319(f249(x89191,x89191,a923),f235(x89191,x89191,x89192))))
% 28.73/28.52 [8933]P1(f319(f319(f321(f931(a925,a925)),f319(f319(f244(a925,a925),x89331),x89332)),f319(f319(f281(a925,a925,a925),a309),f299(a925,a309))))+~P1(f319(f319(f227(a925),x89331),x89332))
% 28.73/28.52 [8979]~P1(f319(f55(f931(x89791,x89791)),f319(f319(f281(x89791,x89791,x89791),x89792),f299(x89791,x89792))))+P1(f319(f55(f931(x89791,x89791)),x89792))
% 28.73/28.52 [9038]~P62(x90381,f319(f254(f931(x90381,x90381)),f319(f249(x90381,x90381,a923),f235(x90381,x90381,x90382))))+P62(x90381,f319(f254(f931(x90381,x90381)),f319(f249(x90381,x90381,a923),x90382)))
% 28.73/28.52 [9241]P62(x92411,x92412)+P1(f319(f319(f321(f931(x92411,x92411)),f319(f319(f244(x92411,x92411),f623(x92412,x92411)),f623(x92412,x92411))),f319(f319(f281(x92411,x92411,x92411),x92412),f299(x92411,x92412))))
% 28.73/28.52 [9242]P62(x92421,x92422)+P1(f319(f319(f321(f931(x92421,x92421)),f319(f319(f244(x92421,x92421),f633(x92422,x92421)),f633(x92422,x92421))),f319(f319(f281(x92421,x92421,x92421),x92422),f299(x92421,x92422))))
% 28.73/28.52 [9361]~P1(f319(f319(f321(f931(a925,a925)),f319(f319(f244(a925,a925),x93611),x93612)),f319(f319(f281(a925,a925,a925),a309),f299(a925,a309))))+P1(f319(f319(f227(a925),x93611),x93612))
% 28.73/28.52 [5286]~P99(x52861)+E(f319(f319(f74(x52861),f319(f95(x52861),a77)),x52862),x52862)
% 28.73/28.52 [5319]~P96(x53191)+E(f319(f319(f102(x53191),f319(f73(x53191),x53192)),x53192),f234(x53191))
% 28.73/28.52 [5320]~P96(x53201)+E(f319(f319(f93(x53201),f319(f73(x53201),x53202)),x53202),f180(x53201))
% 28.73/28.52 [5321]~P69(x53211)+E(f319(f319(f74(x53211),f319(f73(x53211),x53212)),x53212),f2(x53211))
% 28.73/28.52 [5322]~P70(x53221)+E(f319(f319(f74(x53221),f319(f73(x53221),x53222)),x53222),f2(x53221))
% 28.73/28.52 [5358]~P99(x53581)+E(f319(f319(f75(x53581),f319(f95(x53581),a89)),x53582),f319(f73(x53581),x53582))
% 28.73/28.52 [5513]~P118(x55131)+E(f319(f319(f75(x55131),f319(f73(x55131),f72(x55131))),x55132),f319(f73(x55131),x55132))
% 28.73/28.52 [5558]E(f319(f69(a1),x55581),f72(a1))+~E(f319(f69(a1),f319(f319(f75(a1),x55581),x55582)),f72(a1))
% 28.73/28.52 [5649]~P99(x56491)+E(f319(f319(f74(x56491),f72(x56491)),f319(f95(x56491),x56492)),f319(f95(x56491),f319(f319(f23(a1),x56492),a89)))
% 28.73/28.52 [5702]~P6(x57021)+E(f32(x57021,f319(f319(f301(x57021),x57022),f180(f932(x57021,a923)))),x57022)
% 28.73/28.52 [5703]~P6(x57031)+E(f31(x57031,f319(f319(f301(x57031),x57032),f180(f932(x57031,a923)))),x57032)
% 28.73/28.52 [5704]~P102(x57041)+E(f10(x57041,f319(f319(f301(x57041),x57042),f180(f932(x57041,a923)))),x57042)
% 28.73/28.52 [5705]~P102(x57051)+E(f13(x57051,f319(f319(f301(x57051),x57052),f180(f932(x57051,a923)))),x57052)
% 28.73/28.52 [5706]~P4(x57061)+E(f14(x57061,f319(f319(f301(x57061),x57062),f180(f932(x57061,a923)))),x57062)
% 28.73/28.52 [5707]~P4(x57071)+E(f15(x57071,f319(f319(f301(x57071),x57072),f180(f932(x57071,a923)))),x57072)
% 28.73/28.52 [5729]E(f319(f319(f74(a925),x57291),f319(f319(f23(a925),x57292),x57291)),x57292)+P1(f319(f319(f227(a925),x57292),x57291))
% 28.73/28.52 [5765]E(x57651,f105(x57652))+P1(f319(f319(f227(a925),f2(a925)),f319(f181(f926(x57652)),x57651)))
% 28.73/28.52 [5891]~P4(x58911)+E(f11(x58911,f224(x58911),f319(f319(f301(x58911),x58912),f180(f932(x58911,a923)))),x58912)
% 28.73/28.52 [5892]~P4(x58921)+E(f12(x58921,f225(x58921),f319(f319(f301(x58921),x58922),f180(f932(x58921,a923)))),x58922)
% 28.73/28.52 [5953]E(f319(f319(f23(a925),x59531),f319(f319(f23(a925),x59531),x59532)),x59532)+~P1(f319(f319(f226(a925),x59532),x59531))
% 28.73/28.52 [5954]E(f319(f319(f74(a925),x59541),f319(f319(f23(a925),x59542),x59541)),x59542)+~P1(f319(f319(f226(a925),x59541),x59542))
% 28.73/28.52 [5975]E(f39(a925,f319(f319(f23(a925),x59751),x59752),x59752),f39(a925,x59751,x59752))+P1(f319(f319(f227(a925),x59751),x59752))
% 28.73/28.52 [5976]E(f39(a925,f319(f319(f23(a925),x59761),x59762),x59762),f39(a925,x59761,x59762))+P1(f319(f319(f227(a925),x59761),x59762))
% 28.73/28.52 [5987]E(f319(f73(a1),f319(f319(f30(a1),x59871),f319(f73(a1),x59872))),f285(x59871,x59872))+P1(f319(f319(f226(a1),f2(a1)),x59872))
% 28.73/28.52 [5989]~E(x59892,f2(a925))+P1(f319(f319(f227(a925),f2(a925)),f319(f319(f236(a925),x59891),x59892)))
% 28.73/28.52 [6044]~P99(x60441)+E(f319(f319(f74(x60441),f319(f73(x60441),f72(x60441))),f319(f95(x60441),x60442)),f319(f95(x60441),f319(f319(f74(a1),x60442),a89)))
% 28.73/28.52 [6046]E(f319(f319(f236(a925),f319(f95(a925),x60461)),x60462),f319(f319(f236(a925),f2(a925)),x60462))+~P1(f319(a185,f319(f95(a1),x60461)))
% 28.73/28.52 [6154]E(f319(f133(a925),f131(a925,f319(f294(a925,x61541),x61542))),x61541)+~P1(f319(f319(f227(a925),x61541),x61542))
% 28.73/28.52 [6170]E(f319(f319(f75(a925),f319(f95(a925),x61701)),f319(f95(a925),x61702)),f319(f95(a925),f319(f319(f75(a1),x61701),x61702)))+P1(f319(f319(f227(a1),x61701),a77))
% 28.73/28.52 [6176]~P131(x61761)+P1(f319(f319(f226(x61761),f2(x61761)),f319(f319(f75(x61761),x61762),x61762)))
% 28.73/28.52 [6188]E(f319(f319(f23(a925),f319(a104,x61881)),x61882),f319(a104,f319(f319(f23(a925),x61881),x61882)))+~P1(f319(f319(f226(a925),x61882),x61881))
% 28.73/28.52 [6192]E(f39(a925,f319(f319(f23(a925),x61921),x61922),x61922),f39(a925,x61921,x61922))+~P1(f319(f319(f226(a925),x61922),x61921))
% 28.73/28.52 [6246]E(f319(f319(f236(a925),f319(a96,x62461)),x62462),f319(a96,f319(f319(f236(a1),x62461),x62462)))+~P1(f319(f319(f226(a1),f2(a1)),x62461))
% 28.73/28.52 [6247]E(f319(f319(f236(a925),f319(a96,x62471)),x62472),f319(a96,f319(f319(f236(a1),x62471),x62472)))+~P1(f319(f319(f226(a1),f2(a1)),x62471))
% 28.73/28.52 [6265]P1(f319(f129(x62651),x62652))+P1(f319(f319(f227(a925),f688(x62652,x62651)),f319(f181(f926(x62651)),x62652)))
% 28.73/28.52 [6266]P1(f319(f129(x62661),x62662))+P1(f319(f319(f227(a925),f694(x62662,x62661)),f319(f181(f926(x62661)),x62662)))
% 28.73/28.52 [6278]~E(x62781,f105(x62782))+~P1(f319(f319(f227(a925),f2(a925)),f319(f181(f926(x62782)),x62781)))
% 28.73/28.52 [6289]E(f136(a925,f131(a925,f319(f294(a925,x62891),x62892))),f319(f319(f23(a925),x62892),f72(a925)))+~P1(f319(f319(f227(a925),x62891),x62892))
% 28.73/28.52 [6292]E(f319(f319(f74(a1),x62921),f319(f92(a1),f319(a104,f419(x62922,x62921)))),x62922)+~P1(f319(f319(f227(a1),x62921),x62922))
% 28.73/28.52 [6299]E(x62991,f2(a925))+E(f319(f319(f75(a925),x62992),f319(f319(f236(a925),x62992),f319(f319(f23(a925),x62991),f72(a925)))),f319(f319(f236(a925),x62992),x62991))
% 28.73/28.52 [6327]E(f319(f319(f75(a925),f319(a96,x63271)),f319(a96,x63272)),f319(a96,f319(f319(f75(a1),x63271),x63272)))+~P1(f319(f319(f226(a1),f2(a1)),x63271))
% 28.73/28.52 [6328]E(f319(f319(f30(a925),f319(a96,x63281)),f319(a96,x63282)),f319(a96,f319(f319(f30(a1),x63281),x63282)))+~P1(f319(f319(f226(a1),f2(a1)),x63281))
% 28.73/28.52 [6342]~P121(x63421)+E(f319(f319(f74(x63421),x63422),x63422),f319(f319(f75(x63421),f319(f319(f74(x63421),f72(x63421)),f72(x63421))),x63422))
% 28.73/28.52 [6363]E(f319(f319(f23(a1),f319(f92(a1),x63631)),f319(f92(a1),x63632)),f319(f92(a1),f319(f319(f23(a925),x63631),x63632)))+~P1(f319(f319(f226(a925),x63632),x63631))
% 28.73/28.52 [6365]E(f319(f319(f244(a1,a1),f319(f95(a1),a89)),f319(f319(f74(a1),x63651),x63652)),f44(x63651,x63652))+~P1(f319(f319(f226(a1),x63652),f2(a1)))
% 28.73/28.52 [6397]E(f171(x63971,x63972),f105(f926(x63971)))+P1(f319(f319(f321(f926(x63971)),f687(x63972,x63971)),f319(f164(f926(x63971)),x63972)))
% 28.73/28.52 [6406]E(f108(a1,f319(f121(a1),x64061),f120(x64062,f319(f319(f74(a1),x64061),f72(a1)))),f120(x64062,x64061))+P1(f319(f319(f227(a1),x64062),x64061))
% 28.73/28.52 [6481]E(f319(f319(f143(a1),x64811),f170(f319(f319(f74(a1),x64811),f72(a1)),x64812)),f170(x64811,x64812))+~P1(f319(f319(f226(a1),x64811),x64812))
% 28.73/28.52 [6521]~P1(f319(f319(f227(a925),x65212),x65211))+P1(f319(f319(f227(a925),f2(a925)),f319(f319(f23(a925),x65211),x65212)))
% 28.73/28.52 [6553]~P1(f319(f319(f227(a925),x65531),f319(a96,x65532)))+P1(f319(f319(f227(a1),f319(f92(a1),x65531)),x65532))
% 28.73/28.52 [6582]~P4(x65821)+E(f319(f319(f102(f932(x65821,a923)),f319(f274(x65821),x65822)),f319(f319(f301(x65821),x65822),f180(f932(x65821,a923)))),f319(f293(x65821),x65822))
% 28.73/28.52 [6583]~P1(f319(f319(f226(a1),f2(a1)),x65831))+P1(f319(f319(f226(a1),f2(a1)),f319(f319(f236(a1),x65831),x65832)))
% 28.73/28.52 [6584]~P1(f319(f319(f227(a925),f2(a925)),x65842))+P1(f319(f319(f227(a925),f2(a925)),f319(f319(f74(a925),x65841),x65842)))
% 28.73/28.52 [6585]~P1(f319(f319(f227(a925),f2(a925)),x65851))+P1(f319(f319(f227(a925),f2(a925)),f319(f319(f74(a925),x65851),x65852)))
% 28.73/28.52 [6586]~P1(f319(f319(f227(a925),f2(a925)),x65861))+P1(f319(f319(f227(a925),f2(a925)),f319(f319(f236(a925),x65861),x65862)))
% 28.73/28.52 [6616]~E(f319(x66161,f2(a925)),f2(a925))+E(f319(f319(f6(a925,a925),x66161),f295(a925,f319(a104,f2(a925)),x66162)),f319(f319(f6(a925,a925),x66161),f295(a925,f2(a925),x66162)))
% 28.73/28.52 [6680]~P99(x66801)+E(f319(f319(f75(x66801),f319(f319(f74(x66801),f72(x66801)),f72(x66801))),f319(f95(x66801),x66802)),f319(f95(x66801),f319(f319(f74(a1),x66802),x66802)))
% 28.73/28.52 [6697]E(f319(f319(f301(a1),x66971),f295(a1,f319(f319(f74(a1),x66971),f72(a1)),x66972)),f295(a1,x66971,x66972))+P1(f319(f319(f227(a1),x66972),x66971))
% 28.73/28.52 [6698]P1(f319(f319(f227(a925),x66981),f319(a96,x66982)))+~P1(f319(f319(f227(a1),f319(f92(a1),x66981)),x66982))
% 28.73/28.52 [6800]E(f319(a96,f319(f319(f236(a1),f319(f95(a1),x68001)),f319(f95(a925),x68002))),f319(f319(f236(a925),f319(f95(a925),x68001)),f319(f95(a925),x68002)))+P1(f319(a185,f319(f95(a1),x68001)))
% 28.73/28.52 [6801]E(f319(a96,f319(f319(f30(a1),f319(f95(a1),x68011)),f319(f95(a1),x68012))),f319(f319(f30(a925),f319(f95(a925),x68011)),f319(f95(a925),x68012)))+P1(f319(a185,f319(f95(a1),x68011)))
% 28.73/28.52 [6863]P1(f319(f319(f227(a925),x68631),x68632))+~P1(f319(f319(f227(a925),f2(a925)),f319(f319(f23(a925),x68632),x68631)))
% 28.73/28.52 [6908]P1(f319(f319(f227(a925),f2(a925)),x69081))+~P1(f319(f319(f227(a925),f2(a925)),f319(f319(f75(a925),x69082),x69081)))
% 28.73/28.52 [6909]P1(f319(f319(f227(a925),f2(a925)),x69091))+~P1(f319(f319(f227(a925),f2(a925)),f319(f319(f75(a925),x69091),x69092)))
% 28.73/28.52 [6927]E(f131(a925,f319(f294(a925,f319(f95(a925),x69271)),f319(f95(a925),x69272))),f105(a925))+P1(f319(f319(f227(a925),f319(f95(a925),x69271)),f319(f95(a925),x69272)))
% 28.73/28.52 [6929]~P1(f319(f319(f226(a1),x69291),f2(a1)))+E(f319(f319(f75(a925),f319(a96,f319(f73(a1),x69291))),f319(a96,f319(f73(a1),x69292))),f319(a96,f319(f319(f75(a1),x69291),x69292)))
% 28.73/28.52 [6985]~E(x69852,f180(f932(x69851,a923)))+P1(f319(f319(f226(f932(x69851,a923)),x69852),f319(f73(f932(x69851,a923)),x69852)))
% 28.73/28.52 [7047]~P99(x70471)+E(f319(f319(f74(x70471),f319(f319(f74(x70471),f2(x70471)),f319(f95(x70471),x70472))),f319(f95(x70471),x70472)),f319(f95(x70471),f319(f319(f74(a1),x70472),x70472)))
% 28.73/28.52 [7104]~P1(f319(f319(f227(a1),x71041),x71042))+P1(f319(f319(f226(a1),f319(f319(f74(a1),x71041),f72(a1))),x71042))
% 28.73/28.52 [7105]~P1(f319(f319(f227(a1),x71051),x71052))+P1(f319(f319(f226(a1),f319(f319(f74(a1),x71051),f72(a1))),x71052))
% 28.73/28.52 [7171]E(x71711,f2(a925))+~P1(f319(f319(f226(a1),f319(f92(a1),x71712)),f319(f73(a1),f319(f92(a1),x71711))))
% 28.73/28.52 [7172]E(x71721,f2(a925))+~P1(f319(f319(f226(a1),f319(f92(a1),x71721)),f319(f73(a1),f319(f92(a1),x71722))))
% 28.73/28.52 [7273]E(f319(f319(f244(a1,a1),f319(f95(a1),a89)),f319(f319(f74(a1),x72731),x72732)),f44(x72731,x72732))+~P1(f319(f319(f226(a1),f2(a1)),f319(f319(f74(a1),x72731),x72732)))
% 28.73/28.52 [7318]~P28(x73181,x73182)+P38(x73181,f319(f243(f932(f931(x73181,x73181),a923),f932(f931(x73181,x73181),a923)),x73182))
% 28.73/28.52 [7337]~P1(f319(f319(f226(a925),f319(a104,f2(a925))),x73371))+P1(f319(f319(f226(a925),f319(a104,f2(a925))),f319(f319(f236(a925),x73371),x73372)))
% 28.73/28.52 [7516]~P1(f319(f319(f226(a1),x75161),x75162))+P1(f319(f319(f226(a1),f319(f319(f74(a1),x75161),x75161)),f319(f319(f74(a1),x75162),x75162)))
% 28.73/28.52 [7517]~P1(f319(f319(f226(a1),x75171),x75172))+P1(f319(f319(f226(a1),f319(f319(f74(a1),x75171),x75171)),f319(f319(f74(a1),x75172),x75172)))
% 28.73/28.52 [7521]~P1(f319(f319(f227(a1),x75211),x75212))+P1(f319(f319(f227(a1),f319(f319(f74(a1),x75211),x75211)),f319(f319(f74(a1),x75212),x75212)))
% 28.73/28.52 [7522]~P1(f319(f319(f227(a1),x75221),x75222))+P1(f319(f319(f227(a1),f319(f319(f74(a1),x75221),x75221)),f319(f319(f74(a1),x75222),x75222)))
% 28.73/28.52 [7577]~P1(f319(f319(f227(a925),f2(a925)),x75771))+P1(f319(f319(f227(a925),f319(f319(f23(a925),x75771),f319(a104,x75772))),x75771))
% 28.73/28.52 [7610]P1(f319(f319(f226(a925),f319(a104,f2(a925))),x76101))+~P1(f319(f319(f226(a925),f319(a104,f2(a925))),f319(f319(f75(a925),x76102),x76101)))
% 28.73/28.52 [7611]P1(f319(f319(f226(a925),f319(a104,f2(a925))),x76111))+~P1(f319(f319(f226(a925),f319(a104,f2(a925))),f319(f319(f75(a925),x76111),x76112)))
% 28.73/28.52 [7615]P1(f319(f319(f226(a925),f319(f319(f156(a925),x76151),x76152)),f319(f157(a925),x76151)))+~P1(f319(f319(f227(a925),x76152),f319(f181(f926(a925)),x76151)))
% 28.73/28.52 [7652]P1(f319(f319(f227(a1),x76521),x76522))+~P1(f319(f319(f226(a1),f319(f319(f74(a1),x76521),f72(a1))),x76522))
% 28.73/28.52 [7661]~P1(f319(f319(f321(a925),x76611),x76612))+P1(f319(f319(f321(a1),f319(f92(a1),x76611)),f319(f302(a925,a1,f92(a1)),x76612)))
% 28.73/28.52 [7694]P1(f319(f55(x76941),f234(f932(x76941,a923))))+~P1(f319(f55(f932(x76942,x76941)),f234(f932(f932(x76942,x76941),a923))))
% 28.73/28.52 [7695]P1(f319(f55(x76951),f234(f932(x76951,a923))))+~P1(f319(f55(f933(x76952,x76951)),f234(f932(f933(x76952,x76951),a923))))
% 28.73/28.52 [7696]P1(f319(f55(x76961),f234(f932(x76961,a923))))+~P1(f319(f55(f933(x76961,x76962)),f234(f932(f933(x76961,x76962),a923))))
% 28.73/28.52 [7733]E(x77331,f180(f932(x77332,a923)))+~P1(f319(f319(f226(f932(x77332,a923)),x77331),f319(f73(f932(x77332,a923)),x77331)))
% 28.73/28.52 [7873]E(f319(f134(f926(x78731),f926(x78731),f126(x78731),f105(x78731)),x78732),f105(x78731))+P1(f319(f319(f321(f926(x78731)),f717(x78732,x78731)),f319(f164(f926(x78731)),x78732)))
% 28.73/28.52 [7874]E(f319(f134(f926(x78741),f926(x78741),f126(x78741),f105(x78741)),x78742),f105(x78741))+P1(f319(f319(f321(f926(x78741)),f718(x78742,x78741)),f319(f164(f926(x78741)),x78742)))
% 28.73/28.52 [8011]E(f171(x80111,f319(f319(f143(f926(x80111)),f105(x80111)),x80112)),f171(x80111,x80112))+~P1(f319(f307(f926(f926(x80111)),f172(x80111)),f319(f319(f143(f926(x80111)),f105(x80111)),x80112)))
% 28.73/28.52 [8109]P1(f319(f319(f226(a1),x81091),x81092))+~P1(f319(f319(f226(a1),f319(f319(f74(a1),x81091),x81091)),f319(f319(f74(a1),x81092),x81092)))
% 28.73/28.52 [8110]P1(f319(f319(f226(a1),x81101),x81102))+~P1(f319(f319(f226(a1),f319(f319(f74(a1),x81101),x81101)),f319(f319(f74(a1),x81102),x81102)))
% 28.73/28.52 [8114]P1(f319(f319(f227(a1),x81141),x81142))+~P1(f319(f319(f227(a1),f319(f319(f74(a1),x81141),x81141)),f319(f319(f74(a1),x81142),x81142)))
% 28.73/28.52 [8115]P1(f319(f319(f227(a1),x81151),x81152))+~P1(f319(f319(f227(a1),f319(f319(f74(a1),x81151),x81151)),f319(f319(f74(a1),x81152),x81152)))
% 28.73/28.52 [8210]~P121(x82101)+E(f319(f319(f75(x82101),f319(f319(f74(x82101),f72(x82101)),f72(x82101))),f319(f319(f6(a925,x82101),f92(x82101)),f295(a925,f72(a925),x82102))),f319(f319(f75(x82101),f319(f92(x82101),x82102)),f319(f319(f74(x82101),f319(f92(x82101),x82102)),f72(x82101))))
% 28.73/28.52 [8245]E(f319(f319(f143(a1),f319(f95(a1),x82451)),f170(f319(f319(f74(a1),f319(f95(a1),x82451)),f72(a1)),f319(f95(a1),x82452))),f170(f319(f95(a1),x82451),f319(f95(a1),x82452)))+~P1(f319(f319(f226(a1),f319(f95(a1),x82451)),f319(f95(a1),x82452)))
% 28.73/28.52 [8260]P1(f319(f319(f321(a925),x82601),x82602))+~P1(f319(f319(f321(a1),f319(f92(a1),x82601)),f319(f302(a925,a1,f92(a1)),x82602)))
% 28.73/28.52 [8419]~P1(f319(f55(x84191),x84192))+E(f319(f302(a925,x84191,f456(x84192,x84191)),f319(f254(a925),f319(f319(f7(a925,a925,a923),f227(a925)),f457(x84192,x84191)))),x84192)
% 28.73/28.52 [8702]P58(x87021,x87022)+P1(f319(f319(f321(f931(x87021,x87021)),f319(f319(f244(x87021,x87021),f540(x87022,x87021)),f540(x87022,x87021))),x87022))
% 28.73/28.52 [8703]P39(x87031,x87032)+P1(f319(f319(f321(f931(x87031,x87031)),f319(f319(f244(x87031,x87031),f808(x87032,x87031)),f811(x87032,x87031))),x87032))
% 28.73/28.52 [8704]P39(x87041,x87042)+P1(f319(f319(f321(f931(x87041,x87041)),f319(f319(f244(x87041,x87041),f811(x87042,x87041)),f812(x87042,x87041))),x87042))
% 28.73/28.52 [8705]P40(x87051,x87052)+P1(f319(f319(f321(f931(x87051,x87051)),f319(f319(f244(x87051,x87051),f728(x87052,x87051)),f727(x87052,x87051))),x87052))
% 28.73/28.52 [8706]P40(x87061,x87062)+P1(f319(f319(f321(f931(x87061,x87061)),f319(f319(f244(x87061,x87061),f727(x87062,x87061)),f728(x87062,x87061))),x87062))
% 28.73/28.52 [8707]P56(x87071,x87072)+P1(f319(f319(f321(f931(x87071,x87071)),f319(f319(f244(x87071,x87071),f822(x87072,x87071)),f823(x87072,x87071))),x87072))
% 28.73/28.52 [8851]~P99(x88511)+E(f319(f319(f23(x88511),f72(x88511)),f319(f95(x88511),x88512)),f319(f95(x88511),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f73(a1),x88512))))
% 28.73/28.52 [8975]~P1(f319(f319(f226(f932(a925,a923)),x89751),x89752))+P1(f319(f319(f226(f932(a1,a923)),f319(f302(a925,a1,f92(a1)),x89751)),f319(f302(a925,a1,f92(a1)),x89752)))
% 28.73/28.52 [8976]~P1(f319(f319(f227(f932(a925,a923)),x89761),x89762))+P1(f319(f319(f227(f932(a1,a923)),f319(f302(a925,a1,f92(a1)),x89761)),f319(f302(a925,a1,f92(a1)),x89762)))
% 28.73/28.52 [9010]~P1(f319(f319(f227(a1),x90101),x90102))+P1(f319(f319(f226(a1),f319(f319(f23(a1),f319(f319(f74(a1),x90101),x90101)),a89)),f319(f319(f74(a1),x90102),x90102)))
% 28.73/28.52 [9011]~P1(f319(f319(f227(a1),x90111),x90112))+P1(f319(f319(f226(a1),f319(f319(f23(a1),f319(f319(f74(a1),x90111),x90111)),a89)),f319(f319(f74(a1),x90112),x90112)))
% 28.73/28.52 [9012]~P1(f319(f319(f227(a1),x90121),x90122))+P1(f319(f319(f227(a1),f319(f319(f23(a1),f319(f319(f74(a1),x90121),x90121)),a89)),f319(f319(f74(a1),x90122),x90122)))
% 28.73/28.52 [9013]~P1(f319(f319(f227(a1),x90131),x90132))+P1(f319(f319(f227(a1),f319(f319(f23(a1),f319(f319(f74(a1),x90131),x90131)),a89)),f319(f319(f74(a1),x90132),x90132)))
% 28.73/28.52 [9086]~P1(f319(f319(f321(a925),x90861),f319(f164(a925),x90862)))+P1(f319(f319(f226(a925),x90861),f319(f134(a925,a925,f74(a925),f2(a925)),x90862)))
% 28.73/28.52 [9180]P47(x91801,x91802)+~P1(f319(f319(f321(f931(x91801,x91801)),f319(f319(f244(x91801,x91801),f532(x91802,x91801)),f532(x91802,x91801))),x91802))
% 28.73/28.52 [9181]P39(x91811,x91812)+~P1(f319(f319(f321(f931(x91811,x91811)),f319(f319(f244(x91811,x91811),f808(x91812,x91811)),f812(x91812,x91811))),x91812))
% 28.73/28.52 [9182]P56(x91821,x91822)+~P1(f319(f319(f321(f931(x91821,x91821)),f319(f319(f244(x91821,x91821),f823(x91822,x91821)),f822(x91822,x91821))),x91822))
% 28.73/28.52 [9323]~P1(f319(f319(f226(f932(a1,a923)),f319(f302(a925,a1,f92(a1)),x93231)),f319(f302(a925,a1,f92(a1)),x93232)))+P1(f319(f319(f226(f932(a925,a923)),x93231),x93232))
% 28.73/28.52 [9324]~P1(f319(f319(f227(f932(a1,a923)),f319(f302(a925,a1,f92(a1)),x93241)),f319(f302(a925,a1,f92(a1)),x93242)))+P1(f319(f319(f227(f932(a925,a923)),x93241),x93242))
% 28.73/28.52 [9410]P1(f319(f319(f227(a1),x94101),x94102))+~P1(f319(f319(f226(a1),f319(f319(f23(a1),f319(f319(f74(a1),x94101),x94101)),a89)),f319(f319(f74(a1),x94102),x94102)))
% 28.73/28.52 [9411]P1(f319(f319(f227(a1),x94111),x94112))+~P1(f319(f319(f226(a1),f319(f319(f23(a1),f319(f319(f74(a1),x94111),x94111)),a89)),f319(f319(f74(a1),x94112),x94112)))
% 28.73/28.52 [9412]P1(f319(f319(f227(a1),x94121),x94122))+~P1(f319(f319(f227(a1),f319(f319(f23(a1),f319(f319(f74(a1),x94121),x94121)),a89)),f319(f319(f74(a1),x94122),x94122)))
% 28.73/28.52 [9413]P1(f319(f319(f227(a1),x94131),x94132))+~P1(f319(f319(f227(a1),f319(f319(f23(a1),f319(f319(f74(a1),x94131),x94131)),a89)),f319(f319(f74(a1),x94132),x94132)))
% 28.73/28.52 [10331]~P111(x103311)+E(f108(f926(x103311),f319(f121(f926(x103311)),f105(x103311)),f319(f319(f319(f86(f927(f926(x103311))),f319(f319(f227(a1),f2(a1)),x103312)),f319(f110(f931(x103311,f926(x103311)),f926(x103311),f123(x103311,f926(x103311),f124(x103311,f319(f319(f23(a1),x103312),f72(a1))),f124(f926(x103311),f319(f319(f23(a1),x103312),f72(a1))))),f319(f249(x103311,f926(x103311),f927(f926(x103311))),f319(f319(f8(f932(f926(x103311),f926(x103311)),f932(f926(x103311),f927(f926(x103311))),x103311),f319(f8(f926(x103311),f927(f926(x103311)),f926(x103311)),f121(f926(x103311)))),f143(x103311))))),f107(f926(x103311)))),f124(f926(x103311),x103312))
% 28.73/28.52 [10353]~P1(f319(f55(x103531),x103532))+E(f319(f181(f926(x103531)),f84(f926(x103531),f319(f319(f18(f926(x103531),a923,a923),f319(f319(f8(a923,f932(a923,a923),f926(x103531)),a317),f319(f319(f7(f926(x103531),f932(x103531,a923),a923),f319(f319(f8(f932(x103531,a923),f932(f932(x103531,a923),a923),f926(x103531)),a316),f164(x103531))),x103532))),f129(x103531)))),f206(x103531,x103532))
% 28.73/28.52 [6288]E(f319(f319(f74(a925),f319(f319(f23(a925),x62881),x62882)),x62882),x62881)+~P1(f319(f319(f226(a925),x62882),x62881))
% 28.73/28.52 [6359]E(f319(f319(f30(a925),f319(f319(f75(a925),x63591),x63592)),x63592),x63591)+~P1(f319(f319(f227(a925),f2(a925)),x63592))
% 28.73/28.52 [6360]E(f319(f319(f30(a925),f319(f319(f75(a925),x63601),x63602)),x63601),x63602)+~P1(f319(f319(f227(a925),f2(a925)),x63601))
% 28.73/28.52 [6364]~P79(x63641)+E(f319(f319(f6(a925,x63641),f319(f156(x63641),x63642)),f319(f294(a925,f2(a925)),f319(f181(f926(x63641)),x63642))),f319(f157(x63641),x63642))
% 28.73/28.52 [6473]E(f39(a925,f319(a104,f319(f319(f75(a925),x64731),x64732)),x64731),f72(a925))+~P1(f319(f319(f227(a925),f72(a925)),x64731))
% 28.73/28.52 [6479]E(f319(a104,f319(f319(f74(a925),f319(f95(a925),x64791)),x64792)),f319(f319(f74(a925),f72(a925)),x64792))+~P1(f319(a185,f319(f95(a1),x64791)))
% 28.73/28.52 [6508]E(f319(a96,f319(f319(f236(a1),f319(f95(a1),x65081)),x65082)),f319(f319(f236(a925),f319(f95(a925),x65081)),x65082))+P1(f319(a185,f319(f95(a1),x65081)))
% 28.73/28.52 [6752]E(f319(f319(f23(a925),x67521),f319(f95(a925),f319(f319(f74(a1),x67522),a89))),f319(f319(f23(a925),f319(a104,x67521)),f319(f95(a925),x67522)))+~P1(f319(f319(f227(a1),a77),x67522))
% 28.73/28.52 [6835]E(x68351,f2(a925))+E(f319(a104,f319(f319(f74(a925),f319(f319(f23(a925),x68351),f72(a925))),x68352)),f319(f319(f74(a925),x68351),x68352))
% 28.73/28.52 [6876]E(x68761,f2(a1))+P1(f319(f319(f227(a1),f2(a1)),f319(f319(f236(a1),f319(f69(a1),x68761)),x68762)))
% 28.73/28.52 [6892]~E(x68922,f2(a925))+P1(f319(f319(f227(a1),f2(a1)),f319(f319(f236(a1),f319(f69(a1),x68921)),x68922)))
% 28.73/28.52 [6932]E(x69321,f2(a925))+E(f319(f319(f74(a925),x69322),f319(f319(f75(a925),f319(f319(f23(a925),x69321),f72(a925))),x69322)),f319(f319(f75(a925),x69321),x69322))
% 28.73/28.52 [6978]~P1(f319(f319(f226(a1),x69781),x69782))+P1(f319(f319(f227(a1),f319(f319(f74(a1),x69781),a89)),x69782))
% 28.73/28.52 [7108]E(f319(f319(f143(a925),x71081),f131(a925,f319(f294(a925,f319(a104,x71081)),x71082))),f131(a925,f319(f294(a925,x71081),x71082)))+~P1(f319(f319(f227(a925),x71081),x71082))
% 28.73/28.52 [7109]E(f319(f319(f143(a925),x71091),f131(a925,f319(f294(a925,f319(a104,x71091)),x71092))),f131(a925,f319(f294(a925,x71091),x71092)))+~P1(f319(f319(f227(a925),x71091),x71092))
% 28.73/28.52 [7309]E(x73091,x73092)+~E(f319(f319(f23(a1),f319(f319(f74(a1),x73091),x73091)),a89),f319(f319(f23(a1),f319(f319(f74(a1),x73092),x73092)),a89))
% 28.73/28.52 [7312]E(x73121,f105(x73122))+E(f258(x73122,f319(f319(f146(x73122,f931(a91,x73122)),f319(f244(a91,x73122),f72(a91))),x73121)),f267(x73122,x73121))
% 28.73/28.52 [7548]P1(f319(f319(f226(a1),x75481),x75482))+~P1(f319(f319(f227(a1),f319(f319(f74(a1),x75481),a89)),x75482))
% 28.73/28.52 [8013]~P1(f319(f319(f227(a925),x80131),x80132))+P1(f319(f319(f321(f931(a925,a925)),f319(f319(f244(a925,a925),x80131),x80132)),a232))
% 28.73/28.52 [8237]~P1(f319(f319(f227(a91),f2(a91)),x82371))+P1(f319(f319(f227(a91),f319(f243(a91,f931(a91,a91)),f319(f259(x82371),x82372))),x82371))
% 28.73/28.52 [8501]~P39(x85011,x85012)+P39(x85011,f319(f319(f102(f932(f931(x85011,x85011),a923)),x85012),f299(x85011,f180(f932(f931(x85011,x85011),a923)))))
% 28.73/28.52 [8502]~P40(x85021,x85022)+P40(x85021,f319(f319(f102(f932(f931(x85021,x85021),a923)),x85022),f299(x85021,f180(f932(f931(x85021,x85021),a923)))))
% 28.73/28.52 [8552]~P92(x85521)+P1(f319(f319(f226(x85521),f319(f69(x85521),f319(f157(x85521),x85522))),f319(f157(x85521),f319(f319(f146(x85521,x85521),f69(x85521)),x85522))))
% 28.73/28.52 [8577]P1(f319(f319(f227(a925),x85771),x85772))+~P1(f319(f319(f321(f931(a925,a925)),f319(f319(f244(a925,a925),x85771),x85772)),a232))
% 28.73/28.52 [8729]E(f319(f319(f244(x87291,x87291),f648(x87292,x87291)),f648(x87292,x87291)),x87292)+~P1(f319(f319(f321(f931(x87291,x87291)),x87292),f299(x87291,f180(f932(f931(x87291,x87291),a923)))))
% 28.73/28.52 [8772]E(f319(f294(a925,x87721),f319(f319(f74(a925),x87721),f319(f29(a925),x87722))),x87722)+~P1(f319(f319(f226(f932(a925,a923)),x87722),f319(f294(a925,x87721),f319(f319(f74(a925),x87721),f319(f29(a925),x87722)))))
% 28.73/28.52 [8793]E(f319(f319(f143(a925),f319(f95(a925),x87931)),f131(a925,f319(f294(a925,f319(a104,f319(f95(a925),x87931))),f319(f95(a925),x87932)))),f131(a925,f319(f294(a925,f319(f95(a925),x87931)),f319(f95(a925),x87932))))+~P1(f319(f319(f227(a925),f319(f95(a925),x87931)),f319(f95(a925),x87932)))
% 28.73/28.52 [9004]P40(x90041,x90042)+~P40(x90041,f319(f319(f102(f932(f931(x90041,x90041),a923)),x90042),f299(x90041,f180(f932(f931(x90041,x90041),a923)))))
% 28.73/28.52 [9131]E(f319(f319(f30(a1),f319(f95(a1),f319(f319(f23(a1),f319(f319(f74(a1),x91311),x91311)),a89))),f319(f95(a1),f319(f319(f74(a1),x91312),x91312))),f319(f319(f30(a1),f319(f95(a1),x91311)),f319(f95(a1),x91312)))+~P1(f319(f319(f226(a1),f2(a1)),f319(f95(a1),x91312)))
% 28.73/28.52 [9226]~P39(x92261,x92262)+P1(f319(f319(f226(f932(f931(x92261,x92261),a923)),f319(f319(f281(x92261,x92261,x92261),x92262),x92262)),x92262))
% 28.73/28.52 [9252]E(f169(f926(x92521),f319(f319(f8(a923,a923,f926(x92521)),a314),f319(f319(f7(f926(x92521),f926(x92521),a923),a316),f105(x92521))),x92522),f171(x92521,f171(x92521,x92522)))+~P14(a925,f319(f160(a925),f319(f319(f146(f926(x92521),a925),f181(f926(x92521))),x92522)))
% 28.73/28.52 [9255]E(f319(f319(f30(a1),f319(f95(a1),f319(f319(f23(a1),f319(f319(f74(a1),x92551),x92551)),a89))),f319(f95(a1),f319(f319(f74(a1),x92552),x92552))),f319(f319(f30(a1),f319(f319(f74(a1),f319(f95(a1),x92551)),f72(a1))),f319(f95(a1),x92552)))+P1(f319(f319(f226(a1),f2(a1)),f319(f95(a1),x92552)))
% 28.73/28.52 [10123]P1(f319(a185,x101232))+E(f319(f319(f80(a1,a925),f319(f319(f23(a1),x101231),x101232)),f319(f319(f18(a1,a925,a925),f319(f319(f7(a1,a925,f932(a925,a925)),f319(f319(f8(a923,f932(a925,f932(a925,a925)),a1),f86(a925)),a185)),f2(a925))),a96)),f319(f319(f23(a925),f319(a96,x101231)),f319(a96,x101232)))
% 28.73/28.52 [10131]E(f319(f319(f80(a1,a925),f319(f95(a1),f319(f319(f74(a1),x101311),f319(f73(a1),x101312)))),f319(f319(f18(a1,a925,a925),f319(f319(f7(a1,a925,f932(a925,a925)),f319(f319(f8(a923,f932(a925,f932(a925,a925)),a1),f86(a925)),a185)),f2(a925))),a96)),f319(f319(f23(a925),f319(f95(a925),x101311)),f319(f95(a925),x101312)))+P1(f319(f319(f227(a1),x101312),a77))
% 28.73/28.52 [10132]~P28(x101321,x101322)+P1(f319(f319(f226(f932(f931(x101321,x101321),a923)),f319(f319(f281(x101321,x101321,x101321),f319(f243(f932(f931(x101321,x101321),a923),f932(f931(x101321,x101321),a923)),x101322)),f319(f248(f932(f931(x101321,x101321),a923),f932(f931(x101321,x101321),a923)),x101322))),f319(f243(f932(f931(x101321,x101321),a923),f932(f931(x101321,x101321),a923)),x101322)))
% 28.73/28.52 [10187]~E(f319(f29(a925),f319(f254(a925),f319(f319(f18(a925,a923,a923),f319(f319(f8(a923,f932(a923,a923),a925),a317),f319(f319(f7(a925,f932(a925,a923),a923),f321(a925)),x101871))),f319(f319(f7(a925,a925,a923),f227(a925)),f319(a104,x101872))))),f2(a925))+~P1(f319(f319(f321(a925),f2(a925)),x101871))
% 28.73/28.52 [10201]E(f291(a925,f319(f319(f18(a925,f932(a925,a923),f932(a925,a923)),f319(f319(f8(f932(a925,f932(a923,a923)),f932(f932(a925,a923),f932(a925,a923)),a925),f18(a925,a923,a923)),f319(f319(f8(f932(a925,a923),f932(a925,f932(a923,a923)),a925),f319(f8(a923,f932(a923,a923),a925),a317)),f279(a925)))),f319(f319(f8(f932(a925,a923),f932(a925,a923),a925),f319(f8(a923,a923,a925),a314)),f319(f7(a925,a925,a923),f279(a925)))),x102011,x102012),f180(f932(a925,a923)))+~P1(f319(f319(f279(a925),x102012),x102011))
% 28.73/28.52 [10204]E(f292(a925,f279(a925),f319(f319(f18(a925,f932(a925,a923),f932(a925,a923)),f319(f319(f8(f932(a925,f932(a923,a923)),f932(f932(a925,a923),f932(a925,a923)),a925),f18(a925,a923,a923)),f319(f319(f8(f932(a925,a923),f932(a925,f932(a923,a923)),a925),f319(f8(a923,f932(a923,a923),a925),a317)),f279(a925)))),f319(f319(f8(f932(a925,a923),f932(a925,a923),a925),f319(f8(a923,a923,a925),a314)),f319(f7(a925,a925,a923),f279(a925)))),x102041,x102042),f180(f932(a925,a923)))+P1(f319(f319(f279(a925),x102041),x102042))
% 28.73/28.52 [10205]E(f292(a925,f279(a925),f319(f319(f18(a925,f932(a925,a923),f932(a925,a923)),f319(f319(f8(f932(a925,f932(a923,a923)),f932(f932(a925,a923),f932(a925,a923)),a925),f18(a925,a923,a923)),f319(f319(f8(f932(a925,a923),f932(a925,f932(a923,a923)),a925),f319(f8(a923,f932(a923,a923),a925),a317)),f279(a925)))),f319(f319(f8(f932(a925,a923),f932(a925,a923),a925),f319(f8(a923,a923,a925),a314)),f319(f7(a925,a925,a923),f279(a925)))),x102051,x102052),f180(f932(a925,a923)))+P1(f319(f319(f279(a925),x102051),x102052))
% 28.73/28.52 [10206]E(f289(a925,f279(a925),f319(f319(f18(a925,f932(a925,a923),f932(a925,a923)),f319(f319(f8(f932(a925,f932(a923,a923)),f932(f932(a925,a923),f932(a925,a923)),a925),f18(a925,a923,a923)),f319(f319(f8(f932(a925,a923),f932(a925,f932(a923,a923)),a925),f319(f8(a923,f932(a923,a923),a925),a317)),f279(a925)))),f319(f319(f8(f932(a925,a923),f932(a925,a923),a925),f319(f8(a923,a923,a925),a314)),f319(f7(a925,a925,a923),f279(a925)))),x102061,x102062),f180(f932(a925,a923)))+P1(f319(f319(f279(a925),x102061),x102062))
% 28.73/28.52 [10207]E(f292(a925,f279(a925),f319(f319(f18(a925,f932(a925,a923),f932(a925,a923)),f319(f319(f8(f932(a925,f932(a923,a923)),f932(f932(a925,a923),f932(a925,a923)),a925),f18(a925,a923,a923)),f319(f319(f8(f932(a925,a923),f932(a925,f932(a923,a923)),a925),f319(f8(a923,f932(a923,a923),a925),a317)),f279(a925)))),f319(f319(f8(f932(a925,a923),f932(a925,a923),a925),f319(f8(a923,a923,a925),a314)),f319(f7(a925,a925,a923),f279(a925)))),x102071,x102072),f180(f932(a925,a923)))+~P1(f319(f319(f279(a925),x102072),x102071))
% 28.73/28.52 [10208]E(f292(a925,f279(a925),f319(f319(f18(a925,f932(a925,a923),f932(a925,a923)),f319(f319(f8(f932(a925,f932(a923,a923)),f932(f932(a925,a923),f932(a925,a923)),a925),f18(a925,a923,a923)),f319(f319(f8(f932(a925,a923),f932(a925,f932(a923,a923)),a925),f319(f8(a923,f932(a923,a923),a925),a317)),f279(a925)))),f319(f319(f8(f932(a925,a923),f932(a925,a923),a925),f319(f8(a923,a923,a925),a314)),f319(f7(a925,a925,a923),f279(a925)))),x102081,x102082),f180(f932(a925,a923)))+~P1(f319(f319(f279(a925),x102082),x102081))
% 28.73/28.52 [10209]E(f292(a925,f279(a925),f319(f319(f18(a925,f932(a925,a923),f932(a925,a923)),f319(f319(f8(f932(a925,f932(a923,a923)),f932(f932(a925,a923),f932(a925,a923)),a925),f18(a925,a923,a923)),f319(f319(f8(f932(a925,a923),f932(a925,f932(a923,a923)),a925),f319(f8(a923,f932(a923,a923),a925),a317)),f279(a925)))),f319(f319(f8(f932(a925,a923),f932(a925,a923),a925),f319(f8(a923,a923,a925),a314)),f319(f7(a925,a925,a923),f279(a925)))),x102091,x102092),f180(f932(a925,a923)))+~P1(f319(f319(f279(a925),x102092),x102091))
% 28.73/28.52 [10210]E(f289(a925,f279(a925),f319(f319(f18(a925,f932(a925,a923),f932(a925,a923)),f319(f319(f8(f932(a925,f932(a923,a923)),f932(f932(a925,a923),f932(a925,a923)),a925),f18(a925,a923,a923)),f319(f319(f8(f932(a925,a923),f932(a925,f932(a923,a923)),a925),f319(f8(a923,f932(a923,a923),a925),a317)),f279(a925)))),f319(f319(f8(f932(a925,a923),f932(a925,a923),a925),f319(f8(a923,a923,a925),a314)),f319(f7(a925,a925,a923),f279(a925)))),x102101,x102102),f180(f932(a925,a923)))+~P1(f319(f319(f279(a925),x102102),x102101))
% 28.73/28.52 [10211]E(f289(a925,f279(a925),f319(f319(f18(a925,f932(a925,a923),f932(a925,a923)),f319(f319(f8(f932(a925,f932(a923,a923)),f932(f932(a925,a923),f932(a925,a923)),a925),f18(a925,a923,a923)),f319(f319(f8(f932(a925,a923),f932(a925,f932(a923,a923)),a925),f319(f8(a923,f932(a923,a923),a925),a317)),f279(a925)))),f319(f319(f8(f932(a925,a923),f932(a925,a923),a925),f319(f8(a923,a923,a925),a314)),f319(f7(a925,a925,a923),f279(a925)))),x102111,x102112),f180(f932(a925,a923)))+~P1(f319(f319(f279(a925),x102112),x102111))
% 28.73/28.52 [10256]E(f39(a1,f319(f95(a1),f319(f319(f23(a1),f319(f319(f74(a1),x102561),x102561)),a89)),f319(f95(a1),f319(f319(f74(a1),x102562),x102562))),f319(f319(f74(a1),f319(f319(f75(a1),f319(f95(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),f39(a1,f319(f95(a1),x102561),f319(f95(a1),x102562)))),f72(a1)))+~P1(f319(f319(f226(a1),f2(a1)),f319(f95(a1),x102562)))
% 28.73/28.52 [10265]E(f39(a1,f319(f95(a1),f319(f319(f23(a1),f319(f319(f74(a1),x102651),x102651)),a89)),f319(f95(a1),f319(f319(f74(a1),x102652),x102652))),f319(f319(f23(a1),f319(f319(f75(a1),f319(f95(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),f39(a1,f319(f319(f74(a1),f319(f95(a1),x102651)),f72(a1)),f319(f95(a1),x102652)))),f72(a1)))+P1(f319(f319(f226(a1),f2(a1)),f319(f95(a1),x102652)))
% 28.73/28.52 [10321]~P6(x103211)+E(f31(x103211,f319(f254(x103211),f319(f319(f8(f932(x103211,a923),a923,x103211),f82(x103211)),f319(f319(f8(f932(x103211,a923),f932(x103211,a923),x103211),f319(f18(x103211,a923,a923),f319(f319(f8(a923,f932(a923,a923),x103211),a322),f319(f319(f7(x103211,f932(x103211,a923),a923),f321(x103211)),x103212)))),f226(x103211))))),f32(x103211,x103212))
% 28.73/28.52 [10346]~P38(x103461,x103462)+P64(x103461,f319(f319(f7(x103461,f932(f931(x103461,x103461),a923),f932(x103461,a923)),f319(f319(f8(f932(x103461,f932(f932(f931(x103461,x103461),a923),a923)),f932(f932(f931(x103461,x103461),a923),f932(x103461,a923)),x103461),f7(x103461,f932(f931(x103461,x103461),a923),a923)),f319(f319(f8(f932(x103461,f931(x103461,x103461)),f932(x103461,f932(f932(f931(x103461,x103461),a923),a923)),x103461),f319(f8(f931(x103461,x103461),f932(f932(f931(x103461,x103461),a923),a923),x103461),f321(f931(x103461,x103461)))),f244(x103461,x103461)))),x103462))
% 28.73/28.52 [10347]~P9(x103471,f234(f932(x103471,a923)),x103472)+P8(x103471,f319(f319(f7(x103471,f932(f931(x103471,x103471),a923),f932(x103471,a923)),f319(f319(f8(f932(x103471,f932(f932(f931(x103471,x103471),a923),a923)),f932(f932(f931(x103471,x103471),a923),f932(x103471,a923)),x103471),f7(x103471,f932(f931(x103471,x103471),a923),a923)),f319(f319(f8(f932(x103471,f931(x103471,x103471)),f932(x103471,f932(f932(f931(x103471,x103471),a923),a923)),x103471),f319(f8(f931(x103471,x103471),f932(f932(f931(x103471,x103471),a923),a923),x103471),f321(f931(x103471,x103471)))),f244(x103471,x103471)))),x103472))
% 28.73/28.52 [10389]P38(x103891,x103892)+~P64(x103891,f319(f319(f7(x103891,f932(f931(x103891,x103891),a923),f932(x103891,a923)),f319(f319(f8(f932(x103891,f932(f932(f931(x103891,x103891),a923),a923)),f932(f932(f931(x103891,x103891),a923),f932(x103891,a923)),x103891),f7(x103891,f932(f931(x103891,x103891),a923),a923)),f319(f319(f8(f932(x103891,f931(x103891,x103891)),f932(x103891,f932(f932(f931(x103891,x103891),a923),a923)),x103891),f319(f8(f931(x103891,x103891),f932(f932(f931(x103891,x103891),a923),a923),x103891),f321(f931(x103891,x103891)))),f244(x103891,x103891)))),x103892))
% 28.73/28.52 [10390]P9(x103901,f234(f932(x103901,a923)),x103902)+~P8(x103901,f319(f319(f7(x103901,f932(f931(x103901,x103901),a923),f932(x103901,a923)),f319(f319(f8(f932(x103901,f932(f932(f931(x103901,x103901),a923),a923)),f932(f932(f931(x103901,x103901),a923),f932(x103901,a923)),x103901),f7(x103901,f932(f931(x103901,x103901),a923),a923)),f319(f319(f8(f932(x103901,f931(x103901,x103901)),f932(x103901,f932(f932(f931(x103901,x103901),a923),a923)),x103901),f319(f8(f931(x103901,x103901),f932(f932(f931(x103901,x103901),a923),a923),x103901),f321(f931(x103901,x103901)))),f244(x103901,x103901)))),x103902))
% 28.73/28.52 [7497]E(f319(f319(f74(a925),f319(f95(a925),f319(f319(f23(a1),x74971),a89))),x74972),f319(a104,f319(f319(f74(a925),f319(f95(a925),x74971)),x74972)))+P1(f319(a185,f319(f95(a1),x74971)))
% 28.73/28.52 [7931]~P99(x79311)+E(f319(f319(f74(x79311),f319(f319(f74(x79311),f72(x79311)),f319(f95(x79311),x79312))),f319(f95(x79311),x79312)),f319(f95(x79311),f319(f319(f23(a1),f319(f319(f74(a1),x79312),x79312)),a89)))
% 28.73/28.52 [8578]~P1(f319(f319(f226(a1),x85781),x85782))+P1(f319(f319(f226(a1),f319(f319(f74(a1),x85781),x85781)),f319(f319(f23(a1),f319(f319(f74(a1),x85782),x85782)),a89)))
% 28.73/28.52 [8579]~P1(f319(f319(f226(a1),x85791),x85792))+P1(f319(f319(f226(a1),f319(f319(f74(a1),x85791),x85791)),f319(f319(f23(a1),f319(f319(f74(a1),x85792),x85792)),a89)))
% 28.73/28.52 [8580]~P1(f319(f319(f226(a1),x85801),x85802))+P1(f319(f319(f227(a1),f319(f319(f74(a1),x85801),x85801)),f319(f319(f23(a1),f319(f319(f74(a1),x85802),x85802)),a89)))
% 28.73/28.52 [8581]~P1(f319(f319(f226(a1),x85811),x85812))+P1(f319(f319(f227(a1),f319(f319(f74(a1),x85811),x85811)),f319(f319(f23(a1),f319(f319(f74(a1),x85812),x85812)),a89)))
% 28.73/28.52 [9014]P1(f319(f319(f226(a1),x90141),x90142))+~P1(f319(f319(f226(a1),f319(f319(f74(a1),x90141),x90141)),f319(f319(f23(a1),f319(f319(f74(a1),x90142),x90142)),a89)))
% 28.73/28.52 [9015]P1(f319(f319(f226(a1),x90151),x90152))+~P1(f319(f319(f226(a1),f319(f319(f74(a1),x90151),x90151)),f319(f319(f23(a1),f319(f319(f74(a1),x90152),x90152)),a89)))
% 28.73/28.52 [9016]P1(f319(f319(f226(a1),x90161),x90162))+~P1(f319(f319(f227(a1),f319(f319(f74(a1),x90161),x90161)),f319(f319(f23(a1),f319(f319(f74(a1),x90162),x90162)),a89)))
% 28.73/28.52 [9017]P1(f319(f319(f226(a1),x90171),x90172))+~P1(f319(f319(f227(a1),f319(f319(f74(a1),x90171),x90171)),f319(f319(f23(a1),f319(f319(f74(a1),x90172),x90172)),a89)))
% 28.73/28.52 [9311]~P1(f319(f319(f226(a1),x93111),x93112))+P1(f319(f319(f226(a1),f319(f319(f23(a1),f319(f319(f74(a1),x93111),x93111)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),x93112),x93112)),a89)))
% 28.73/28.52 [9312]~P1(f319(f319(f226(a1),x93121),x93122))+P1(f319(f319(f226(a1),f319(f319(f23(a1),f319(f319(f74(a1),x93121),x93121)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),x93122),x93122)),a89)))
% 28.73/28.52 [9313]~P1(f319(f319(f227(a1),x93131),x93132))+P1(f319(f319(f227(a1),f319(f319(f23(a1),f319(f319(f74(a1),x93131),x93131)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),x93132),x93132)),a89)))
% 28.73/28.52 [9314]~P1(f319(f319(f227(a1),x93141),x93142))+P1(f319(f319(f227(a1),f319(f319(f23(a1),f319(f319(f74(a1),x93141),x93141)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),x93142),x93142)),a89)))
% 28.73/28.52 [9586]P1(f319(f319(f226(a1),x95861),x95862))+~P1(f319(f319(f226(a1),f319(f319(f23(a1),f319(f319(f74(a1),x95861),x95861)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),x95862),x95862)),a89)))
% 28.73/28.52 [9587]P1(f319(f319(f226(a1),x95871),x95872))+~P1(f319(f319(f226(a1),f319(f319(f23(a1),f319(f319(f74(a1),x95871),x95871)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),x95872),x95872)),a89)))
% 28.73/28.52 [9588]P1(f319(f319(f227(a1),x95881),x95882))+~P1(f319(f319(f227(a1),f319(f319(f23(a1),f319(f319(f74(a1),x95881),x95881)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),x95882),x95882)),a89)))
% 28.73/28.52 [9589]P1(f319(f319(f227(a1),x95891),x95892))+~P1(f319(f319(f227(a1),f319(f319(f23(a1),f319(f319(f74(a1),x95891),x95891)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),x95892),x95892)),a89)))
% 28.73/28.52 [9622]~P1(f319(f55(x96221),x96222))+P1(f319(f55(f932(x96221,a923)),f319(f254(f932(x96221,a923)),f319(f319(f7(f932(x96221,a923),f932(x96221,a923),a923),f226(f932(x96221,a923))),x96222))))
% 28.73/28.52 [9674]~E(f319(f277(f931(a925,a925),f931(a925,a925),a100),f319(f319(f301(f931(a925,a925)),x96741),f180(f932(f931(a925,a925),a923)))),f319(f277(f931(a925,a925),f931(a925,a925),a100),f319(f319(f301(f931(a925,a925)),x96742),f180(f932(f931(a925,a925),a923)))))+P1(f319(f319(f321(f931(f931(a925,a925),f931(a925,a925))),f319(f319(f244(f931(a925,a925),f931(a925,a925)),x96741),x96742)),a100))
% 28.73/28.52 [9761]E(f319(f277(f931(a925,a925),f931(a925,a925),a100),f319(f319(f301(f931(a925,a925)),x97611),f180(f932(f931(a925,a925),a923)))),f319(f277(f931(a925,a925),f931(a925,a925),a100),f319(f319(f301(f931(a925,a925)),x97612),f180(f932(f931(a925,a925),a923)))))+~P1(f319(f319(f321(f931(f931(a925,a925),f931(a925,a925))),f319(f319(f244(f931(a925,a925),f931(a925,a925)),x97611),x97612)),a100))
% 28.73/28.52 [9799]P1(f319(f319(f226(a1),f2(a1)),f663(x97991,x97992)))+E(f319(f254(a1),f319(f319(f18(a1,a923,a923),f319(f319(f8(a923,f932(a923,a923),a1),a317),f319(f226(a1),f2(a1)))),x97991)),f319(f254(a1),f319(f319(f18(a1,a923,a923),f319(f319(f8(a923,f932(a923,a923),a1),a317),f319(f226(a1),f2(a1)))),x97992)))
% 28.73/28.52 [10330]~P6(x103301)+E(f32(x103301,f319(f254(x103301),f319(f319(f8(f932(x103301,a923),a923,x103301),f82(x103301)),f319(f319(f8(f932(x103301,a923),f932(x103301,a923),x103301),f319(f18(x103301,a923,a923),f319(f319(f8(a923,f932(a923,a923),x103301),a322),f319(f319(f7(x103301,f932(x103301,a923),a923),f321(x103301)),x103302)))),f319(f7(x103301,x103301,a923),f226(x103301)))))),f31(x103301,x103302))
% 28.73/28.52 [10352]P1(f319(f319(f321(a925),f2(a925)),x103521))+E(f319(f29(a925),f319(f254(a925),f319(f319(f18(a925,a923,a923),f319(f319(f8(a923,f932(a923,a923),a925),a317),f319(f319(f7(a925,f932(a925,a923),a923),f319(f319(f8(a925,f932(f932(a925,a923),a923),a925),f321(a925)),a104)),x103521))),f319(f319(f7(a925,a925,a923),f227(a925)),x103522)))),f319(f29(a925),f319(f254(a925),f319(f319(f18(a925,a923,a923),f319(f319(f8(a923,f932(a923,a923),a925),a317),f319(f319(f7(a925,f932(a925,a923),a923),f321(a925)),x103521))),f319(f319(f7(a925,a925,a923),f227(a925)),f319(a104,x103522))))))
% 28.73/28.52 [7799]~P99(x77991)+E(f319(f319(f75(x77991),x77992),f319(f95(x77991),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))),x77992)
% 28.73/28.52 [8062]~P99(x80621)+E(f319(f319(f74(x80621),f319(f95(x80621),x80622)),f72(x80621)),f319(f95(x80621),f319(f319(f74(a1),x80622),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))))
% 28.73/28.52 [8208]P1(f319(f319(f226(a1),f2(a1)),f319(f95(a1),x82082)))+E(f319(f319(f236(a1),x82081),f319(f95(a925),f319(f319(f23(a1),f319(f319(f74(a1),x82082),x82082)),a89))),f72(a1))
% 28.73/28.52 [9649]~P1(f319(f319(f226(a1),f2(a1)),f319(f95(a1),x96492)))+E(f319(f319(f236(a1),x96491),f319(f95(a925),f319(f319(f23(a1),f319(f319(f74(a1),x96492),x96492)),a89))),f319(f319(f80(a1,a1),f319(f319(f236(a1),x96491),f319(f95(a925),x96492))),f319(f319(f18(a1,a1,a1),f319(f319(f8(a1,f932(a1,a1),a1),f75(a1)),f319(f75(a1),x96491))),f5(a1))))
% 28.73/28.52 [10037]~P1(f319(f319(f226(a925),f673(x100372,x100371)),f319(x100371,f673(x100372,x100371))))+P1(f319(f55(a925),f319(f254(a925),f319(f319(f7(a925,a925,a923),f319(f319(f8(a925,f932(a925,a923),a925),f226(a925)),x100371)),x100372))))
% 28.73/28.52 [10177]~P1(f319(f319(f226(a925),f319(f95(a925),x101771)),f319(a104,x101772)))+P1(f319(f319(f80(a1,a923),f319(f95(a1),f319(f319(f74(a1),x101771),a89))),f319(f319(f18(a1,a923,a923),f319(f319(f8(a923,f932(a923,a923),a1),a322),f319(f319(f8(a923,a923,a1),a314),a185))),f319(f319(f7(a1,a925,a923),f319(f319(f8(a925,f932(a925,a923),a1),f226(a925)),a96)),x101772))))
% 28.73/28.52 [10178]~P1(f319(f319(f227(a925),f319(f95(a925),x101781)),f319(a104,x101782)))+P1(f319(f319(f80(a1,a923),f319(f95(a1),f319(f319(f74(a1),x101781),a89))),f319(f319(f18(a1,a923,a923),f319(f319(f8(a923,f932(a923,a923),a1),a322),f319(f319(f8(a923,a923,a1),a314),a185))),f319(f319(f7(a1,a925,a923),f319(f319(f8(a925,f932(a925,a923),a1),f227(a925)),a96)),x101782))))
% 28.73/28.52 [10240]P1(f319(f319(f226(a925),f319(f95(a925),x102401)),f319(a104,x102402)))+~P1(f319(f319(f80(a1,a923),f319(f95(a1),f319(f319(f74(a1),x102401),a89))),f319(f319(f18(a1,a923,a923),f319(f319(f8(a923,f932(a923,a923),a1),a322),f319(f319(f8(a923,a923,a1),a314),a185))),f319(f319(f7(a1,a925,a923),f319(f319(f8(a925,f932(a925,a923),a1),f226(a925)),a96)),x102402))))
% 28.73/28.52 [10241]P1(f319(f319(f227(a925),f319(f95(a925),x102411)),f319(a104,x102412)))+~P1(f319(f319(f80(a1,a923),f319(f95(a1),f319(f319(f74(a1),x102411),a89))),f319(f319(f18(a1,a923,a923),f319(f319(f8(a923,f932(a923,a923),a1),a322),f319(f319(f8(a923,a923,a1),a314),a185))),f319(f319(f7(a1,a925,a923),f319(f319(f8(a925,f932(a925,a923),a1),f227(a925)),a96)),x102412))))
% 28.73/28.52 [10271]~P1(f319(f319(f226(a925),f319(a104,x102712)),f319(f95(a925),x102711)))+P1(f319(f319(f80(a1,a923),f319(f95(a1),f319(f319(f74(a1),x102711),a89))),f319(f319(f18(a1,a923,a923),f319(f319(f8(a923,f932(a923,a923),a1),a317),f319(f319(f8(a923,a923,a1),a314),a185))),f319(f319(f18(a1,a923,a923),f319(f319(f8(a923,f932(a923,a923),a1),a322),f319(f319(f8(a923,a923,a1),a314),a185))),f319(f319(f8(a925,a923,a1),f319(f226(a925),x102712)),a96)))))
% 28.73/28.52 [10272]~P1(f319(f319(f227(a925),f319(a104,x102722)),f319(f95(a925),x102721)))+P1(f319(f319(f80(a1,a923),f319(f95(a1),f319(f319(f74(a1),x102721),a89))),f319(f319(f18(a1,a923,a923),f319(f319(f8(a923,f932(a923,a923),a1),a317),f319(f319(f8(a923,a923,a1),a314),a185))),f319(f319(f18(a1,a923,a923),f319(f319(f8(a923,f932(a923,a923),a1),a322),f319(f319(f8(a923,a923,a1),a314),a185))),f319(f319(f8(a925,a923,a1),f319(f227(a925),x102722)),a96)))))
% 28.73/28.52 [10319]P1(f319(f319(f226(a925),f319(a104,x103191)),f319(f95(a925),x103192)))+~P1(f319(f319(f80(a1,a923),f319(f95(a1),f319(f319(f74(a1),x103192),a89))),f319(f319(f18(a1,a923,a923),f319(f319(f8(a923,f932(a923,a923),a1),a317),f319(f319(f8(a923,a923,a1),a314),a185))),f319(f319(f18(a1,a923,a923),f319(f319(f8(a923,f932(a923,a923),a1),a322),f319(f319(f8(a923,a923,a1),a314),a185))),f319(f319(f8(a925,a923,a1),f319(f226(a925),x103191)),a96)))))
% 28.73/28.52 [10320]P1(f319(f319(f227(a925),f319(a104,x103201)),f319(f95(a925),x103202)))+~P1(f319(f319(f80(a1,a923),f319(f95(a1),f319(f319(f74(a1),x103202),a89))),f319(f319(f18(a1,a923,a923),f319(f319(f8(a923,f932(a923,a923),a1),a317),f319(f319(f8(a923,a923,a1),a314),a185))),f319(f319(f18(a1,a923,a923),f319(f319(f8(a923,f932(a923,a923),a1),a322),f319(f319(f8(a923,a923,a1),a314),a185))),f319(f319(f8(a925,a923,a1),f319(f227(a925),x103201)),a96)))))
% 28.73/28.52 [10399]~P1(f319(f319(f321(a925),f2(a925)),x103991))+E(f319(a104,f319(f29(a925),f319(f254(a925),f319(f319(f18(a925,a923,a923),f319(f319(f8(a923,f932(a923,a923),a925),a317),f319(f319(f7(a925,f932(a925,a923),a923),f319(f319(f8(a925,f932(f932(a925,a923),a923),a925),f321(a925)),a104)),x103991))),f319(f319(f7(a925,a925,a923),f227(a925)),x103992))))),f319(f29(a925),f319(f254(a925),f319(f319(f18(a925,a923,a923),f319(f319(f8(a923,f932(a923,a923),a925),a317),f319(f319(f7(a925,f932(a925,a923),a923),f321(a925)),x103991))),f319(f319(f7(a925,a925,a923),f227(a925)),f319(a104,x103992))))))
% 28.73/28.52 [8755]~P99(x87551)+E(f319(f319(f75(x87551),f319(f95(x87551),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))),x87552),x87552)
% 28.73/28.52 [8817]~P99(x88171)+E(f319(f319(f74(x88171),f72(x88171)),f319(f95(x88171),x88172)),f319(f95(x88171),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),x88172)))
% 28.73/28.52 [8879]~P99(x88791)+E(f319(f319(f23(x88791),f319(f95(x88791),x88792)),f72(x88791)),f319(f95(x88791),f319(f319(f74(a1),x88792),f319(f73(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))))
% 28.73/28.52 [9034]~P1(f319(f319(f227(a925),f319(f95(a925),a77)),x90342))+E(f319(f319(f23(a925),x90341),f319(f319(f23(a925),x90342),f319(f95(a925),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),f319(f319(f23(a925),f319(a104,x90341)),x90342))
% 28.73/28.52 [9692]~P121(x96921)+E(f319(f319(f75(x96921),x96922),x96922),f319(f319(f236(x96921),x96922),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))))
% 28.73/28.52 [9693]~P87(x96931)+E(f319(f319(f236(x96931),x96932),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),f319(f319(f75(x96931),x96932),x96932))
% 28.73/28.52 [9695]~P99(x96951)+E(f319(f319(f75(x96951),x96952),f319(f95(x96951),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),f319(f319(f74(x96951),x96952),x96952))
% 28.73/28.52 [9943]~P145(x99431)+E(f319(f319(f236(x99431),f319(f73(x99431),x99432)),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),f319(f319(f236(x99431),x99432),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))))
% 28.73/28.52 [9944]~P126(x99441)+E(f319(f319(f236(x99441),f319(f69(x99441),x99442)),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),f319(f319(f236(x99441),x99442),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))))
% 28.73/28.52 [9940]~P99(x99401)+E(f319(f319(f75(x99401),f319(f95(x99401),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),x99402),f319(f319(f74(x99401),x99402),x99402))
% 28.73/28.52 [10072]~P126(x100721)+E(f319(f69(x100721),f319(f319(f236(x100721),x100722),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))))),f319(f319(f236(x100721),x100722),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))))
% 28.73/28.52 [10139]~P126(x101391)+P1(f319(f319(f226(x101391),f2(x101391)),f319(f319(f236(x101391),x101392),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))))))
% 28.73/28.52 [10310]~E(f319(a104,x103102),f319(f95(a925),x103101))+P1(f319(f319(f80(a1,a923),f319(f95(a1),f319(f319(f74(a1),x103101),a89))),f319(f319(f18(a1,a923,a923),f319(f319(f8(a923,f932(a923,a923),a1),a317),f319(f319(f8(a923,a923,a1),a314),a185))),f319(f319(f18(a1,a923,a923),f319(f319(f8(a923,f932(a923,a923),a1),a322),f319(f319(f8(a923,a923,a1),a314),a185))),f319(f319(f7(a1,a925,a923),f319(f319(f8(a925,f932(a925,a923),a1),a316),a96)),x103102)))))
% 28.73/28.52 [10311]~E(f319(f95(a925),x103111),f319(a104,x103112))+P1(f319(f319(f80(a1,a923),f319(f95(a1),f319(f319(f74(a1),x103111),a89))),f319(f319(f18(a1,a923,a923),f319(f319(f8(a923,f932(a923,a923),a1),a317),f319(f319(f8(a923,a923,a1),a314),a185))),f319(f319(f18(a1,a923,a923),f319(f319(f8(a923,f932(a923,a923),a1),a322),f319(f319(f8(a923,a923,a1),a314),a185))),f319(f319(f7(a1,a925,a923),f319(f319(f8(a925,f932(a925,a923),a1),a316),a96)),x103112)))))
% 28.73/28.52 [10355]E(f319(a104,x103551),f319(f95(a925),x103552))+~P1(f319(f319(f80(a1,a923),f319(f95(a1),f319(f319(f74(a1),x103552),a89))),f319(f319(f18(a1,a923,a923),f319(f319(f8(a923,f932(a923,a923),a1),a317),f319(f319(f8(a923,a923,a1),a314),a185))),f319(f319(f18(a1,a923,a923),f319(f319(f8(a923,f932(a923,a923),a1),a322),f319(f319(f8(a923,a923,a1),a314),a185))),f319(f319(f7(a1,a925,a923),f319(f319(f8(a925,f932(a925,a923),a1),a316),a96)),x103551)))))
% 28.73/28.52 [10356]E(f319(f95(a925),x103561),f319(a104,x103562))+~P1(f319(f319(f80(a1,a923),f319(f95(a1),f319(f319(f74(a1),x103561),a89))),f319(f319(f18(a1,a923,a923),f319(f319(f8(a923,f932(a923,a923),a1),a317),f319(f319(f8(a923,a923,a1),a314),a185))),f319(f319(f18(a1,a923,a923),f319(f319(f8(a923,f932(a923,a923),a1),a322),f319(f319(f8(a923,a923,a1),a314),a185))),f319(f319(f7(a1,a925,a923),f319(f319(f8(a925,f932(a925,a923),a1),a316),a96)),x103562)))))
% 28.73/28.52 [10400]~P17(x104001,x104002)+P1(f319(f319(f321(f932(x104001,a923)),f830(x104002,x104001)),f319(f319(f8(f932(x104001,a923),a923,f932(x104001,a923)),f81(x104001)),f319(f319(f8(f932(x104001,a923),f932(x104001,a923),f932(x104001,a923)),f319(f18(x104001,a923,a923),f319(f319(f8(a923,f932(a923,a923),x104001),a317),f319(f319(f18(x104001,x104001,a923),x104002),f5(x104001))))),f319(f319(f7(f932(x104001,a923),f932(x104001,f932(x104001,a923)),f932(x104001,a923)),f319(f319(f8(f932(f932(x104001,a923),a923),f932(f932(x104001,f932(x104001,a923)),f932(x104001,a923)),f932(x104001,a923)),f8(f932(x104001,a923),a923,x104001)),a316)),x104002)))))
% 28.73/28.52 [10137]~P99(x101371)+E(f319(f319(f236(x101371),f319(f95(x101371),a89)),f319(f319(f75(a925),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),x101372)),f72(x101371))
% 28.73/28.52 [10138]~P145(x101381)+E(f319(f319(f236(x101381),f319(f73(x101381),f72(x101381))),f319(f319(f75(a925),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),x101382)),f72(x101381))
% 28.73/28.52 [10141]~P87(x101411)+E(f319(f319(f236(x101411),x101412),f319(f95(a925),f319(f319(f23(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))),a89))),f319(f319(f75(x101411),f319(f319(f75(x101411),x101412),x101412)),x101412))
% 28.73/28.52 [10335]~P1(f319(f319(f226(a1),f2(a1)),x103352))+E(f39(a1,f319(f319(f74(a1),f72(a1)),f319(f319(f75(a1),f319(f95(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),x103351)),f319(f319(f75(a1),f319(f95(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),x103352)),f319(f319(f74(a1),f72(a1)),f319(f319(f75(a1),f319(f95(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),f39(a1,x103351,x103352))))
% 28.73/28.52 [10358]~P1(f319(f319(f226(a1),f2(a1)),x103582))+E(f319(f319(f30(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f75(a1),f319(f95(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),x103581))),f319(f319(f75(a1),f319(f95(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),x103582)),f319(f319(f30(a1),x103581),x103582))
% 28.73/28.52 [10360]~P1(f319(f319(f226(a1),x103602),f2(a1)))+E(f319(f319(f30(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f75(a1),f319(f95(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),x103601))),f319(f319(f75(a1),f319(f95(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),x103602)),f319(f319(f30(a1),f319(f319(f74(a1),x103601),f72(a1))),x103602))
% 28.73/28.52 [10361]~P1(f319(f319(f226(a1),x103612),f2(a1)))+E(f39(a1,f319(f319(f74(a1),f72(a1)),f319(f319(f75(a1),f319(f95(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),x103611)),f319(f319(f75(a1),f319(f95(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),x103612)),f319(f319(f23(a1),f319(f319(f75(a1),f319(f95(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),f39(a1,f319(f319(f74(a1),x103611),f72(a1)),x103612))),f72(a1)))
% 28.73/28.52 [10231]~P99(x102311)+E(f319(f319(f236(x102311),f319(f95(x102311),a89)),f319(a104,f319(f319(f75(a925),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),x102312))),f319(f95(x102311),a89))
% 28.73/28.52 [10233]~P145(x102331)+E(f319(f319(f236(x102331),f319(f73(x102331),f72(x102331))),f319(a104,f319(f319(f75(a925),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),x102332))),f319(f73(x102331),f72(x102331)))
% 28.73/28.52 [5151]P39(x51511,x51512)+~P9(x51511,x51513,x51512)
% 28.73/28.52 [5152]P39(x51521,x51522)+~P9(x51521,x51523,x51522)
% 28.73/28.52 [5153]P56(x51531,x51532)+~P9(x51531,x51533,x51532)
% 28.73/28.52 [5154]P56(x51541,x51542)+~P9(x51541,x51543,x51542)
% 28.73/28.52 [5327]~P9(x53271,x53272,x53273)+P57(x53271,x53272,x53273)
% 28.73/28.52 [5328]~P9(x53281,x53282,x53283)+P57(x53281,x53282,x53283)
% 28.73/28.52 [8275]~E(x82752,x82753)+P35(x82751,x82751,a316,x82752,x82753)
% 28.73/28.52 [8830]E(x88301,x88302)+~P35(x88303,x88303,a316,x88301,x88302)
% 28.73/28.52 [4958]E(f161(x49581,x49582,x49583),f105(x49581))+~E(x49582,f2(a925))
% 28.73/28.52 [4959]E(f161(x49591,x49592,x49593),f105(x49591))+~E(x49592,f2(a925))
% 28.73/28.52 [5126]~E(f161(x51262,x51261,x51263),f105(x51262))+E(x51261,f2(a925))
% 28.73/28.52 [5127]~E(f161(x51272,x51271,x51273),f105(x51272))+E(x51271,f2(a925))
% 28.73/28.52 [5333]~P38(x53331,x53333)+P38(x53331,f313(x53331,x53332,x53333))
% 28.73/28.52 [5445]~P30(x54451,x54452,x54453)+P32(a1,x54451,f170(x54452,x54453))
% 28.73/28.52 [5511]P30(x55111,x55112,x55113)+~P32(a1,x55111,f170(x55112,x55113))
% 28.73/28.52 [5582]~P9(x55821,x55822,x55823)+P9(f926(x55821),f153(x55821,x55822),f150(x55821,x55823))
% 28.73/28.52 [5583]~P57(x55831,x55832,x55833)+P57(f926(x55831),f153(x55831,x55832),f150(x55831,x55833))
% 28.73/28.52 [5694]P59(x56941,x56942,x56943)+~E(f610(x56943,x56942,x56941),f611(x56943,x56942,x56941))
% 28.73/28.52 [5695]P60(x56951,x56952,x56953)+~E(f626(x56953,x56952,x56951),f627(x56953,x56952,x56951))
% 28.73/28.52 [8281]~E(x82812,x82813)+P27(x82811,x82811,f25(x82811),x82812,x82813)
% 28.73/28.52 [8838]E(x88381,x88382)+~P27(x88383,x88383,f25(x88383),x88381,x88382)
% 28.73/28.52 [4914]~E(f319(f160(x49142),x49141),x49143)+E(x49141,f319(f160(x49142),x49143))
% 28.73/28.52 [4915]~E(x49152,f319(f160(x49151),x49153))+E(f319(f160(x49151),x49152),x49153)
% 28.73/28.52 [4965]E(x49651,x49652)+~E(f319(f160(x49653),x49651),f319(f160(x49653),x49652))
% 28.73/28.52 [5178]~P8(x51783,x51781)+P1(f319(f319(x51781,x51782),x51782))
% 28.73/28.52 [5179]~P50(x51793,x51791)+P1(f319(f319(x51791,x51792),x51792))
% 28.73/28.52 [5180]~P64(x51801,x51802)+P1(f319(f307(x51801,x51802),x51803))
% 28.73/28.52 [5181]~P64(x51811,x51812)+P1(f319(f307(x51811,x51812),x51813))
% 28.73/28.52 [5245]~P38(x52451,x52452)+P38(f926(x52451),f319(f135(x52451,x52452),x52453))
% 28.73/28.52 [5250]~P1(f319(x52502,x52503))+~E(f319(f254(x52501),x52502),f180(f932(x52501,a923)))
% 28.73/28.52 [5251]~P1(f319(x52512,x52513))+~E(f180(f932(x52511,a923)),f319(f254(x52511),x52512))
% 28.73/28.52 [5263]E(x52631,f2(a925))+E(f136(x52632,f161(x52632,x52631,x52633)),x52633)
% 28.73/28.52 [5279]~P1(f319(x52791,x52793))+P1(f319(x52791,f84(x52792,x52791)))
% 28.73/28.52 [5280]~P1(f319(x52801,x52803))+P1(f319(x52801,f84(x52802,x52801)))
% 28.73/28.52 [5281]~P1(f319(x52811,x52813))+P1(f319(x52811,f84(x52812,x52811)))
% 28.73/28.52 [5282]~P1(f319(x52821,x52823))+P1(f319(x52821,f84(x52822,x52821)))
% 28.73/28.52 [5283]~P1(f319(x52831,x52833))+P1(f319(x52831,f756(x52831,x52832)))
% 28.73/28.52 [5295]E(x52951,f2(a925))+E(f319(f133(x52952),f161(x52952,x52951,x52953)),x52953)
% 28.73/28.52 [5408]~E(x54082,x54083)+P1(f319(f319(f321(x54081),x54082),f319(a316,x54083)))
% 28.73/28.52 [5423]~E(x54232,f2(a925))+E(f319(f164(x54231),f161(x54231,x54232,x54233)),f180(f932(x54231,a923)))
% 28.73/28.52 [5467]E(f319(f160(x54671),x54672),f319(f319(f143(x54671),x54673),f105(x54671)))+~E(x54672,f319(f319(f143(x54671),x54673),f105(x54671)))
% 28.73/28.52 [5468]~E(x54683,f319(f319(f143(x54681),x54682),f105(x54681)))+E(f319(f319(f143(x54681),x54682),f105(x54681)),f319(f160(x54681),x54683))
% 28.73/28.52 [5507]~P34(x55071,x55072,x55073)+P34(x55071,x55072,f319(f160(x55071),x55073))
% 28.73/28.52 [5508]~P32(x55081,x55082,x55083)+P32(x55081,x55082,f319(f160(x55081),x55083))
% 28.73/28.52 [5512]E(f319(f29(x55121),f328(x55122,x55123,x55121)),x55122)+~E(f319(f29(x55121),x55123),f319(a104,x55122))
% 28.73/28.52 [5518]~P38(x55181,x55183)+P1(f319(f319(f321(x55181),x55182),f308(x55181,x55183)))
% 28.73/28.52 [5519]~P38(x55191,x55193)+P1(f319(f319(f321(x55191),x55192),f308(x55191,x55193)))
% 28.73/28.52 [5523]~E(f319(f160(x55232),x55231),f319(f319(f143(x55232),x55233),f105(x55232)))+E(x55231,f319(f319(f143(x55232),x55233),f105(x55232)))
% 28.73/28.52 [5524]~E(f319(f319(f143(x55242),x55243),f105(x55242)),f319(f160(x55242),x55241))+E(x55241,f319(f319(f143(x55242),x55243),f105(x55242)))
% 28.73/28.52 [5547]E(f79(f931(a925,a925),f42(x55471,x55472)),x55473)+~P1(f319(f42(x55471,x55472),x55473))
% 28.73/28.52 [5586]P34(x55861,x55862,x55863)+~P34(x55861,x55862,f319(f160(x55861),x55863))
% 28.73/28.52 [5587]P32(x55871,x55872,x55873)+~P32(x55871,x55872,f319(f160(x55871),x55873))
% 28.73/28.52 [5625]P1(f319(f319(x56251,x56252),x56252))+~P1(f319(f262(x56253,x56251),x56252))
% 28.73/28.52 [5626]~P1(f319(f319(x56262,x56263),x56263))+P1(f319(f262(x56261,x56262),x56263))
% 28.73/28.52 [5648]~E(x56482,f105(x56481))+P1(f319(f319(f321(f926(x56481)),x56482),f153(x56481,x56483)))
% 28.73/28.52 [5657]~P57(x56571,x56572,x56573)+P57(x56571,x56572,f319(f278(x56571,x56571),x56573))
% 28.73/28.52 [5658]~P60(x56581,x56582,x56583)+P60(x56581,x56582,f319(f278(x56581,x56581),x56583))
% 28.73/28.52 [5675]~P65(x56751)+E(f39(x56751,f39(x56751,x56752,x56753),x56753),f39(x56751,x56752,x56753))
% 28.73/28.52 [5776]E(x57761,x57762)+~P1(f319(f319(f321(x57763),x57761),f319(a316,x57762)))
% 28.73/28.52 [5822]~P149(x58221)+E(f182(x58221,x58222,f2(a925),x58223),x58223)
% 28.73/28.52 [5844]P57(x58441,x58442,x58443)+~P57(x58441,x58442,f319(f278(x58441,x58441),x58443))
% 28.73/28.52 [5845]P60(x58451,x58452,x58453)+~P60(x58451,x58452,f319(f278(x58451,x58451),x58453))
% 28.73/28.52 [5849]~P4(x58492)+E(f142(x58491,x58492,x58493,f105(x58491)),f105(x58491))
% 28.73/28.52 [5862]E(f162(x58621,x58622,f144(x58621,x58623)),f144(x58621,f162(x58621,x58622,x58623)))+~P1(f319(f129(x58621),x58623))
% 28.73/28.52 [5961]~P1(f319(f319(x59613,x59612),x59612))+P1(f319(f319(f321(x59611),x59612),f262(x59611,x59613)))
% 28.73/28.52 [5963]E(f319(f128(x59631,x59632),x59633),f105(x59631))+P1(f319(x59632,f695(x59633,x59632,x59631)))
% 28.73/28.52 [6022]E(f62(x60221,x60222,x60223),x60222)+P1(f319(x60223,f757(x60222,x60221,x60223)))
% 28.73/28.52 [6120]~P1(f319(f129(x61201),x61202))+P1(f319(f129(x61201),f168(x61201,x61202,x61203)))
% 28.73/28.52 [6121]~P1(f319(f129(x61211),x61213))+P1(f319(f129(x61211),f162(x61211,x61212,x61213)))
% 28.73/28.52 [6122]~P1(f319(f129(x61221),x61223))+P1(f319(f129(x61221),f169(x61221,x61222,x61223)))
% 28.73/28.52 [6123]~P1(f319(f129(x61231),x61233))+P1(f319(f129(x61231),f132(x61231,x61232,x61233)))
% 28.73/28.52 [6124]~P151(x61241,x61243,x61242)+P1(f319(x61241,f39(a1,x61242,x61243)))
% 28.73/28.52 [6140]~P34(x61403,x61401,x61402)+P1(f319(x61401,f771(x61402,x61401,x61403)))
% 28.73/28.52 [6141]~P36(x61413,x61411,x61412)+P1(f319(x61411,f775(x61412,x61411,x61413)))
% 28.73/28.52 [6142]~P36(x61423,x61421,x61422)+P1(f319(x61421,f787(x61422,x61421,x61423)))
% 28.73/28.52 [6143]~P34(x61433,x61431,x61432)+P1(f319(x61431,f814(x61432,x61431,x61433)))
% 28.73/28.52 [6144]~P34(x61443,x61441,x61442)+P1(f319(x61441,f816(x61441,x61442,x61443)))
% 28.73/28.52 [6149]P1(f319(f319(x61491,x61492),x61492))+~P1(f319(f319(f321(x61493),x61492),f262(x61493,x61491)))
% 28.73/28.52 [6164]E(f319(f128(x61641,x61642),x61643),f169(x61641,x61642,x61643))+P1(f319(x61642,f743(x61643,x61642,x61641)))
% 28.73/28.52 [6206]~P1(f319(f129(x62061),x62063))+P1(f319(f129(f926(x62061)),f49(x62061,x62062,x62063)))
% 28.73/28.52 [6241]~P113(x62411)+E(f319(f319(f93(f932(x62411,a923)),f319(f274(x62411),x62412)),f295(x62411,x62412,x62413)),f180(f932(x62411,a923)))
% 28.73/28.52 [6242]~P113(x62421)+E(f319(f319(f93(f932(x62421,a923)),f319(f293(x62421),x62422)),f297(x62421,x62422,x62423)),f180(f932(x62421,a923)))
% 28.73/28.52 [6243]~P113(x62431)+E(f319(f319(f93(f932(x62431,a923)),f319(f293(x62431),x62432)),f298(x62431,x62432,x62433)),f180(f932(x62431,a923)))
% 28.73/28.52 [6469]E(f319(f128(x64691,x64692),x64693),x64693)+~P1(f319(x64692,f726(x64693,x64692,x64691)))
% 28.73/28.52 [6471]E(f319(f319(f301(x64711),f420(x64712,x64713,x64711)),f328(x64712,x64713,x64711)),x64713)+~E(f319(f29(x64711),x64713),f319(a104,x64712))
% 28.73/28.52 [6486]P151(x64861,x64862,x64863)+~P1(f319(x64861,f39(a1,x64863,x64862)))
% 28.73/28.52 [6536]P32(x65361,x65362,x65363)+~P1(f319(x65362,f776(x65363,x65362,x65361)))
% 28.73/28.52 [6537]P32(x65371,x65372,x65373)+~P1(f319(x65372,f785(x65372,x65373,x65371)))
% 28.73/28.52 [6538]P32(x65381,x65382,x65383)+~P1(f319(x65382,f786(x65383,x65382,x65381)))
% 28.73/28.52 [6539]P30(x65391,x65392,x65393)+~P1(f319(x65391,f801(x65393,x65392,x65391)))
% 28.73/28.52 [6540]P31(x65401,x65402,x65403)+~P1(f319(x65401,f857(x65403,x65402,x65401)))
% 28.73/28.52 [6542]E(f169(x65421,x65422,x65423),x65423)+~P1(f319(x65422,f739(x65423,x65422,x65421)))
% 28.73/28.52 [6623]~P1(f319(x66232,f598(x66233,x66232,x66231)))+P1(f319(f240(x66231,x66232),x66233))
% 28.73/28.52 [6624]~P1(f319(x66242,f696(x66243,x66242,x66241)))+P1(f319(f152(x66241,x66242),x66243))
% 28.73/28.52 [6877]~P1(f319(f307(x68771,x68772),f524(x68773,x68772,x68771)))+P1(f319(f307(x68771,x68772),x68773))
% 28.73/28.52 [6878]~P1(f319(f307(x68781,x68782),f539(x68783,x68782,x68781)))+P1(f319(f307(x68781,x68782),x68783))
% 28.73/28.52 [7498]~P65(x74981)+E(f319(f319(f74(x74981),f319(f319(f75(x74981),x74982),f319(f319(f30(x74981),x74983),x74982))),f39(x74981,x74983,x74982)),x74983)
% 28.73/28.52 [7528]P30(x75281,x75282,x75283)+P1(f319(f319(f321(a1),f801(x75283,x75282,x75281)),f295(a1,x75282,x75283)))
% 28.73/28.52 [7952]E(f319(f319(f244(x79521,x79521),f555(x79522,x79523,x79521)),f555(x79522,x79523,x79521)),x79523)+~P1(f319(f319(f321(f931(x79521,x79521)),x79523),f255(x79521,x79522)))
% 28.73/28.52 [8070]~P1(f319(f319(f321(x80701),f560(x80703,x80702,x80701)),f308(x80701,x80703)))+P1(f319(f319(f321(x80701),x80702),f308(x80701,x80703)))
% 28.73/28.52 [8071]~P1(f319(f319(f321(x80711),f612(x80713,x80712,x80711)),f308(x80711,x80713)))+P1(f319(f319(f321(x80711),x80712),f308(x80711,x80713)))
% 28.73/28.52 [8072]~P1(f319(f319(f321(x80721),f613(x80723,x80722,x80721)),f308(x80721,x80723)))+P1(f319(f319(f321(x80721),x80722),f308(x80721,x80723)))
% 28.73/28.52 [8166]P34(a1,x81661,f170(x81662,x81663))+P30(f319(f66(a923,a923,a1,a314),x81661),x81662,x81663)
% 28.73/28.52 [8255]~P65(x82551)+E(f319(f319(f74(x82551),f319(f319(f75(x82551),f319(f319(f30(x82551),x82552),x82553)),x82553)),f39(x82551,x82552,x82553)),x82552)
% 28.73/28.52 [8256]~P65(x82561)+E(f319(f319(f74(x82561),f319(f319(f75(x82561),f319(f319(f30(x82561),x82562),x82563)),x82563)),f39(x82561,x82562,x82563)),x82562)
% 28.73/28.52 [8303]~E(f319(f29(x83031),x83032),f319(a104,x83033))+~P1(f319(f319(f321(x83031),f420(x83033,x83032,x83031)),f328(x83033,x83032,x83031)))
% 28.73/28.52 [8747]~P34(a1,x87471,f170(x87472,x87473))+~P30(f319(f66(a923,a923,a1,a314),x87471),x87472,x87473)
% 28.73/28.52 [8935]P1(f319(f319(f226(f932(f931(x89351,x89351),a923)),f299(x89351,x89352)),f299(x89351,x89353)))+~P1(f319(f319(f226(f932(f931(x89351,x89351),a923)),x89352),f299(x89351,x89353)))
% 28.73/28.52 [9072]~P27(x90721,x90722,x90723,f234(f932(x90721,a923)),f234(f932(x90722,a923)))+P26(x90721,x90722,x90723,f234(f932(x90721,a923)))
% 28.73/28.52 [9073]~P27(x90731,x90732,x90733,f234(f932(x90731,a923)),f234(f932(x90732,a923)))+P26(x90731,x90732,x90733,f234(f932(x90731,a923)))
% 28.73/28.52 [9222]E(x92221,f105(x92222))+~P1(f319(f319(f321(f931(f926(x92222),f926(x92222))),f319(f319(f244(f926(x92222),f926(x92222)),x92221),f105(x92222))),f150(x92222,x92223)))
% 28.73/28.52 [9246]E(x92461,f105(x92462))+~P1(f319(f319(f321(f931(f926(x92462),f926(x92462))),f319(f319(f244(f926(x92462),f926(x92462)),f105(x92462)),x92461)),f150(x92462,x92463)))
% 28.73/28.52 [9373]E(f319(f319(f143(x93731),f712(x93732,x93733,x93731)),f713(x93732,x93733,x93731)),x93733)+~P1(f319(f319(f321(f931(f926(x93731),f926(x93731))),f319(f319(f244(f926(x93731),f926(x93731)),f105(x93731)),x93733)),f139(x93731,x93732)))
% 28.73/28.52 [9615]~P131(x96151)+~P1(f319(f319(f227(x96151),f319(f319(f74(x96151),f319(f319(f75(x96151),x96152),x96152)),f319(f319(f75(x96151),x96153),x96153))),f2(x96151)))
% 28.73/28.52 [9667]P1(f319(f55(x96671),x96672))+~P1(f319(f319(f321(f931(f932(x96671,a923),f932(x96671,a923))),f319(f319(f244(f932(x96671,a923),f932(x96671,a923)),x96673),x96672)),f306(x96671)))
% 28.73/28.52 [9975]~P48(x99751,x99752,x99753)+P1(f319(f319(f226(a1),f319(f319(f66(f931(a1,a1),a1,x99751,f243(a1,a1)),f204(x99751)),f222(x99751,x99752,f219(x99751,x99753)))),f2(a1)))
% 28.73/28.52 [9976]~P49(x99761,x99762,x99763)+P1(f319(f319(f227(a1),f319(f319(f66(f931(a1,a1),a1,x99761,f243(a1,a1)),f204(x99761)),f222(x99761,x99762,f219(x99761,x99763)))),f2(a1)))
% 28.73/28.52 [10105]P49(x101051,x101052,x101053)+~P1(f319(f319(f227(a1),f319(f319(f66(f931(a1,a1),a1,x101051,f243(a1,a1)),f204(x101051)),f222(x101051,x101052,f219(x101051,x101053)))),f2(a1)))
% 28.73/28.52 [10106]P48(x101061,x101062,x101063)+~P1(f319(f319(f226(a1),f319(f319(f66(f931(a1,a1),a1,x101061,f243(a1,a1)),f204(x101061)),f222(x101061,x101062,f219(x101061,x101063)))),f2(a1)))
% 28.73/28.52 [10460]~P126(x104601)+~P1(f319(f319(f227(x104601),f319(f319(f74(x104601),f319(f319(f236(x104601),x104602),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))))),f319(f319(f236(x104601),x104603),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))))),f2(x104601)))
% 28.73/28.52 [4942]~E(x49423,f105(x49421))+E(f319(f319(f126(x49421),x49422),x49423),x49422)
% 28.73/28.52 [4943]~E(x49432,f105(x49431))+E(f319(f319(f126(x49431),x49432),x49433),x49433)
% 28.73/28.52 [4944]~E(x49443,f105(x49441))+E(f319(f319(f126(x49441),x49442),x49443),x49442)
% 28.73/28.52 [4945]~E(x49452,f105(x49451))+E(f319(f319(f126(x49451),x49452),x49453),x49453)
% 28.73/28.52 [4951]~E(x49512,f2(a925))+E(f319(f319(f167(x49511),x49512),x49513),f105(x49511))
% 28.73/28.52 [4960]~E(x49603,f105(x49601))+E(f319(f319(f167(x49601),x49602),x49603),f105(x49601))
% 28.73/28.52 [4999]~E(x49991,x49993)+E(x49991,f319(f319(f126(x49992),f105(x49992)),x49993))
% 28.73/28.52 [5089]~P115(x50892)+E(f319(f234(f932(x50891,x50892)),x50893),f234(x50892))
% 28.73/28.52 [5090]~P109(x50902)+E(f319(f180(f932(x50901,x50902)),x50903),f180(x50902))
% 28.73/28.52 [5091]~P109(x50912)+E(f319(f180(f932(x50911,x50912)),x50913),f180(x50912))
% 28.73/28.52 [5107]E(x51071,f105(x51072))+~E(f319(f319(f126(x51072),x51071),x51073),x51073)
% 28.73/28.52 [5108]E(x51081,f105(x51082))+~E(f319(f319(f126(x51082),x51083),x51081),x51083)
% 28.73/28.52 [5109]E(x51091,f105(x51092))+~E(f319(f319(f126(x51092),x51093),x51091),x51093)
% 28.73/28.52 [5110]E(x51101,f105(x51102))+~E(f319(f319(f126(x51102),x51101),x51103),x51103)
% 28.73/28.52 [5116]E(x51161,f105(x51162))+~E(f319(f319(f126(x51162),x51163),x51161),f105(x51162))
% 28.73/28.52 [5117]E(x51171,f105(x51172))+~E(f319(f319(f126(x51172),x51171),x51173),f105(x51172))
% 28.73/28.52 [5118]E(x51181,f105(x51182))+~E(f319(f319(f126(x51182),x51183),x51181),f105(x51182))
% 28.73/28.52 [5119]E(x51191,f105(x51192))+~E(f319(f319(f126(x51192),x51191),x51193),f105(x51192))
% 28.73/28.52 [5144]~E(x51442,f2(a925))+E(f319(f319(f75(a925),x51441),x51442),f319(f319(f75(a925),x51443),x51442))
% 28.73/28.52 [5145]~E(x51451,f2(a925))+E(f319(f319(f75(a925),x51451),x51452),f319(f319(f75(a925),x51451),x51453))
% 28.73/28.52 [5146]~E(x51461,f2(a925))+E(f319(f319(f75(a925),x51461),x51462),f319(f319(f75(a925),x51461),x51463))
% 28.73/28.52 [5204]~P102(x52041)+E(f319(f319(f102(x52041),x52042),x52043),f319(f319(f102(x52041),x52043),x52042))
% 28.73/28.52 [5205]~P107(x52051)+E(f319(f319(f102(x52051),x52052),x52053),f319(f319(f102(x52051),x52053),x52052))
% 28.73/28.52 [5206]~P107(x52061)+E(f319(f319(f102(x52061),x52062),x52063),f319(f319(f102(x52061),x52063),x52062))
% 28.73/28.52 [5207]~P102(x52071)+E(f319(f319(f93(x52071),x52072),x52073),f319(f319(f93(x52071),x52073),x52072))
% 28.73/28.52 [5208]~P108(x52081)+E(f319(f319(f93(x52081),x52082),x52083),f319(f319(f93(x52081),x52083),x52082))
% 28.73/28.52 [5209]~P108(x52091)+E(f319(f319(f93(x52091),x52092),x52093),f319(f319(f93(x52091),x52093),x52092))
% 28.73/28.52 [5210]~P121(x52101)+E(f319(f319(f75(x52101),x52102),x52103),f319(f319(f75(x52101),x52103),x52102))
% 28.73/28.52 [5211]~P121(x52111)+E(f319(f319(f74(x52111),x52112),x52113),f319(f319(f74(x52111),x52113),x52112))
% 28.73/28.52 [5212]~P4(x52121)+E(f319(f319(f224(x52121),x52122),x52123),f319(f319(f224(x52121),x52123),x52122))
% 28.73/28.52 [5213]~P4(x52131)+E(f319(f319(f224(x52131),x52132),x52133),f319(f319(f224(x52131),x52133),x52132))
% 28.73/28.52 [5214]~P4(x52141)+E(f319(f319(f225(x52141),x52142),x52143),f319(f319(f225(x52141),x52143),x52142))
% 28.73/28.52 [5215]~P4(x52151)+E(f319(f319(f225(x52151),x52152),x52153),f319(f319(f225(x52151),x52153),x52152))
% 28.73/28.52 [5277]E(f39(a925,x52771,x52772),f2(a925))+~E(x52771,f319(f319(f75(a925),x52772),x52773))
% 28.73/28.52 [5278]E(f39(a1,x52781,x52782),f2(a1))+~E(x52781,f319(f319(f75(a1),x52782),x52783))
% 28.73/28.52 [5345]E(x53451,x53452)+~E(f319(f319(f74(a925),x53453),x53451),f319(f319(f74(a925),x53453),x53452))
% 28.73/28.52 [5346]E(x53461,x53462)+~E(f319(f319(f74(a925),x53461),x53463),f319(f319(f74(a925),x53462),x53463))
% 28.73/28.52 [5359]~P96(x53591)+E(f319(f319(f93(x53591),x53592),f319(f73(x53591),x53593)),f319(f319(f23(x53591),x53592),x53593))
% 28.73/28.52 [5360]~P69(x53601)+E(f319(f319(f74(x53601),x53602),f319(f73(x53601),x53603)),f319(f319(f23(x53601),x53602),x53603))
% 28.73/28.52 [5361]~P70(x53611)+E(f319(f319(f74(x53611),x53612),f319(f73(x53611),x53613)),f319(f319(f23(x53611),x53612),x53613))
% 28.73/28.52 [5362]~P118(x53621)+E(f319(f319(f74(x53621),x53622),f319(f73(x53621),x53623)),f319(f319(f23(x53621),x53622),x53623))
% 28.73/28.52 [5363]~P69(x53631)+E(f319(f319(f23(x53631),x53632),f319(f73(x53631),x53633)),f319(f319(f74(x53631),x53632),x53633))
% 28.73/28.52 [5401]~P1(f319(x54013,x54012))+P1(f319(f319(f321(x54011),x54012),x54013))
% 28.73/28.52 [5402]~P79(x54022)+E(f319(f319(f6(x54021,x54022),x54023),f180(f932(x54021,a923))),f2(x54022))
% 28.73/28.52 [5403]~P79(x54032)+E(f319(f319(f6(x54031,x54032),x54033),f180(f932(x54031,a923))),f2(x54032))
% 28.73/28.52 [5404]~P78(x54042)+E(f319(f319(f9(x54041,x54042),x54043),f180(f932(x54041,a923))),f72(x54042))
% 28.73/28.52 [5405]~P78(x54052)+E(f319(f319(f9(x54051,x54052),x54053),f180(f932(x54051,a923))),f72(x54052))
% 28.73/28.52 [5457]~E(x54572,f319(f319(f74(a925),x54571),x54573))+P1(f319(f319(f226(a925),x54571),x54572))
% 28.73/28.52 [5460]~E(x54602,f180(f932(x54601,a923)))+E(f319(f319(f54(x54601),x54602),x54603),f180(f932(f932(x54601,a923),a923)))
% 28.73/28.52 [5461]~E(x54612,f180(f932(x54611,a923)))+E(f180(f932(f932(x54611,a923),a923)),f319(f319(f54(x54611),x54612),x54613))
% 28.73/28.52 [5527]~E(f319(f276(x55272,x55273),x55271),f180(f932(x55273,a923)))+E(x55271,f180(f932(f931(x55272,x55273),a923)))
% 28.73/28.52 [5528]~E(f319(f256(x55282,x55283),x55281),f180(f932(x55282,a923)))+E(x55281,f180(f932(f931(x55282,x55283),a923)))
% 28.73/28.52 [5560]E(f319(f276(x55601,x55602),x55603),f180(f932(x55602,a923)))+~E(x55603,f180(f932(f931(x55601,x55602),a923)))
% 28.73/28.52 [5561]E(f319(f256(x55611,x55612),x55613),f180(f932(x55611,a923)))+~E(x55613,f180(f932(f931(x55611,x55612),a923)))
% 28.73/28.52 [5564]E(f266(x55641,x55642,x55643),f319(f319(f23(a91),x55642),x55643))+P1(f319(f319(f227(a91),x55642),x55643))
% 28.73/28.52 [5580]P1(f319(x55801,x55802))+~P1(f319(f319(f321(x55803),x55802),x55801))
% 28.73/28.52 [5618]E(x56181,x56182)+~E(f319(f73(f932(x56183,a923)),x56181),f319(f73(f932(x56183,a923)),x56182))
% 28.73/28.52 [5627]~E(x56271,f180(f932(x56272,a923)))+~P1(f319(f319(f321(x56272),x56273),x56271))
% 28.73/28.52 [5628]~E(x56281,f180(f932(x56282,a923)))+~P1(f319(f319(f321(x56282),x56283),x56281))
% 28.73/28.52 [5629]~E(x56291,f180(f932(x56292,a923)))+~P1(f319(f319(f321(x56292),x56293),x56291))
% 28.73/28.52 [5659]~E(x56592,f319(f319(f74(a1),x56591),f319(f92(a1),x56593)))+P1(f319(f319(f226(a1),x56591),x56592))
% 28.73/28.52 [5673]E(f319(f319(f301(x56731),x56732),x56733),x56733)+~P1(f319(f319(f321(x56731),x56732),x56733))
% 28.73/28.52 [5684]E(x56841,f180(f932(x56842,a923)))+~E(f319(f319(f54(x56842),x56841),x56843),f180(f932(f932(x56842,a923),a923)))
% 28.73/28.52 [5685]E(x56851,f180(f932(x56852,a923)))+~E(f180(f932(f932(x56852,a923),a923)),f319(f319(f54(x56852),x56851),x56853))
% 28.73/28.52 [5691]~P116(x56911)+E(f319(f319(f75(x56911),f319(f73(x56911),x56912)),f319(f73(x56911),x56913)),f319(f319(f75(x56911),x56912),x56913))
% 28.73/28.52 [5693]~P72(x56931)+E(f319(f319(f283(x56931),f319(f73(x56931),x56932)),f319(f73(x56931),x56933)),f319(f319(f283(x56931),x56932),x56933))
% 28.73/28.52 [5724]~P1(f319(x57243,x57242))+P1(f319(f319(f321(x57241),x57242),f319(f254(x57241),x57243)))
% 28.73/28.52 [5725]~P1(f319(x57253,x57252))+P1(f319(f319(f321(x57251),x57252),f319(f254(x57251),x57253)))
% 28.73/28.52 [5749]E(x57491,f2(a925))+E(f319(f164(x57492),f161(x57492,x57491,x57493)),f319(f319(f301(x57492),x57493),f180(f932(x57492,a923))))
% 28.73/28.52 [5750]E(x57501,f2(a925))+E(f319(f164(x57502),f161(x57502,x57501,x57503)),f319(f319(f301(x57502),x57503),f180(f932(x57502,a923))))
% 28.73/28.52 [5769]E(f162(x57691,x57692,x57693),x57693)+P1(f319(f319(f321(x57691),x57692),f319(f164(x57691),x57693)))
% 28.73/28.52 [5853]~P1(f319(f129(x58531),x58533))+P1(f319(f129(x58531),f319(f128(x58531,x58532),x58533)))
% 28.73/28.52 [5897]~P65(x58971)+E(f319(f319(f30(x58971),f39(x58971,x58972,x58973)),x58973),f2(x58971))
% 28.73/28.52 [5916]E(f168(x59161,f319(f319(f143(x59161),x59162),f105(x59161)),x59163),f105(x59161))+P1(f319(f319(f321(a925),f2(a925)),x59163))
% 28.73/28.52 [5922]E(x59221,f2(a925))+E(f319(f163(x59222),f161(x59222,x59221,x59223)),f161(x59222,f319(f319(f23(a925),x59221),f72(a925)),x59223))
% 28.73/28.52 [5972]E(f319(f319(f143(x59721),x59722),x59723),f132(x59721,x59722,x59723))+P1(f319(f319(f321(x59721),x59722),f319(f164(x59721),x59723)))
% 28.73/28.52 [5973]E(f319(f319(f143(x59731),x59732),x59733),f132(x59731,x59732,x59733))+P1(f319(f319(f321(x59731),x59732),f319(f164(x59731),x59733)))
% 28.73/28.52 [5982]E(x59821,x59822)+~E(f319(f319(f75(a925),f319(a104,x59823)),x59821),f319(f319(f75(a925),f319(a104,x59823)),x59822))
% 28.73/28.52 [5983]~E(x59832,f319(f319(f74(a1),x59831),f319(f92(a1),f319(a104,x59833))))+P1(f319(f319(f227(a1),x59831),x59832))
% 28.73/28.52 [6045]~P31(x60451,x60452,x60453)+P32(a925,x60451,f131(a925,f319(f294(a925,x60452),x60453)))
% 28.73/28.52 [6099]~E(x60993,f105(x60991))+E(f319(f319(f319(f175(f926(x60991),f926(x60991)),x60992),f159(x60991)),x60993),f105(x60991))
% 28.73/28.52 [6101]P1(f319(x61011,x61012))+~P1(f319(f319(f321(x61013),x61012),f319(f254(x61013),x61011)))
% 28.73/28.52 [6102]P1(f319(x61021,x61022))+~P1(f319(f319(f321(x61023),x61022),f319(f254(x61023),x61021)))
% 28.73/28.52 [6103]P1(f319(x61031,x61032))+~P1(f319(f319(f321(x61033),x61032),f319(f254(x61033),x61031)))
% 28.73/28.52 [6135]E(x61351,x61352)+~E(f319(f319(f301(x61353),x61351),f180(f932(x61353,a923))),f319(f319(f301(x61353),x61352),f180(f932(x61353,a923))))
% 28.73/28.52 [6151]~P113(x61511)+E(f319(f319(f93(f932(x61511,a923)),f319(f274(x61511),x61512)),f319(f294(x61511,x61512),x61513)),f180(f932(x61511,a923)))
% 28.73/28.52 [6189]E(f132(x61891,x61892,x61893),x61893)+~P1(f319(f319(f321(x61891),x61892),f319(f164(x61891),x61893)))
% 28.73/28.52 [6190]E(f132(x61901,x61902,x61903),x61903)+~P1(f319(f319(f321(x61901),x61902),f319(f164(x61901),x61903)))
% 28.73/28.52 [6215]~P68(x62151)+E(f319(f302(x62151,x62151,f73(x62151)),f319(f294(x62151,x62152),x62153)),f297(x62151,f319(f73(x62151),x62153),f319(f73(x62151),x62152)))
% 28.73/28.52 [6220]P1(f319(f319(f321(x62201),x62202),f319(f164(x62201),x62203)))+~P1(f319(f319(f164(x62201),x62203),x62202))
% 28.73/28.52 [6221]P1(f319(f319(f321(x62211),x62212),f319(f164(x62211),x62213)))+~P1(f319(f319(f164(x62211),x62213),x62212))
% 28.73/28.52 [6226]E(f319(f181(f926(x62261)),f162(x62261,x62262,x62263)),f319(f181(f926(x62261)),x62263))+P1(f319(f319(f321(x62261),x62262),f319(f164(x62261),x62263)))
% 28.73/28.52 [6244]P1(f319(x62441,x62442))+~P1(f319(f319(f321(x62443),x62442),f180(f932(x62443,a923))))
% 28.73/28.52 [6245]~P1(f319(x62452,x62453))+P1(f319(f319(f321(x62451),f756(x62452,x62451)),f234(f932(x62451,a923))))
% 28.73/28.52 [6277]~P113(x62771)+E(f319(f319(f93(f932(x62771,a923)),f319(f294(x62771,x62772),x62773)),f319(f275(x62771),x62773)),f180(f932(x62771,a923)))
% 28.73/28.52 [6297]~P68(x62971)+E(f319(f302(x62971,x62971,f73(x62971)),f295(x62971,x62972,x62973)),f295(x62971,f319(f73(x62971),x62973),f319(f73(x62971),x62972)))
% 28.73/28.52 [6298]~P68(x62981)+E(f319(f302(x62981,x62981,f73(x62981)),f298(x62981,x62982,x62983)),f298(x62981,f319(f73(x62981),x62983),f319(f73(x62981),x62982)))
% 28.73/28.52 [6303]~P1(f319(x63031,x63032))+~P1(f319(f319(f321(x63033),x63032),f180(f932(x63033,a923))))
% 28.73/28.52 [6356]~P1(f319(f319(f321(x63561),x63563),f319(f164(x63561),x63562)))+P1(f319(f319(f164(x63561),x63562),x63563))
% 28.73/28.52 [6357]~P1(f319(f319(f321(x63571),x63573),f319(f164(x63571),x63572)))+P1(f319(f319(f164(x63571),x63572),x63573))
% 28.73/28.52 [6361]E(f168(x63611,f319(f319(f143(x63611),x63612),f105(x63611)),x63613),f319(f319(f143(x63611),x63612),f105(x63611)))+~P1(f319(f319(f321(a925),f2(a925)),x63613))
% 28.73/28.52 [6366]P31(x63661,x63662,x63663)+~P32(a925,x63661,f131(a925,f319(f294(a925,x63662),x63663)))
% 28.73/28.52 [6369]~P68(x63691)+E(f319(f302(x63691,x63691,f73(x63691)),f297(x63691,x63692,x63693)),f319(f294(x63691,f319(f73(x63691),x63693)),f319(f73(x63691),x63692)))
% 28.73/28.52 [6389]~P66(x63891)+E(f39(x63891,f319(f73(x63891),f39(x63891,x63892,x63893)),x63893),f39(x63891,f319(f73(x63891),x63892),x63893))
% 28.73/28.52 [6484]~P1(f319(f55(f931(x64842,x64841)),x64843))+P1(f319(f55(x64841),f319(f276(x64842,x64841),x64843)))
% 28.73/28.52 [6485]~P1(f319(f55(f931(x64851,x64852)),x64853))+P1(f319(f55(x64851),f319(f256(x64851,x64852),x64853)))
% 28.73/28.52 [6490]~P113(x64901)+E(f319(f319(f93(f932(x64901,a923)),f295(x64901,x64902,x64903)),f319(f296(x64901),x64903)),f180(f932(x64901,a923)))
% 28.73/28.52 [6491]~P113(x64911)+E(f319(f319(f93(f932(x64911,a923)),f297(x64911,x64912,x64913)),f319(f296(x64911),x64913)),f180(f932(x64911,a923)))
% 28.73/28.52 [6492]~P113(x64921)+E(f319(f319(f93(f932(x64921,a923)),f298(x64921,x64922,x64923)),f319(f275(x64921),x64923)),f180(f932(x64921,a923)))
% 28.73/28.52 [6563]E(f319(f319(f156(x65631),x65632),f658(x65632,x65633,x65631)),x65633)+~P1(f319(f319(f321(x65631),x65633),f319(f164(x65631),x65632)))
% 28.73/28.52 [6708]E(x67081,f105(x67082))+~E(f319(f319(f319(f175(f926(x67082),f926(x67082)),x67083),f159(x67082)),x67081),f105(x67082))
% 28.73/28.52 [6815]~P1(f319(f55(f931(x68152,x68151)),x68153))+P1(f319(f55(f931(x68151,x68152)),f319(f278(x68152,x68151),x68153)))
% 28.73/28.52 [6838]E(x68381,x68382)+~E(f282(a925,f279(a925),x68383,x68381),f319(f319(f301(a925),x68382),f180(f932(a925,a923))))
% 28.73/28.52 [6839]E(x68391,x68392)+~E(f282(a925,f279(a925),x68391,x68392),f319(f319(f301(a925),x68393),f180(f932(a925,a923))))
% 28.73/28.52 [6970]P60(x69701,x69702,x69703)+P1(f319(f319(f321(x69701),f627(x69703,x69702,x69701)),x69702))
% 28.73/28.52 [6971]P60(x69711,x69712,x69713)+P1(f319(f319(f321(x69711),f626(x69713,x69712,x69711)),x69712))
% 28.73/28.52 [6981]P1(f319(f307(x69811,x69812),x69813))+P1(f319(f319(x69812,f524(x69813,x69812,x69811)),x69813))
% 28.73/28.52 [6982]P1(f319(f307(x69821,x69822),x69823))+P1(f319(f319(x69822,f539(x69823,x69822,x69821)),x69823))
% 28.73/28.52 [7013]E(f319(f181(f926(x70131)),f162(x70131,x70132,x70133)),f319(f319(f23(a925),f319(f181(f926(x70131)),x70133)),f72(a925)))+~P1(f319(f319(f321(x70131),x70132),f319(f164(x70131),x70133)))
% 28.73/28.52 [7052]P1(f319(f240(x70521,x70522),x70523))+P1(f319(f319(f321(x70521),f598(x70523,x70522,x70521)),x70523))
% 28.73/28.52 [7063]~P1(f319(f55(f931(x70632,x70631)),f319(f278(x70631,x70632),x70633)))+P1(f319(f55(f931(x70631,x70632)),x70633))
% 28.73/28.52 [7121]~P1(f319(f319(f321(x71211),x71212),f319(f164(x71211),f106(x71211,x71213))))+P1(f319(f319(f321(x71211),x71212),f319(f164(x71211),x71213)))
% 28.73/28.52 [7155]E(f319(f128(x71551,x71552),x71553),x71553)+P1(f319(f319(f321(x71551),f726(x71553,x71552,x71551)),f319(f164(x71551),x71553)))
% 28.73/28.52 [7169]E(f319(f128(x71691,x71692),x71693),f105(x71691))+P1(f319(f319(f321(x71691),f695(x71693,x71692,x71691)),f319(f164(x71691),x71693)))
% 28.73/28.52 [7193]P32(x71931,x71932,x71933)+P1(f319(f319(f321(x71931),f776(x71933,x71932,x71931)),f319(f164(x71931),x71933)))
% 28.73/28.52 [7194]P32(x71941,x71942,x71943)+P1(f319(f319(f321(x71941),f786(x71943,x71942,x71941)),f319(f164(x71941),x71943)))
% 28.73/28.52 [7195]P32(x71951,x71952,x71953)+P1(f319(f319(f321(x71951),f785(x71952,x71953,x71951)),f319(f164(x71951),x71953)))
% 28.73/28.52 [7198]E(f169(x71981,x71982,x71983),x71983)+P1(f319(f319(f321(x71981),f739(x71983,x71982,x71981)),f319(f164(x71981),x71983)))
% 28.73/28.52 [7274]P1(f319(f152(x72741,x72742),x72743))+P1(f319(f319(f321(x72741),f696(x72743,x72742,x72741)),f319(f164(x72741),x72743)))
% 28.73/28.52 [7283]~P34(x72831,x72833,x72832)+P1(f319(f319(f321(x72831),f771(x72832,x72833,x72831)),f319(f164(x72831),x72832)))
% 28.73/28.52 [7284]~P36(x72841,x72843,x72842)+P1(f319(f319(f321(x72841),f775(x72842,x72843,x72841)),f319(f164(x72841),x72842)))
% 28.73/28.52 [7285]~P36(x72851,x72853,x72852)+P1(f319(f319(f321(x72851),f787(x72852,x72853,x72851)),f319(f164(x72851),x72852)))
% 28.73/28.52 [7286]~P34(x72861,x72863,x72862)+P1(f319(f319(f321(x72861),f814(x72862,x72863,x72861)),f319(f164(x72861),x72862)))
% 28.73/28.52 [7287]~P34(x72871,x72872,x72873)+P1(f319(f319(f321(x72871),f816(x72872,x72873,x72871)),f319(f164(x72871),x72873)))
% 28.73/28.52 [7322]P1(f319(f319(f321(x73221),x73222),f472(x73223,x73222,x73221)))+~P1(f319(f319(f321(x73221),x73222),f31(f932(x73221,a923),x73223)))
% 28.73/28.52 [7323]~P79(x73231)+E(f319(f319(f74(x73231),f319(f319(f6(a925,x73231),x73232),f319(f274(a925),x73233))),f319(x73232,x73233)),f319(f319(f6(a925,x73231),x73232),f319(f274(a925),f319(a104,x73233))))
% 28.73/28.52 [7335]P31(x73351,x73352,x73353)+P1(f319(f319(f321(a925),f857(x73353,x73352,x73351)),f319(f294(a925,x73352),x73353)))
% 28.73/28.52 [7415]~P34(x74152,x74151,x74153)+P1(f319(x74151,f319(f319(f156(x74152),x74153),f772(x74153,x74151,x74152))))
% 28.73/28.52 [7428]~P1(f319(f319(f321(x74281),x74282),f473(x74282,x74283,x74281)))+P1(f319(f319(f321(x74281),x74282),f32(f932(x74281,a923),x74283)))
% 28.73/28.52 [7461]~P79(x74611)+E(f319(f319(f74(x74611),f319(f319(f6(a925,x74611),x74612),f319(f293(a925),x74613))),f319(x74612,f319(a104,x74613))),f319(f319(f6(a925,x74611),x74612),f319(f293(a925),f319(a104,x74613))))
% 28.73/28.52 [7598]P1(f319(f319(f321(f926(x75981)),x75982),f153(x75981,x75983)))+P1(f319(f319(f321(x75981),f678(x75983,x75982,x75981)),f319(f164(x75981),x75982)))
% 28.73/28.52 [7613]~P1(f319(f319(f321(f926(x76131)),x76132),f153(x76131,f308(x76131,x76133))))+P1(f319(f319(f321(f926(x76131)),x76132),f308(f926(x76131),f149(x76131,x76133))))
% 28.73/28.52 [7637]~P1(f319(f319(f321(f926(x76371)),x76372),f308(f926(x76371),f149(x76371,x76373))))+P1(f319(f319(f321(f926(x76371)),x76372),f153(x76371,f308(x76371,x76373))))
% 28.73/28.52 [7670]E(f319(f319(f319(f175(f926(x76701),f926(x76701)),x76702),f159(x76701)),x76703),x76703)+~P1(f319(f319(f226(a925),f319(f181(f926(x76701)),x76703)),f72(a925)))
% 28.73/28.52 [7703]E(f319(f319(f126(x77031),f773(x77032,x77033,x77031)),f319(f319(f143(x77031),x77033),f774(x77032,x77033,x77031))),x77032)+~P1(f319(f319(f321(x77031),x77033),f319(f164(x77031),x77032)))
% 28.73/28.52 [7704]E(f319(f319(f126(x77041),f779(x77042,x77043,x77041)),f319(f319(f143(x77041),x77043),f780(x77042,x77043,x77041))),x77042)+~P1(f319(f319(f321(x77041),x77043),f319(f164(x77041),x77042)))
% 28.73/28.52 [7705]E(f319(f319(f126(x77051),f781(x77052,x77053,x77051)),f319(f319(f143(x77051),x77053),f782(x77052,x77053,x77051))),x77052)+~P1(f319(f319(f321(x77051),x77053),f319(f164(x77051),x77052)))
% 28.73/28.52 [7724]~P26(x77241,x77242,x77243,f234(f932(x77241,a923)))+P26(f926(x77241),f926(x77242),f319(f146(x77241,x77242),x77243),f234(f932(f926(x77241),a923)))
% 28.73/28.52 [7725]~P26(x77251,x77252,x77253,f234(f932(x77251,a923)))+P26(f926(x77251),f926(x77252),f319(f146(x77251,x77252),x77253),f234(f932(f926(x77251),a923)))
% 28.73/28.52 [7875]E(x78751,f319(f319(f74(a925),f319(f319(f75(a925),f319(f243(a925,a925),x78752)),x78753)),f319(f248(a925,a925),x78752)))+~P1(f319(f42(x78751,x78753),x78752))
% 28.73/28.52 [7882]P26(x78821,x78822,x78823,f234(f932(x78821,a923)))+~P26(f926(x78821),f926(x78822),f319(f146(x78821,x78822),x78823),f234(f932(f926(x78821),a923)))
% 28.73/28.52 [7883]P26(x78831,x78832,x78833,f234(f932(x78831,a923)))+~P26(f926(x78831),f926(x78832),f319(f146(x78831,x78832),x78833),f234(f932(f926(x78831),a923)))
% 28.73/28.52 [7927]P1(f319(f319(f321(f932(x79271,a923)),f473(x79272,x79273,x79271)),x79273))+P1(f319(f319(f321(x79271),x79272),f32(f932(x79271,a923),x79273)))
% 28.73/28.52 [8016]P1(f319(f319(f321(f926(x80161)),x80162),f153(x80161,x80163)))+~P1(f319(f319(f321(x80161),f678(x80163,x80162,x80161)),x80163))
% 28.73/28.52 [8119]P32(x81191,x81192,x81193)+~P1(f319(x81192,f319(f319(f156(x81191),x81193),f778(x81193,x81192,x81191))))
% 28.73/28.52 [8144]E(x81441,x81442)+~E(f319(f319(f7(x81443,f932(x81443,a923),a923),f321(x81443)),x81441),f319(f319(f7(x81443,f932(x81443,a923),a923),f321(x81443)),x81442))
% 28.73/28.52 [8152]~P1(f319(f319(f321(f931(x81521,x81521)),x81523),f255(x81521,x81522)))+P1(f319(f319(f321(x81521),f555(x81522,x81523,x81521)),x81522))
% 28.73/28.52 [8154]~P1(f319(f319(f321(x81541),x81543),f31(f932(x81541,a923),x81542)))+P1(f319(f319(f321(f932(x81541,a923)),f472(x81542,x81543,x81541)),x81542))
% 28.73/28.52 [8212]P1(f319(f319(f226(f932(x82121,a923)),x82122),f32(f932(x82121,a923),x82123)))+P1(f319(f319(f321(f932(x82121,a923)),f631(x82122,x82123,x82121)),x82123))
% 28.73/28.52 [8276]P26(x82761,x82762,f85(x82762,x82761,f234(f932(x82762,a923)),x82763),f234(f932(x82761,a923)))+~E(f319(f302(x82762,x82761,x82763),f234(f932(x82762,a923))),f234(f932(x82761,a923)))
% 28.73/28.52 [8302]~P1(f319(f319(f226(f932(x83021,a923)),x83022),f631(x83022,x83023,x83021)))+P1(f319(f319(f226(f932(x83021,a923)),x83022),f32(f932(x83021,a923),x83023)))
% 28.73/28.52 [8330]~P1(f319(f319(f321(x83301),x83302),f319(f164(x83301),f779(x83303,x83302,x83301))))+~P1(f319(f319(f321(x83301),x83302),f319(f164(x83301),x83303)))
% 28.73/28.52 [8331]~P1(f319(f319(f321(x83311),x83312),f319(f164(x83311),f782(x83313,x83312,x83311))))+~P1(f319(f319(f321(x83311),x83312),f319(f164(x83311),x83313)))
% 28.73/28.52 [8358]P31(f319(f66(a923,a923,a925,a314),x83581),x83582,x83583)+P34(a925,x83581,f131(a925,f319(f294(a925,x83582),x83583)))
% 28.73/28.52 [8522]E(x85221,f105(x85222))+P1(f319(f319(f321(x85222),f319(f243(x85222,f931(a91,a91)),f319(f267(x85222,x85221),x85223))),f319(f164(x85222),x85221)))
% 28.73/28.52 [8622]~P77(x86221)+E(f319(f134(x86221,x86221,f319(f7(x86221,x86221,x86221),f74(x86221)),x86222),f319(f160(x86221),x86223)),f319(f134(x86221,x86221,f74(x86221),x86222),x86223))
% 28.73/28.52 [8818]~P26(x88182,x88181,x88183,f234(f932(x88182,a923)))+E(f319(f302(x88181,x88182,f85(x88182,x88181,f234(f932(x88182,a923)),x88183)),f234(f932(x88181,a923))),f234(f932(x88182,a923)))
% 28.73/28.52 [8888]~P31(f319(f66(a923,a923,a925,a314),x88881),x88882,x88883)+~P34(a925,x88881,f131(a925,f319(f294(a925,x88882),x88883)))
% 28.73/28.52 [9030]~P27(x90301,x90302,x90303,f234(f932(x90301,a923)),f234(f932(x90302,a923)))+E(f319(f302(x90301,x90302,x90303),f234(f932(x90301,a923))),f234(f932(x90302,a923)))
% 28.73/28.52 [9031]~P27(x90311,x90312,x90313,f234(f932(x90311,a923)),f234(f932(x90312,a923)))+E(f319(f302(x90311,x90312,x90313),f234(f932(x90311,a923))),f234(f932(x90312,a923)))
% 28.73/28.52 [9137]~P4(x91371)+E(f319(f164(x91371),f141(x91371,x91371,f5(x91371),x91372,x91373)),f319(f319(f301(x91371),x91372),f319(f164(x91371),x91373)))
% 28.73/28.52 [9148]~E(f319(x91483,f319(f85(x91481,x91482,f234(f932(x91481,a923)),x91483),f792(x91483,x91482,x91481))),f792(x91483,x91482,x91481))+E(f319(f302(x91481,x91482,x91483),f234(f932(x91481,a923))),f234(f932(x91482,a923)))
% 28.73/28.52 [9150]P1(f319(f319(f227(a925),f2(a925)),f634(x91501,x91502,x91503)))+~P1(f319(f319(f321(f931(x91503,x91503)),x91502),f319(f319(f281(x91503,x91503,x91503),x91501),f299(x91503,x91501))))
% 28.73/28.52 [9433]~P62(x94331,x94332)+~P1(f319(f319(f321(f931(x94331,x94331)),f319(f319(f244(x94331,x94331),x94333),x94333)),f319(f319(f281(x94331,x94331,x94331),x94332),f299(x94331,x94332))))
% 28.73/28.52 [9536]~P27(x95362,x95361,x95363,f234(f932(x95362,a923)),f234(f932(x95361,a923)))+P27(x95361,x95362,f85(x95362,x95361,f234(f932(x95362,a923)),x95363),f234(f932(x95361,a923)),f234(f932(x95362,a923)))
% 28.73/28.52 [9570]~E(f319(f319(f93(f932(f931(x95701,x95701),a923)),f319(f278(x95701,x95701),x95702)),f299(x95701,x95702)),f180(f932(f931(x95701,x95701),a923)))+~P1(f319(f319(f321(f931(x95701,x95701)),f319(f319(f244(x95701,x95701),x95703),x95703)),f319(f319(f281(x95701,x95701,x95701),x95702),f299(x95701,x95702))))
% 28.73/28.52 [9754]~P1(f319(f55(x97541),x97542))+P1(f319(f319(f226(a925),f319(f29(x97541),f319(f319(f23(f932(x97541,a923)),x97542),f319(f319(f301(x97541),x97543),f180(f932(x97541,a923)))))),f319(f29(x97541),x97542)))
% 28.73/28.52 [5264]~E(x52643,f105(x52641))+E(f136(x52641,f319(f319(f143(x52641),x52642),x52643)),x52642)
% 28.73/28.52 [5265]~E(x52653,f105(x52651))+E(f136(x52651,f319(f319(f143(x52651),x52652),x52653)),x52652)
% 28.73/28.52 [5274]~E(x52743,f105(x52741))+E(f106(x52741,f319(f319(f143(x52741),x52742),x52743)),f105(x52741))
% 28.73/28.52 [5305]E(x53051,f105(x53052))+E(f136(x53052,f319(f319(f143(x53052),x53053),x53051)),f136(x53052,x53051))
% 28.73/28.52 [5306]E(x53061,f105(x53062))+E(f136(x53062,f319(f319(f143(x53062),x53063),x53061)),f136(x53062,x53061))
% 28.73/28.52 [5307]E(x53071,f105(x53072))+E(f136(x53072,f319(f319(f126(x53072),x53073),x53071)),f136(x53072,x53071))
% 28.73/28.52 [5308]E(x53081,f105(x53082))+E(f136(x53082,f319(f319(f126(x53082),x53083),x53081)),f136(x53082,x53081))
% 28.73/28.52 [5315]~E(x53153,f105(x53151))+E(f106(x53151,f319(f319(f126(x53151),x53152),x53153)),f106(x53151,x53152))
% 28.73/28.52 [5316]~E(x53163,f105(x53161))+E(f136(x53161,f319(f319(f126(x53161),x53162),x53163)),f136(x53161,x53162))
% 28.73/28.52 [5317]~E(x53173,f105(x53171))+E(f136(x53171,f319(f319(f126(x53171),x53172),x53173)),f136(x53171,x53172))
% 28.73/28.52 [5352]E(x53521,f105(x53522))+E(f319(f133(x53522),f319(f319(f126(x53522),x53521),x53523)),f319(f133(x53522),x53521))
% 28.73/28.52 [5353]E(x53531,f105(x53532))+E(f319(f133(x53532),f319(f319(f126(x53532),x53531),x53533)),f319(f133(x53532),x53531))
% 28.73/28.52 [5381]~E(x53812,f105(x53811))+E(f319(f133(x53811),f319(f319(f126(x53811),x53812),x53813)),f319(f133(x53811),x53813))
% 28.73/28.52 [5433]~P102(x54331)+E(f319(f319(f102(x54331),x54332),f319(f319(f93(x54331),x54332),x54333)),x54332)
% 28.73/28.52 [5434]~P102(x54341)+E(f319(f319(f93(x54341),x54342),f319(f319(f102(x54341),x54342),x54343)),x54342)
% 28.73/28.52 [5435]~P4(x54351)+E(f319(f319(f224(x54351),x54352),f319(f319(f225(x54351),x54352),x54353)),x54352)
% 28.73/28.52 [5436]~P4(x54361)+E(f319(f319(f225(x54361),x54362),f319(f319(f224(x54361),x54362),x54363)),x54362)
% 28.73/28.52 [5455]~P65(x54551)+E(f39(x54551,f319(f319(f75(x54551),x54552),x54553),x54553),f2(x54551))
% 28.73/28.52 [5456]~P65(x54561)+E(f39(x54561,f319(f319(f75(x54561),x54562),x54563),x54562),f2(x54561))
% 28.73/28.52 [5522]~P70(x55221)+E(f319(f73(x55221),f319(f319(f23(x55221),x55222),x55223)),f319(f319(f23(x55221),x55223),x55222))
% 28.73/28.52 [5584]E(x55841,f105(x55842))+E(f106(x55842,f319(f319(f143(x55842),x55843),x55841)),f319(f319(f143(x55842),x55843),f106(x55842,x55841)))
% 28.73/28.52 [5585]E(x55851,f105(x55852))+E(f106(x55852,f319(f319(f126(x55852),x55853),x55851)),f319(f319(f126(x55852),x55853),f106(x55852,x55851)))
% 28.73/28.52 [5588]~P6(x55881)+E(f32(x55881,f319(f319(f301(x55881),x55882),x55883)),f319(f319(f93(x55881),x55882),f32(x55881,x55883)))
% 28.73/28.52 [5589]~P6(x55891)+E(f31(x55891,f319(f319(f301(x55891),x55892),x55893)),f319(f319(f102(x55891),x55892),f31(x55891,x55893)))
% 28.73/28.52 [5634]~P102(x56341)+E(f319(f319(f102(x56341),x56342),f319(f319(f102(x56341),x56342),x56343)),f319(f319(f102(x56341),x56342),x56343))
% 28.73/28.52 [5635]~P107(x56351)+E(f319(f319(f102(x56351),x56352),f319(f319(f102(x56351),x56352),x56353)),f319(f319(f102(x56351),x56352),x56353))
% 28.73/28.52 [5636]~P107(x56361)+E(f319(f319(f102(x56361),x56362),f319(f319(f102(x56361),x56362),x56363)),f319(f319(f102(x56361),x56362),x56363))
% 28.73/28.52 [5637]~P102(x56371)+E(f319(f319(f93(x56371),x56372),f319(f319(f93(x56371),x56372),x56373)),f319(f319(f93(x56371),x56372),x56373))
% 28.73/28.52 [5638]~P108(x56381)+E(f319(f319(f93(x56381),x56382),f319(f319(f93(x56381),x56382),x56383)),f319(f319(f93(x56381),x56382),x56383))
% 28.73/28.52 [5639]~P108(x56391)+E(f319(f319(f93(x56391),x56392),f319(f319(f93(x56391),x56392),x56393)),f319(f319(f93(x56391),x56392),x56393))
% 28.73/28.52 [5640]~P101(x56401)+E(f319(f319(f75(x56401),x56402),f319(f319(f75(x56401),x56402),x56403)),f319(f319(f75(x56401),x56402),x56403))
% 28.73/28.52 [5641]~P4(x56411)+E(f319(f319(f224(x56411),x56412),f319(f319(f224(x56411),x56412),x56413)),f319(f319(f224(x56411),x56412),x56413))
% 28.73/28.52 [5642]~P4(x56421)+E(f319(f319(f224(x56421),x56422),f319(f319(f224(x56421),x56422),x56423)),f319(f319(f224(x56421),x56422),x56423))
% 28.73/28.52 [5643]~P4(x56431)+E(f319(f319(f225(x56431),x56432),f319(f319(f225(x56431),x56432),x56433)),f319(f319(f225(x56431),x56432),x56433))
% 28.73/28.52 [5644]~P4(x56441)+E(f319(f319(f225(x56441),x56442),f319(f319(f225(x56441),x56442),x56443)),f319(f319(f225(x56441),x56442),x56443))
% 28.73/28.52 [5651]~P65(x56511)+E(f39(x56511,f319(f319(f74(x56511),x56512),x56513),x56513),f39(x56511,x56512,x56513))
% 28.73/28.52 [5652]~P65(x56521)+E(f39(x56521,f319(f319(f74(x56521),x56522),x56523),x56522),f39(x56521,x56523,x56522))
% 28.73/28.52 [5660]~P116(x56601)+E(f319(f319(f75(x56601),x56602),f319(f73(x56601),x56603)),f319(f73(x56601),f319(f319(f75(x56601),x56602),x56603)))
% 28.73/28.52 [5661]~P72(x56611)+E(f319(f319(f283(x56611),x56612),f319(f73(x56611),x56613)),f319(f73(x56611),f319(f319(f283(x56611),x56612),x56613)))
% 28.73/28.52 [5662]~P88(x56621)+E(f319(f319(f74(x56621),x56622),f319(f157(x56621),x56623)),f319(f157(x56621),f319(f319(f143(x56621),x56622),x56623)))
% 28.73/28.52 [5690]~P116(x56901)+E(f319(f319(f75(x56901),f319(f73(x56901),x56902)),x56903),f319(f319(f75(x56901),x56902),f319(f73(x56901),x56903)))
% 28.73/28.52 [5696]~P9(x56961,x56962,x56963)+E(f31(f932(x56961,a923),f319(f319(f54(x56961),x56962),x56963)),x56962)
% 28.73/28.52 [5760]~P121(x57601)+E(f319(f319(f75(x57601),x57602),f319(f319(f236(x57601),x57602),x57603)),f319(f319(f236(x57601),x57602),f319(a104,x57603)))
% 28.73/28.52 [5761]~P119(x57611)+E(f319(f319(f75(x57611),x57612),f319(f319(f236(x57611),x57612),x57613)),f319(f319(f236(x57611),x57612),f319(a104,x57613)))
% 28.73/28.52 [5762]~P121(x57621)+E(f319(f319(f75(x57621),x57622),f319(f319(f236(x57621),x57622),x57623)),f319(f319(f236(x57621),x57622),f319(a104,x57623)))
% 28.73/28.52 [5772]~P69(x57721)+E(f319(f319(f74(x57721),f319(f73(x57721),x57722)),f319(f319(f74(x57721),x57722),x57723)),x57723)
% 28.73/28.52 [5795]~P149(x57951)+E(f319(f319(f236(x57951),f319(f92(x57951),x57952)),x57953),f319(f92(x57951),f319(f319(f236(a925),x57952),x57953)))
% 28.73/28.52 [5796]~P145(x57961)+E(f319(f319(f236(x57961),f319(f94(x57961),x57962)),x57963),f319(f94(x57961),f319(f319(f236(a1),x57962),x57963)))
% 28.73/28.52 [5802]~P92(x58021)+E(f319(f69(x58021),f319(f319(f23(x58021),x58022),x58023)),f319(f69(x58021),f319(f319(f23(x58021),x58023),x58022)))
% 28.73/28.52 [5804]~P126(x58041)+E(f319(f319(f75(x58041),f76(x58041,x58042)),f76(x58041,x58043)),f76(x58041,f319(f319(f75(x58041),x58042),x58043)))
% 28.73/28.52 [5808]E(x58081,f105(x58082))+E(f319(f319(f126(x58082),f319(f163(x58082),x58081)),x58083),f319(f163(x58082),f319(f319(f126(x58082),x58081),x58083)))
% 28.73/28.52 [5813]~E(x58132,f319(a104,f319(f319(f74(a925),x58131),x58133)))+P1(f319(f319(f227(a925),x58131),x58132))
% 28.73/28.52 [5814]~P116(x58141)+E(f319(f319(f75(x58141),f319(f73(x58141),x58142)),x58143),f319(f73(x58141),f319(f319(f75(x58141),x58142),x58143)))
% 28.73/28.52 [5815]~P124(x58151)+E(f319(f319(f283(x58151),f319(f73(x58151),x58152)),x58153),f319(f73(x58151),f319(f319(f283(x58151),x58152),x58153)))
% 28.73/28.52 [5816]~P126(x58161)+E(f319(f319(f236(x58161),f319(f69(x58161),x58162)),x58163),f319(f69(x58161),f319(f319(f236(x58161),x58162),x58163)))
% 28.73/28.52 [5915]E(f845(x59151,x59152,x59153),f856(x59151,x59152,x59153))+E(f319(f319(f93(f932(x59153,a923)),x59152),x59151),f180(f932(x59153,a923)))
% 28.73/28.52 [5930]~P79(x59302)+E(f319(f319(f6(x59301,x59302),f319(f16(x59302,x59301),f2(x59302))),x59303),f2(x59302))
% 28.73/28.52 [5931]~P78(x59312)+E(f319(f319(f9(x59311,x59312),f319(f16(x59312,x59311),f72(x59312))),x59313),f72(x59312))
% 28.73/28.52 [5933]~P149(x59331)+E(f319(f319(f75(x59331),f319(f92(x59331),x59332)),f319(f92(x59331),x59333)),f319(f92(x59331),f319(f319(f75(a925),x59332),x59333)))
% 28.73/28.52 [5934]~P149(x59341)+E(f319(f319(f74(x59341),f319(f92(x59341),x59342)),f319(f92(x59341),x59343)),f319(f92(x59341),f319(f319(f74(a925),x59342),x59343)))
% 28.73/28.52 [5935]~P145(x59351)+E(f319(f319(f23(x59351),f319(f94(x59351),x59352)),f319(f94(x59351),x59353)),f319(f94(x59351),f319(f319(f23(a1),x59352),x59353)))
% 28.73/28.52 [5936]~P145(x59361)+E(f319(f319(f75(x59361),f319(f94(x59361),x59362)),f319(f94(x59361),x59363)),f319(f94(x59361),f319(f319(f75(a1),x59362),x59363)))
% 28.73/28.52 [5937]~P145(x59371)+E(f319(f319(f74(x59371),f319(f94(x59371),x59372)),f319(f94(x59371),x59373)),f319(f94(x59371),f319(f319(f74(a1),x59372),x59373)))
% 28.73/28.52 [5938]~P99(x59381)+E(f319(f319(f23(x59381),f319(f95(x59381),x59382)),f319(f95(x59381),x59383)),f319(f95(x59381),f319(f319(f23(a1),x59382),x59383)))
% 28.73/28.52 [5939]~P99(x59391)+E(f319(f319(f75(x59391),f319(f95(x59391),x59392)),f319(f95(x59391),x59393)),f319(f95(x59391),f319(f319(f75(a1),x59392),x59393)))
% 28.73/28.52 [5940]~P99(x59401)+E(f319(f319(f74(x59401),f319(f95(x59401),x59402)),f319(f95(x59401),x59403)),f319(f95(x59401),f319(f319(f74(a1),x59402),x59403)))
% 28.73/28.52 [5941]~P99(x59411)+E(f319(f319(f75(x59411),f319(f95(x59411),x59412)),f319(f95(x59411),x59413)),f319(f95(x59411),f319(f319(f75(a1),x59412),x59413)))
% 28.73/28.52 [5942]~P99(x59421)+E(f319(f319(f74(x59421),f319(f95(x59421),x59422)),f319(f95(x59421),x59423)),f319(f95(x59421),f319(f319(f74(a1),x59422),x59423)))
% 28.73/28.52 [5990]~E(x59903,x59902)+P1(f319(f319(f226(f932(x59901,a923)),x59902),x59903))
% 28.73/28.52 [5991]~E(x59912,x59913)+P1(f319(f319(f226(f932(x59911,a923)),x59912),x59913))
% 28.73/28.52 [5992]~E(x59922,x59923)+P1(f319(f319(f226(f932(x59921,a923)),x59922),x59923))
% 28.73/28.52 [5993]~E(x59932,x59933)+P1(f319(f319(f226(f932(x59931,a923)),x59932),x59933))
% 28.73/28.52 [5994]~E(x59942,x59943)+P1(f319(f319(f226(f932(x59941,a923)),x59942),x59943))
% 28.73/28.52 [5995]~E(x59952,x59953)+P1(f319(f319(f226(f932(x59951,a923)),x59952),x59953))
% 28.73/28.52 [5996]~E(x59962,x59963)+P1(f319(f319(f226(f932(x59961,a923)),x59962),x59963))
% 28.73/28.52 [6001]~P96(x60011)+E(f319(f319(f93(x60011),f319(f73(x60011),x60012)),f319(f73(x60011),x60013)),f319(f73(x60011),f319(f319(f102(x60011),x60012),x60013)))
% 28.73/28.52 [6002]~P96(x60021)+E(f319(f319(f102(x60021),f319(f73(x60021),x60022)),f319(f73(x60021),x60023)),f319(f73(x60021),f319(f319(f93(x60021),x60022),x60023)))
% 28.73/28.52 [6003]~P69(x60031)+E(f319(f319(f74(x60031),f319(f73(x60031),x60032)),f319(f73(x60031),x60033)),f319(f73(x60031),f319(f319(f74(x60031),x60033),x60032)))
% 28.73/28.52 [6004]~P70(x60041)+E(f319(f319(f74(x60041),f319(f73(x60041),x60042)),f319(f73(x60041),x60043)),f319(f73(x60041),f319(f319(f74(x60041),x60042),x60043)))
% 28.73/28.52 [6005]~P84(x60051)+E(f319(f319(f225(x60051),f319(f73(x60051),x60052)),f319(f73(x60051),x60053)),f319(f73(x60051),f319(f319(f224(x60051),x60052),x60053)))
% 28.73/28.52 [6006]~P84(x60061)+E(f319(f319(f224(x60061),f319(f73(x60061),x60062)),f319(f73(x60061),x60063)),f319(f73(x60061),f319(f319(f225(x60061),x60062),x60063)))
% 28.73/28.52 [6007]~P126(x60071)+E(f319(f319(f75(x60071),f319(f69(x60071),x60072)),f319(f69(x60071),x60073)),f319(f69(x60071),f319(f319(f75(x60071),x60072),x60073)))
% 28.73/28.52 [6008]~P74(x60081)+E(f319(f319(f283(x60081),f319(f69(x60081),x60082)),f319(f69(x60081),x60083)),f319(f69(x60081),f319(f319(f283(x60081),x60082),x60083)))
% 28.73/28.52 [6009]~P88(x60091)+E(f319(f319(f74(x60091),f319(f157(x60091),x60092)),f319(f157(x60091),x60093)),f319(f157(x60091),f319(f319(f126(x60091),x60092),x60093)))
% 28.73/28.52 [6010]E(x60101,f180(f932(x60102,a923)))+~E(f319(f319(f102(f932(x60102,a923)),x60103),x60101),f180(f932(x60102,a923)))
% 28.73/28.52 [6011]E(x60111,f180(f932(x60112,a923)))+~E(f319(f319(f102(f932(x60112,a923)),x60111),x60113),f180(f932(x60112,a923)))
% 28.73/28.52 [6012]~P152(x60121,x60123,x60122)+P1(f319(x60121,f319(f319(f30(a1),x60122),x60123)))
% 28.73/28.52 [6068]~P1(f319(f55(x60681),x60683))+P1(f319(f55(x60681),f319(f319(f301(x60681),x60682),x60683)))
% 28.73/28.52 [6069]~P1(f319(f55(x60691),x60693))+P1(f319(f55(x60691),f319(f319(f301(x60691),x60692),x60693)))
% 28.73/28.52 [6070]~P1(f319(f129(x60701),x60703))+P1(f319(f129(x60701),f319(f319(f167(x60701),x60702),x60703)))
% 28.73/28.52 [6071]~P1(f319(f129(x60711),x60713))+P1(f319(f129(x60711),f319(f319(f130(x60711),x60712),x60713)))
% 28.73/28.52 [6104]~P102(x61041)+P1(f319(f319(f226(x61041),x61042),f319(f319(f102(x61041),x61043),x61042)))
% 28.73/28.52 [6105]~P107(x61051)+P1(f319(f319(f226(x61051),x61052),f319(f319(f102(x61051),x61053),x61052)))
% 28.73/28.52 [6106]~P102(x61061)+P1(f319(f319(f226(x61061),x61062),f319(f319(f102(x61061),x61062),x61063)))
% 28.73/28.52 [6107]~P107(x61071)+P1(f319(f319(f226(x61071),x61072),f319(f319(f102(x61071),x61072),x61073)))
% 28.73/28.52 [6108]~P4(x61081)+P1(f319(f319(f226(x61081),x61082),f319(f319(f225(x61081),x61083),x61082)))
% 28.73/28.52 [6109]~P4(x61091)+P1(f319(f319(f226(x61091),x61092),f319(f319(f225(x61091),x61092),x61093)))
% 28.73/28.52 [6110]~P121(x61101)+P1(f319(f319(f279(x61101),x61102),f319(f319(f75(x61101),x61103),x61102)))
% 28.73/28.52 [6111]~P121(x61111)+P1(f319(f319(f279(x61111),x61112),f319(f319(f75(x61111),x61112),x61113)))
% 28.73/28.52 [6125]~E(x61251,f2(a925))+E(f319(f319(f30(a925),f319(f319(f75(a925),x61251),x61252)),f319(f319(f75(a925),x61251),x61253)),f2(a925))
% 28.73/28.52 [6208]~P99(x62081)+E(f319(f319(f23(x62081),f319(f95(x62081),x62082)),f319(f95(x62081),x62083)),f319(f95(x62081),f319(f319(f74(a1),x62082),f319(f73(a1),x62083))))
% 28.73/28.52 [6267]E(x62671,f2(a925))+E(f319(f319(f30(a925),f319(f319(f75(a925),x62671),x62672)),f319(f319(f75(a925),x62671),x62673)),f319(f319(f30(a925),x62672),x62673))
% 28.73/28.52 [6295]E(f144(x62951,f319(f319(f143(x62951),x62952),x62953)),f319(f319(f143(x62951),x62952),f144(x62951,x62953)))+P1(f319(f319(f321(x62951),x62952),f319(f164(x62951),x62953)))
% 28.73/28.52 [6331]P152(x63311,x63312,x63313)+~P1(f319(x63311,f319(f319(f30(a1),x63313),x63312)))
% 28.73/28.52 [6402]E(x64021,f105(x64022))+E(f319(f319(f143(x64022),f319(f133(x64022),x64021)),f319(f319(f167(x64022),x64023),f319(f163(x64022),x64021))),f319(f319(f167(x64022),f319(a104,x64023)),x64021))
% 28.73/28.52 [6409]E(f319(f319(f23(f932(x64091,a923)),x64092),x64093),x64092)+~E(f319(f319(f93(f932(x64091,a923)),x64092),x64093),f180(f932(x64091,a923)))
% 28.73/28.52 [6424]E(f144(x64241,f319(f319(f143(x64241),x64242),x64243)),f144(x64241,x64243))+~P1(f319(f319(f321(x64241),x64242),f319(f164(x64241),x64243)))
% 28.73/28.52 [6453]~P1(f319(f319(f226(a925),x64531),x64533))+P1(f319(f319(f226(a925),x64531),f319(f319(f74(a925),x64532),x64533)))
% 28.73/28.52 [6454]~P1(f319(f319(f226(a925),x64541),x64543))+P1(f319(f319(f226(a925),x64541),f319(f319(f74(a925),x64542),x64543)))
% 28.73/28.52 [6455]~P1(f319(f319(f226(a925),x64551),x64552))+P1(f319(f319(f226(a925),x64551),f319(f319(f74(a925),x64552),x64553)))
% 28.73/28.52 [6456]~P1(f319(f319(f226(a925),x64561),x64562))+P1(f319(f319(f226(a925),x64561),f319(f319(f74(a925),x64562),x64563)))
% 28.73/28.52 [6457]~P1(f319(f319(f227(a925),x64571),x64573))+P1(f319(f319(f227(a925),x64571),f319(f319(f74(a925),x64572),x64573)))
% 28.73/28.52 [6458]~P1(f319(f319(f227(a925),x64581),x64583))+P1(f319(f319(f227(a925),x64581),f319(f319(f74(a925),x64582),x64583)))
% 28.73/28.52 [6459]~P1(f319(f319(f227(a925),x64591),x64592))+P1(f319(f319(f227(a925),x64591),f319(f319(f74(a925),x64592),x64593)))
% 28.73/28.52 [6460]~P1(f319(f319(f227(a925),x64601),x64602))+P1(f319(f319(f227(a925),x64601),f319(f319(f74(a925),x64602),x64603)))
% 28.73/28.52 [6498]P1(f319(f55(x64981),x64982))+~P1(f319(f55(x64981),f319(f319(f301(x64981),x64983),x64982)))
% 28.73/28.52 [6499]P1(f319(f129(x64991),x64992))+~P1(f319(f129(x64991),f319(f319(f143(x64991),x64993),x64992)))
% 28.73/28.52 [6500]P1(f319(f129(x65001),x65002))+~P1(f319(f129(x65001),f319(f319(f126(x65001),x65003),x65002)))
% 28.73/28.52 [6501]P1(f319(f129(x65011),x65012))+~P1(f319(f129(x65011),f319(f319(f126(x65011),x65012),x65013)))
% 28.73/28.52 [6552]~P121(x65521)+E(f319(f319(f74(x65521),x65522),f319(f319(f75(x65521),x65523),x65522)),f319(f319(f75(x65521),f319(f319(f74(x65521),x65523),f72(x65521))),x65522))
% 28.73/28.52 [6599]~E(x65991,x65992)+~P1(f319(f319(f227(f932(x65993,a923)),x65991),x65992))
% 28.73/28.52 [6645]P1(f319(f319(f321(x66451),x66452),x66453))+P1(f319(f319(f321(x66451),x66452),f319(f73(f932(x66451,a923)),x66453)))
% 28.73/28.52 [6646]P1(f319(f319(f321(x66461),x66462),x66463))+P1(f319(f319(f321(x66461),x66462),f319(f73(f932(x66461,a923)),x66463)))
% 28.73/28.52 [6652]E(f136(x66521,f319(f319(f130(x66521),x66522),x66523)),f136(x66521,x66523))+~P1(f319(f319(f227(a925),x66522),f319(f181(f926(x66521)),x66523)))
% 28.73/28.52 [6653]E(f319(f319(f167(x66531),x66532),f106(x66531,x66533)),f319(f319(f167(x66531),x66532),x66533))+~P1(f319(f319(f227(a925),x66532),f319(f181(f926(x66531)),x66533)))
% 28.73/28.52 [6710]E(f319(f319(f319(f175(f926(x67101),f926(x67101)),x67102),f159(x67101)),x67103),x67103)+~E(f39(a925,x67102,f319(f181(f926(x67101)),x67103)),f2(a925))
% 28.73/28.52 [6717]~P9(x67171,x67173,x67172)+E(f319(f319(f281(x67171,x67171,x67171),f319(f278(x67171,x67171),x67172)),x67172),x67172)
% 28.73/28.52 [6759]~E(f319(f319(f102(f932(x67591,a923)),x67592),x67593),x67593)+P1(f319(f319(f226(f932(x67591,a923)),x67592),x67593))
% 28.73/28.52 [6764]~P59(x67641,x67641,x67643)+P59(x67641,x67641,f319(f319(f175(f931(x67641,x67641),a923),x67642),x67643))
% 28.73/28.52 [6768]~P1(f319(f319(f321(x67681),x67683),f319(f164(x67681),x67682)))+P1(f319(f319(f227(a925),f2(a925)),f319(f181(f926(x67681)),x67682)))
% 28.73/28.52 [6783]~E(x67832,x67833)+P1(f319(f319(f321(x67831),x67832),f319(f319(f301(x67831),x67833),f180(f932(x67831,a923)))))
% 28.73/28.52 [6794]~P92(x67941)+E(f319(f69(x67941),f319(f319(f74(x67941),f319(f69(x67941),x67942)),f319(f69(x67941),x67943))),f319(f319(f74(x67941),f319(f69(x67941),x67942)),f319(f69(x67941),x67943)))
% 28.73/28.52 [6804]E(f319(f319(f30(a925),f319(f319(f75(a925),x68041),x68042)),f319(f319(f75(a925),x68041),x68043)),f319(f319(f30(a925),x68042),x68043))+~P1(f319(f319(f227(a925),f2(a925)),x68041))
% 28.73/28.52 [6950]~P1(f319(f55(x69501),x69503))+E(f319(f319(f58(x69501,f932(x69501,a923),f301(x69501)),x69502),x69503),f319(f319(f102(f932(x69501,a923)),x69503),x69502))
% 28.73/28.52 [7006]E(f319(f319(f102(f932(x70061,a923)),x70062),x70063),x70062)+~P1(f319(f319(f226(f932(x70061,a923)),x70063),x70062))
% 28.73/28.52 [7007]E(f319(f319(f102(f932(x70071,a923)),x70072),x70073),x70073)+~P1(f319(f319(f226(f932(x70071,a923)),x70072),x70073))
% 28.73/28.52 [7008]E(f319(f319(f102(f932(x70081,a923)),x70082),x70083),x70083)+~P1(f319(f319(f226(f932(x70081,a923)),x70082),x70083))
% 28.73/28.52 [7009]E(f319(f319(f93(f932(x70091,a923)),x70092),x70093),x70093)+~P1(f319(f319(f226(f932(x70091,a923)),x70093),x70092))
% 28.73/28.52 [7010]E(f319(f319(f93(f932(x70101,a923)),x70102),x70103),x70102)+~P1(f319(f319(f226(f932(x70101,a923)),x70102),x70103))
% 28.73/28.52 [7061]~P1(f319(f129(x70611),x70612))+E(f319(f319(f23(f932(x70611,a923)),f319(f164(x70611),x70612)),f319(f319(f301(x70611),x70613),f180(f932(x70611,a923)))),f319(f164(x70611),f162(x70611,x70613,x70612)))
% 28.73/28.52 [7116]P38(x71161,x71162)+~P38(x71161,f319(f319(f175(f931(x71161,x71161),a923),x71163),x71162))
% 28.73/28.52 [7132]~E(x71321,f2(a925))+P1(f319(f319(f279(a925),f319(f319(f75(a925),x71321),x71322)),f319(f319(f75(a925),x71321),x71323)))
% 28.73/28.52 [7181]P1(f319(f43(x71811,x71812),f319(a45,x71813)))+~P1(f319(f43(f319(f73(a1),x71811),f319(f73(a1),x71812)),x71813))
% 28.73/28.52 [7186]E(f319(f319(f23(f932(x71861,a923)),f319(f319(f301(x71861),x71862),x71863)),f319(f319(f301(x71861),x71862),f180(f932(x71861,a923)))),x71863)+P1(f319(f319(f321(x71861),x71862),x71863))
% 28.73/28.52 [7208]E(f319(f319(f93(f932(x72081,a923)),f319(f164(x72081),x72082)),f319(f164(x72081),x72083)),f180(f932(x72081,a923)))+~P1(f319(f129(x72081),f319(f319(f126(x72081),x72082),x72083)))
% 28.73/28.52 [7223]~P1(f319(f319(f321(x72231),x72232),f319(f164(x72231),x72233)))+~P1(f319(f129(x72231),f319(f319(f143(x72231),x72232),x72233)))
% 28.73/28.52 [7294]P32(x72941,x72942,x72943)+P1(f319(f319(f227(a925),f778(x72943,x72942,x72941)),f319(f181(f926(x72941)),x72943)))
% 28.73/28.52 [7304]E(f319(f319(f93(f932(x73041,a923)),x73042),x73043),f180(f932(x73041,a923)))+P1(f319(f319(f321(x73041),f845(x73043,x73042,x73041)),x73042))
% 28.73/28.52 [7305]E(f319(f319(f93(f932(x73051,a923)),x73052),x73053),f180(f932(x73051,a923)))+P1(f319(f319(f321(x73051),f856(x73053,x73052,x73051)),x73053))
% 28.73/28.52 [7308]E(f106(x73081,f319(f319(f167(x73081),x73082),x73083)),f319(f319(f167(x73081),f319(f319(f23(a925),x73082),f72(a925))),x73083))+~P1(f319(f319(f226(a925),x73082),f319(f181(f926(x73081)),x73083)))
% 28.73/28.52 [7368]~P34(x73683,x73682,x73681)+P1(f319(f319(f227(a925),f772(x73681,x73682,x73683)),f319(f181(f926(x73683)),x73681)))
% 28.73/28.52 [7388]P1(f319(f319(f227(a925),f2(a925)),x73881))+P1(f319(f319(f226(a925),f319(f319(f75(a925),x73882),x73881)),f319(f319(f75(a925),x73883),x73881)))
% 28.73/28.52 [7389]P1(f319(f319(f227(a925),f2(a925)),x73891))+P1(f319(f319(f226(a925),f319(f319(f75(a925),x73891),x73892)),f319(f319(f75(a925),x73891),x73893)))
% 28.73/28.52 [7390]~P1(f319(f319(f321(x73901),x73902),x73903))+~P1(f319(f319(f321(x73901),x73902),f319(f73(f932(x73901,a923)),x73903)))
% 28.73/28.52 [7391]~P1(f319(f319(f321(x73911),x73912),x73913))+~P1(f319(f319(f321(x73911),x73912),f319(f73(f932(x73911,a923)),x73913)))
% 28.73/28.52 [7392]~P1(f319(f319(f321(x73921),x73922),x73923))+~P1(f319(f319(f321(x73921),x73922),f319(f73(f932(x73921,a923)),x73923)))
% 28.73/28.52 [7396]~P1(f319(f319(f227(f932(x73961,a923)),x73962),x73963))+P1(f319(f319(f226(f932(x73961,a923)),x73962),x73963))
% 28.73/28.52 [7397]~P1(f319(f319(f227(f932(x73971,a923)),x73972),x73973))+P1(f319(f319(f226(f932(x73971,a923)),x73972),x73973))
% 28.73/28.52 [7398]~P1(f319(f319(f227(f932(x73981,a923)),x73982),x73983))+P1(f319(f319(f226(f932(x73981,a923)),x73982),x73983))
% 28.73/28.52 [7506]~P1(f319(f319(f226(a925),x75063),x75062))+P1(f319(f319(f226(a925),f319(f319(f23(a925),x75061),x75062)),f319(f319(f23(a925),x75061),x75063)))
% 28.73/28.52 [7507]~P1(f319(f319(f226(a925),x75071),x75073))+P1(f319(f319(f226(a925),f319(f319(f23(a925),x75071),x75072)),f319(f319(f23(a925),x75073),x75072)))
% 28.73/28.52 [7508]~P1(f319(f319(f226(a925),x75082),x75083))+P1(f319(f319(f226(a925),f319(f319(f75(a925),x75081),x75082)),f319(f319(f75(a925),x75081),x75083)))
% 28.73/28.52 [7509]~P1(f319(f319(f226(a925),x75092),x75093))+P1(f319(f319(f226(a925),f319(f319(f75(a925),x75091),x75092)),f319(f319(f75(a925),x75091),x75093)))
% 28.73/28.52 [7510]~P1(f319(f319(f226(a925),x75101),x75103))+P1(f319(f319(f226(a925),f319(f319(f75(a925),x75101),x75102)),f319(f319(f75(a925),x75103),x75102)))
% 28.73/28.52 [7511]~P1(f319(f319(f226(a925),x75111),x75113))+P1(f319(f319(f226(a925),f319(f319(f75(a925),x75111),x75112)),f319(f319(f75(a925),x75113),x75112)))
% 28.73/28.52 [7512]~P1(f319(f319(f226(a925),x75122),x75123))+P1(f319(f319(f226(a925),f319(f319(f74(a925),x75121),x75122)),f319(f319(f74(a925),x75121),x75123)))
% 28.73/28.52 [7513]~P1(f319(f319(f226(a925),x75131),x75133))+P1(f319(f319(f226(a925),f319(f319(f74(a925),x75131),x75132)),f319(f319(f74(a925),x75133),x75132)))
% 28.73/28.52 [7514]~P1(f319(f319(f226(a925),x75141),x75143))+P1(f319(f319(f226(a925),f319(f319(f30(a925),x75141),x75142)),f319(f319(f30(a925),x75143),x75142)))
% 28.73/28.52 [7515]~P1(f319(f319(f226(a1),x75152),x75153))+P1(f319(f319(f226(a1),f319(f319(f74(a1),x75151),x75152)),f319(f319(f74(a1),x75151),x75153)))
% 28.73/28.52 [7518]~P1(f319(f319(f227(a925),x75182),x75183))+P1(f319(f319(f227(a925),f319(f319(f74(a925),x75181),x75182)),f319(f319(f74(a925),x75181),x75183)))
% 28.73/28.52 [7519]~P1(f319(f319(f227(a925),x75191),x75193))+P1(f319(f319(f227(a925),f319(f319(f74(a925),x75191),x75192)),f319(f319(f74(a925),x75193),x75192)))
% 28.73/28.52 [7520]~P1(f319(f319(f227(a1),x75201),x75203))+P1(f319(f319(f227(a1),f319(f319(f74(a1),x75201),x75202)),f319(f319(f74(a1),x75203),x75202)))
% 28.73/28.52 [7523]~P1(f319(f319(f279(a925),x75232),x75233))+P1(f319(f319(f279(a925),f319(f319(f75(a925),x75231),x75232)),f319(f319(f75(a925),x75231),x75233)))
% 28.73/28.52 [7596]E(x75961,x75962)+~P1(f319(f319(f321(x75963),x75961),f319(f319(f301(x75963),x75962),f180(f932(x75963,a923)))))
% 28.73/28.52 [7597]E(x75971,x75972)+~P1(f319(f319(f321(x75973),x75971),f319(f319(f301(x75973),x75972),f180(f932(x75973,a923)))))
% 28.73/28.52 [7599]~E(f319(f319(f93(f932(x75991,a923)),x75992),x75993),f180(f932(x75991,a923)))+P1(f319(f319(f226(f932(x75991,a923)),x75992),f319(f73(f932(x75991,a923)),x75993)))
% 28.73/28.52 [7603]P1(f319(f319(f321(f932(x76031,a923)),x76032),f319(f300(x76031),x76033)))+~P1(f319(f319(f226(f932(x76031,a923)),x76032),x76033))
% 28.73/28.52 [7604]P1(f319(f319(f321(f932(x76041,a923)),x76042),f319(f300(x76041),x76043)))+~P1(f319(f319(f226(f932(x76041,a923)),x76042),x76043))
% 28.73/28.52 [7609]P1(f319(f319(f321(x76091),f737(x76092,x76093,x76091)),x76093))+P1(f319(f319(f226(f932(x76091,a923)),x76093),x76092))
% 28.73/28.52 [7654]E(f319(f319(f143(x76541),f319(f319(f156(x76541),x76542),x76543)),f319(f319(f130(x76541),f319(a104,x76543)),x76542)),f319(f319(f130(x76541),x76543),x76542))+~P1(f319(f319(f227(a925),x76543),f319(f181(f926(x76541)),x76542)))
% 28.73/28.52 [7680]P1(f319(f319(f321(f931(x76801,x76801)),x76802),f299(x76801,x76803)))+~P1(f319(f319(f321(f931(x76801,x76801)),x76802),x76803))
% 28.73/28.52 [7688]~P1(f319(f319(f321(f932(x76881,a923)),x76882),f319(f300(x76881),x76883)))+P1(f319(f319(f226(f932(x76881,a923)),x76882),x76883))
% 28.73/28.52 [7689]~P1(f319(f319(f321(f932(x76891,a923)),x76892),f319(f300(x76891),x76893)))+P1(f319(f319(f226(f932(x76891,a923)),x76892),x76893))
% 28.73/28.52 [7731]P1(f319(f319(f226(f932(x77311,a923)),x77312),f31(f932(x77311,a923),x77313)))+~P1(f319(f319(f321(f932(x77311,a923)),x77312),x77313))
% 28.73/28.52 [7755]~P145(x77551)+E(f319(f319(f75(x77551),f319(f319(f236(x77551),f319(f73(x77551),f72(x77551))),x77552)),f319(f319(f236(x77551),x77553),x77552)),f319(f319(f236(x77551),f319(f73(x77551),x77553)),x77552))
% 28.73/28.52 [7777]E(f319(f319(f156(x77771),x77772),f319(f319(f23(a925),f319(f181(f926(x77771)),x77772)),f319(a104,x77773))),f319(f319(f156(x77771),f319(f160(x77771),x77772)),x77773))+~P1(f319(f319(f227(a925),x77773),f319(f181(f926(x77771)),x77772)))
% 28.73/28.52 [7794]~E(f319(f319(f93(f932(x77941,a923)),f880(x77943,x77942,x77941)),x77943),f180(f932(x77941,a923)))+E(f319(f319(f93(f932(x77941,a923)),f31(f932(x77941,a923),x77942)),x77943),f180(f932(x77941,a923)))
% 28.73/28.52 [7858]~P1(f319(f319(f321(x78583),x78582),f319(f164(x78583),x78581)))+P1(f319(f319(f227(a925),f658(x78581,x78582,x78583)),f319(f181(f926(x78583)),x78581)))
% 28.73/28.52 [7866]P1(f319(f319(f321(x78661),f319(f319(f156(x78661),x78662),x78663)),f319(f164(x78661),x78662)))+~P1(f319(f319(f227(a925),x78663),f319(f181(f926(x78661)),x78662)))
% 28.73/28.52 [7963]~P1(f319(x79632,f740(x79633,x79632,x79631)))+E(f319(f319(f130(x79631),f319(f181(f926(x79631)),f169(x79631,x79632,x79633))),x79633),f105(x79631))
% 28.73/28.52 [7976]P1(f319(f319(f226(f932(f926(x79761),a923)),f153(x79761,x79762)),f153(x79761,x79763)))+~P1(f319(f319(f226(f932(x79761,a923)),x79762),x79763))
% 28.73/28.52 [7977]P1(f319(f319(f226(f932(f926(x79771),a923)),f152(x79771,x79772)),f152(x79771,x79773)))+~P1(f319(f319(f226(f932(x79771,a923)),x79772),x79773))
% 28.73/28.52 [8003]E(f319(f319(f93(f932(x80031,a923)),f31(f932(x80031,a923),x80032)),x80033),f180(f932(x80031,a923)))+P1(f319(f319(f321(f932(x80031,a923)),f880(x80033,x80032,x80031)),x80032))
% 28.73/28.52 [8005]~P1(f319(f319(f321(f932(x80051,a923)),x80053),x80052))+P1(f319(f319(f226(f932(x80051,a923)),f32(f932(x80051,a923),x80052)),x80053))
% 28.73/28.52 [8007]E(f319(f319(f93(f932(x80071,a923)),x80072),x80073),f180(f932(x80071,a923)))+~P1(f319(f319(f226(f932(x80071,a923)),x80072),f319(f73(f932(x80071,a923)),x80073)))
% 28.73/28.52 [8057]E(f319(f319(f23(a925),f319(f319(f74(a925),f319(f157(a925),x80571)),x80572)),f319(f319(f156(a925),x80571),x80573)),f319(f157(a925),f319(f319(f151(a925,x80571),x80573),x80572)))+~P1(f319(f319(f227(a925),x80573),f319(f181(f926(a925)),x80571)))
% 28.73/28.52 [8108]P1(f319(f319(f226(a925),x81081),x81082))+~P1(f319(f319(f226(a925),f319(f319(f74(a925),x81083),x81081)),f319(f319(f74(a925),x81083),x81082)))
% 28.73/28.52 [8111]P1(f319(f319(f227(a925),x81111),x81112))+~P1(f319(f319(f227(a925),f319(f319(f74(a925),x81113),x81111)),f319(f319(f74(a925),x81113),x81112)))
% 28.73/28.52 [8112]P1(f319(f319(f227(a925),x81121),x81122))+~P1(f319(f319(f227(a925),f319(f319(f75(a925),x81123),x81121)),f319(f319(f75(a925),x81123),x81122)))
% 28.73/28.52 [8113]P1(f319(f319(f227(a925),x81131),x81132))+~P1(f319(f319(f227(a925),f319(f319(f75(a925),x81131),x81133)),f319(f319(f75(a925),x81132),x81133)))
% 28.73/28.52 [8142]P1(f319(f319(f227(a925),f2(a925)),x81421))+~P1(f319(f319(f227(a925),f319(f319(f75(a925),x81422),x81421)),f319(f319(f75(a925),x81423),x81421)))
% 28.73/28.52 [8143]P1(f319(f319(f227(a925),f2(a925)),x81431))+~P1(f319(f319(f227(a925),f319(f319(f75(a925),x81431),x81432)),f319(f319(f75(a925),x81431),x81433)))
% 28.73/28.52 [8182]~P1(f319(f319(f321(x81821),f737(x81823,x81822,x81821)),x81823))+P1(f319(f319(f226(f932(x81821,a923)),x81822),x81823))
% 28.73/28.52 [8219]E(f239(x82191,x82192,x82193),x82192)+~P1(f319(f319(f226(f932(x82191,a923)),x82193),f319(f319(f301(x82191),x82192),f180(f932(x82191,a923)))))
% 28.73/28.52 [8269]~P1(f319(f129(x82691),x82693))+E(f319(f128(x82691,f319(f319(f8(a923,a923,x82691),a314),f319(a316,x82692))),x82693),f162(x82691,x82692,x82693))
% 28.73/28.52 [8294]E(f319(f319(f130(x82941),f319(f181(f926(x82941)),f169(x82941,x82942,x82943))),x82943),f105(x82941))+P1(f319(f319(f321(x82941),f740(x82943,x82942,x82941)),f319(f164(x82941),x82943)))
% 28.73/28.52 [8298]E(f319(f319(f126(x82981),f319(f319(f167(x82981),x82982),x82983)),f319(f319(f143(x82981),f319(f319(f156(x82981),x82983),x82982)),f105(x82981))),f319(f319(f167(x82981),f319(a104,x82982)),x82983))+~P1(f319(f319(f227(a925),x82982),f319(f181(f926(x82981)),x82983)))
% 28.73/28.52 [8363]E(f319(f128(x83631,f319(f319(f8(a923,a923,x83631),a314),f319(a316,x83632))),x83633),x83633)+P1(f319(f319(f321(x83631),x83632),f319(f164(x83631),x83633)))
% 28.73/28.52 [8369]P1(f319(f319(f226(f932(f932(x83691,a923),a923)),f240(x83691,x83692)),f240(x83691,x83693)))+~P1(f319(f319(f226(f932(x83691,a923)),x83692),x83693))
% 28.73/28.52 [8389]P1(f319(f319(f321(f932(x83891,a923)),f656(x83892,x83893,x83891)),x83893))+P1(f319(f319(f226(f932(x83891,a923)),f31(f932(x83891,a923),x83893)),x83892))
% 28.73/28.52 [8410]~P1(f319(f129(x84101),x84103))+P1(f319(f129(x84101),f319(f319(f319(f175(f926(x84101),f926(x84101)),x84102),f159(x84101)),x84103)))
% 28.73/28.52 [8415]~P1(f319(f319(f226(a925),x84152),x84153))+P1(f319(f319(f226(a925),f319(f319(f75(a925),f319(a104,x84151)),x84152)),f319(f319(f75(a925),f319(a104,x84151)),x84153)))
% 28.73/28.52 [8416]~P1(f319(f319(f227(a925),x84162),x84163))+P1(f319(f319(f227(a925),f319(f319(f75(a925),f319(a104,x84161)),x84162)),f319(f319(f75(a925),f319(a104,x84161)),x84163)))
% 28.73/28.52 [8436]P1(f319(f319(f226(f932(f932(x84361,a923),a923)),f319(f300(x84361),x84362)),f319(f300(x84361),x84363)))+~P1(f319(f319(f226(f932(x84361,a923)),x84362),x84363))
% 28.73/28.52 [8506]~E(f319(f302(x85061,x85062,x85063),f234(f932(x85061,a923))),f234(f932(x85062,a923)))+E(f319(f66(x85061,x85062,x85062,x85063),f85(x85061,x85062,f234(f932(x85061,a923)),x85063)),f25(x85062))
% 28.73/28.52 [8600]~P1(f319(f319(f226(f932(x86001,a923)),x86003),x86002))+P1(f319(f319(f226(f932(x86001,a923)),f319(f73(f932(x86001,a923)),x86002)),f319(f73(f932(x86001,a923)),x86003)))
% 28.73/28.52 [8601]~P1(f319(f319(f226(f932(x86011,a923)),x86013),x86012))+P1(f319(f319(f226(f932(x86011,a923)),f319(f73(f932(x86011,a923)),x86012)),f319(f73(f932(x86011,a923)),x86013)))
% 28.73/28.52 [8635]E(f319(f302(a925,a925,f319(f319(f7(a925,a925,a925),f23(a925)),x86351)),f319(f294(a925,x86352),x86353)),f319(f294(a925,f319(f319(f23(a925),x86352),x86351)),f319(f319(f23(a925),x86353),x86351)))+~P1(f319(f319(f227(a925),x86351),x86353))
% 28.73/28.52 [8661]~P88(x86611)+E(f319(f319(f74(x86611),x86612),f319(f134(x86611,x86611,f74(x86611),f2(x86611)),x86613)),f319(f134(x86611,x86611,f74(x86611),x86612),x86613))
% 28.73/28.52 [8720]~P1(f319(f319(f226(f932(x87201,a923)),f656(x87203,x87202,x87201)),x87203))+P1(f319(f319(f226(f932(x87201,a923)),f31(f932(x87201,a923),x87202)),x87203))
% 28.73/28.52 [8741]~P92(x87411)+P1(f319(f319(f226(x87411),f319(f69(x87411),f319(f319(f23(x87411),x87412),x87413))),f319(f319(f74(x87411),f319(f69(x87411),x87412)),f319(f69(x87411),x87413))))
% 28.73/28.52 [8742]~P92(x87421)+P1(f319(f319(f226(x87421),f319(f69(x87421),f319(f319(f74(x87421),x87422),x87423))),f319(f319(f74(x87421),f319(f69(x87421),x87422)),f319(f69(x87421),x87423))))
% 28.73/28.52 [8753]E(f319(f319(f74(a1),f319(f319(f75(a1),x87531),f39(a1,f319(f319(f30(a1),x87532),x87531),x87533))),f39(a1,x87532,x87531)),f39(a1,x87532,f319(f319(f75(a1),x87531),x87533)))+~P1(f319(f319(f227(a1),f2(a1)),x87533))
% 28.73/28.52 [8759]E(f319(f319(f126(x87591),f319(f319(f167(x87591),x87592),x87593)),f319(f319(f143(x87591),f319(f133(x87591),f319(f319(f130(x87591),x87592),x87593))),f105(x87591))),f319(f319(f167(x87591),f319(a104,x87592)),x87593))+~P1(f319(f319(f227(a925),x87592),f319(f181(f926(x87591)),x87593)))
% 28.73/28.52 [8779]E(f319(f260(x87791,f319(f319(f146(x87791,f931(a91,x87791)),f319(f244(a91,x87791),f72(a91))),x87792)),f319(a3,x87793)),f319(f319(f156(x87791),x87792),x87793))+~P1(f319(f319(f227(a925),x87793),f319(f181(f926(x87791)),x87792)))
% 28.73/28.52 [8848]P1(f319(f319(f321(f931(x88481,x88481)),x88482),f319(f319(f281(x88481,x88481,x88481),x88483),f299(x88481,x88483))))+~P1(f319(f319(f321(f931(x88481,x88481)),x88482),x88483))
% 28.73/28.52 [8859]E(f319(f302(x88591,x88592,x88593),f234(f932(x88591,a923))),f234(f932(x88592,a923)))+~E(f319(f66(x88591,x88592,x88592,x88593),f85(x88591,x88592,f234(f932(x88591,a923)),x88593)),f25(x88592))
% 28.73/28.52 [8868]P1(f319(f319(f226(a925),x88681),x88682))+~P1(f319(f319(f226(a925),f319(f319(f75(a925),f319(a104,x88683)),x88681)),f319(f319(f75(a925),f319(a104,x88683)),x88682)))
% 28.73/28.52 [8869]P1(f319(f319(f227(a925),x88691),x88692))+~P1(f319(f319(f227(a925),f319(f319(f75(a925),f319(a104,x88693)),x88691)),f319(f319(f75(a925),f319(a104,x88693)),x88692)))
% 28.73/28.52 [8884]P1(f319(f319(f226(f932(x88841,a923)),x88842),x88843))+~P1(f319(f319(f226(f932(x88841,a923)),f319(f73(f932(x88841,a923)),x88843)),f319(f73(f932(x88841,a923)),x88842)))
% 28.73/28.52 [8907]P1(f319(f129(x89071),x89072))+~P1(f319(f129(x89071),f319(f319(f319(f175(f926(x89071),f926(x89071)),x89073),f159(x89071)),x89072)))
% 28.73/28.52 [8980]E(f319(f277(x89801,x89801,f299(x89801,x89802)),x89803),x89803)+~P1(f319(f319(f226(f932(x89801,a923)),f319(f277(x89801,x89801,x89802),x89803)),x89803))
% 28.73/28.52 [9029]~P4(x90291)+P14(x90291,f319(f128(x90291,f319(f319(f7(x90291,x90291,a923),a316),f319(x90292,x90293))),x90293))
% 28.73/28.52 [9036]~P1(f319(f319(f226(a925),x90361),x90362))+P1(f319(f319(f226(a925),x90361),f319(f134(a925,a925,f74(a925),x90362),x90363)))
% 28.73/28.52 [9123]~P1(f319(f319(f321(f931(x91231,x91231)),x91232),f299(x91231,x91233)))+P1(f319(f319(f321(f931(x91231,x91231)),x91232),f319(f319(f175(f931(x91231,x91231),a923),f632(x91233,x91232,x91231)),x91233)))
% 28.73/28.52 [9208]~P88(x92081)+E(f319(f319(f74(x92081),x92082),f319(f134(x92081,x92081,f319(f7(x92081,x92081,x92081),f74(x92081)),f2(x92081)),f319(f160(x92081),x92083))),f319(f134(x92081,x92081,f74(x92081),x92082),x92083))
% 28.73/28.52 [9327]~P27(x93272,x93271,x93273,f234(f932(x93272,a923)),f234(f932(x93271,a923)))+E(f85(x93271,x93272,f234(f932(x93271,a923)),f85(x93272,x93271,f234(f932(x93272,a923)),x93273)),x93273)
% 28.73/28.52 [9483]P59(x94831,x94832,x94833)+P1(f319(f319(f321(f931(x94831,x94832)),f319(f319(f244(x94831,x94832),f625(x94833,x94832,x94831)),f611(x94833,x94832,x94831))),x94833))
% 28.73/28.52 [9484]P59(x94841,x94842,x94843)+P1(f319(f319(f321(f931(x94841,x94842)),f319(f319(f244(x94841,x94842),f625(x94843,x94842,x94841)),f610(x94843,x94842,x94841))),x94843))
% 28.73/28.52 [9555]~P1(f319(f319(f321(f931(x95551,x95551)),x95552),f319(f319(f281(x95551,x95551,x95551),x95553),f299(x95551,x95553))))+P1(f319(f319(f321(f931(x95551,x95551)),x95552),f319(f319(f175(f931(x95551,x95551),a923),f634(x95553,x95552,x95551)),x95553)))
% 28.73/28.52 [9556]~P1(f319(x95561,f319(f319(f156(x95562),x95563),f319(f181(f926(x95562)),f169(x95562,x95561,x95563)))))+~P1(f319(f319(f227(a925),f319(f181(f926(x95562)),f169(x95562,x95561,x95563))),f319(f181(f926(x95562)),x95563)))
% 28.73/28.52 [9647]~P1(f319(f319(f226(f932(x96471,a923)),x96472),x96473))+P1(f319(f319(f226(f932(x96471,a923)),f319(f319(f7(x96471,f932(x96471,a923),a923),f321(x96471)),x96472)),f319(f319(f7(x96471,f932(x96471,a923),a923),f321(x96471)),x96473)))
% 28.73/28.52 [9706]~P1(f319(f319(f321(f931(f932(x97061,a923),f932(x97061,a923))),f319(f319(f244(f932(x97061,a923),f932(x97061,a923)),x97062),x97063)),f306(x97061)))+P1(f319(f319(f227(f932(x97061,a923)),x97062),x97063))
% 28.73/28.52 [9730]P60(x97301,x97302,x97303)+~P1(f319(f319(f321(f931(x97301,x97301)),f319(f319(f244(x97301,x97301),f627(x97303,x97302,x97301)),f626(x97303,x97302,x97301))),x97303))
% 28.73/28.52 [9731]P60(x97311,x97312,x97313)+~P1(f319(f319(f321(f931(x97311,x97311)),f319(f319(f244(x97311,x97311),f626(x97313,x97312,x97311)),f627(x97313,x97312,x97311))),x97313))
% 28.73/28.52 [9768]~P1(f319(f319(f321(f931(f926(x97681),f926(x97681))),f319(f319(f244(f926(x97681),f926(x97681)),x97682),x97682)),f139(x97681,x97683)))+P1(f319(f319(f321(f931(x97681,x97681)),f319(f319(f244(x97681,x97681),f677(x97682,x97683,x97681)),f677(x97682,x97683,x97681))),x97683))
% 28.73/28.52 [9820]P1(f319(f319(f226(f932(x98201,a923)),x98202),x98203))+~P1(f319(f319(f226(f932(x98201,a923)),f319(f319(f7(x98201,f932(x98201,a923),a923),f321(x98201)),x98202)),f319(f319(f7(x98201,f932(x98201,a923),a923),f321(x98201)),x98203)))
% 28.73/28.52 [9902]E(f319(f319(f23(a925),f319(f319(f6(a925,a925),x99021),f319(f274(a925),x99022))),f319(f319(f6(a925,a925),x99023),f319(f274(a925),x99022))),f319(f319(f6(a925,a925),f319(f319(f18(a925,a925,a925),f319(f319(f8(a925,f932(a925,a925),a925),f23(a925)),x99021)),x99023)),f319(f274(a925),x99022)))+~P1(f319(f319(f226(a925),f319(x99023,f436(x99022,x99021,x99023))),f319(x99021,f436(x99022,x99021,x99023))))
% 28.73/28.52 [5850]~P69(x58501)+E(f319(f319(f23(x58501),f319(f319(f74(x58501),x58502),x58503)),x58503),x58502)
% 28.73/28.52 [5851]~P69(x58511)+E(f319(f319(f74(x58511),f319(f319(f23(x58511),x58512),x58513)),x58513),x58512)
% 28.73/28.52 [6079]~P69(x60791)+E(f319(f319(f74(x60791),x60792),f319(f319(f74(x60791),f319(f73(x60791),x60792)),x60793)),x60793)
% 28.73/28.52 [6167]~P87(x61671)+E(f319(f319(f75(x61671),f319(f319(f236(x61671),x61672),x61673)),x61672),f319(f319(f236(x61671),x61672),f319(a104,x61673)))
% 28.73/28.52 [6168]~P121(x61681)+E(f319(f319(f75(x61681),f319(f319(f236(x61681),x61682),x61683)),x61682),f319(f319(f236(x61681),x61682),f319(a104,x61683)))
% 28.73/28.52 [6386]~P126(x63861)+E(f319(f69(x63861),f319(f319(f236(x63861),f319(f73(x63861),x63862)),x63863)),f319(f69(x63861),f319(f319(f236(x63861),x63862),x63863)))
% 28.73/28.52 [6436]~P87(x64361)+E(f319(f319(f75(x64361),f319(f319(f236(x64361),x64362),x64363)),x64362),f319(f319(f75(x64361),x64362),f319(f319(f236(x64361),x64362),x64363)))
% 28.73/28.52 [6489]E(f319(f319(f23(a91),f319(f319(f74(a91),x64891),x64892)),x64893),f266(x64891,x64892,x64893))+~P1(f319(f319(f227(a91),x64892),x64893))
% 28.73/28.52 [6513]~E(f319(f319(f130(x65131),x65133),x65132),f105(x65131))+P1(f319(f319(f226(a925),f319(f181(f926(x65131)),x65132)),x65133))
% 28.73/28.52 [6651]E(f319(f319(f75(a925),f319(f95(a925),x66511)),f319(f319(f75(a925),f319(f95(a925),x66512)),x66513)),f2(a925))+~P1(f319(f319(f227(a1),x66511),a77))
% 28.73/28.52 [6667]~P72(x66671)+E(f319(f319(f236(x66671),f319(f319(f283(x66671),f72(x66671)),x66672)),x66673),f319(f319(f283(x66671),f72(x66671)),f319(f319(f236(x66671),x66672),x66673)))
% 28.73/28.52 [6746]E(f319(f319(f23(a925),f319(f319(f74(a925),x67461),x67462)),x67463),f319(f319(f23(a925),x67461),f319(f319(f23(a925),x67463),x67462)))+~P1(f319(f319(f226(a925),x67462),x67463))
% 28.73/28.52 [6747]E(f319(f319(f23(a925),f319(f319(f74(a925),x67471),x67472)),x67473),f319(f319(f74(a925),x67471),f319(f319(f23(a925),x67472),x67473)))+~P1(f319(f319(f226(a925),x67473),x67472))
% 28.73/28.52 [6748]E(f319(f319(f23(a925),f319(f319(f74(a925),x67481),x67482)),x67483),f319(f319(f74(a925),x67481),f319(f319(f23(a925),x67482),x67483)))+~P1(f319(f319(f226(a925),x67483),x67482))
% 28.73/28.52 [6785]~P102(x67851)+P1(f319(f319(f226(x67851),f319(f319(f93(x67851),x67852),x67853)),x67853))
% 28.73/28.52 [6786]~P108(x67861)+P1(f319(f319(f226(x67861),f319(f319(f93(x67861),x67862),x67863)),x67863))
% 28.73/28.52 [6787]~P102(x67871)+P1(f319(f319(f226(x67871),f319(f319(f93(x67871),x67872),x67873)),x67872))
% 28.73/28.52 [6788]~P108(x67881)+P1(f319(f319(f226(x67881),f319(f319(f93(x67881),x67882),x67883)),x67882))
% 28.73/28.52 [6789]~P4(x67891)+P1(f319(f319(f226(x67891),f319(f319(f224(x67891),x67892),x67893)),x67893))
% 28.73/28.52 [6790]~P4(x67901)+P1(f319(f319(f226(x67901),f319(f319(f224(x67901),x67902),x67903)),x67902))
% 28.73/28.52 [6803]E(f319(f319(f30(a1),f319(f319(f30(a1),x68031),x68032)),x68033),f319(f319(f30(a1),x68031),f319(f319(f75(a1),x68032),x68033)))+~P1(f319(f319(f227(a1),f2(a1)),x68033))
% 28.73/28.52 [6859]~P121(x68591)+E(f319(f319(f74(x68591),f319(f319(f75(x68591),x68592),x68593)),x68593),f319(f319(f75(x68591),f319(f319(f74(x68591),x68592),f72(x68591))),x68593))
% 28.73/28.52 [6860]~P99(x68601)+E(f319(f319(f75(x68601),f319(f73(x68601),f319(f95(x68601),x68602))),x68603),f319(f319(f75(x68601),f319(f95(x68601),f319(f73(a1),x68602))),x68603))
% 28.73/28.52 [6935]~P88(x69351)+E(f319(f157(x69351),f319(f319(f146(x69352,x69351),f319(f16(x69351,x69352),f2(x69351))),x69353)),f2(x69351))
% 28.73/28.52 [6951]E(f319(f319(f74(a925),f319(f95(a925),x69511)),f319(f319(f74(a925),f319(f95(a925),x69512)),x69513)),f319(f319(f74(a925),f319(f95(a925),x69512)),x69513))+~P1(f319(a185,f319(f95(a1),x69511)))
% 28.73/28.52 [6966]~P6(x69661)+E(f32(x69661,f319(f319(f301(x69661),x69662),f319(f319(f301(x69661),x69663),f180(f932(x69661,a923))))),f319(f319(f93(x69661),x69662),x69663))
% 28.73/28.52 [6967]~P6(x69671)+E(f31(x69671,f319(f319(f301(x69671),x69672),f319(f319(f301(x69671),x69673),f180(f932(x69671,a923))))),f319(f319(f102(x69671),x69672),x69673))
% 28.73/28.52 [6989]E(f319(f319(f167(x69891),x69892),x69893),x69893)+~P1(f319(f319(f226(a925),f319(f181(f926(x69891)),x69893)),x69892))
% 28.73/28.52 [7000]E(f319(f319(f130(x70001),x70002),x70003),f105(x70001))+~P1(f319(f319(f226(a925),f319(f181(f926(x70001)),x70003)),x70002))
% 28.73/28.52 [7001]E(f319(f319(f130(x70011),x70012),x70013),f105(x70011))+~P1(f319(f319(f226(a925),f319(f181(f926(x70011)),x70013)),x70012))
% 28.73/28.52 [7011]E(f319(f319(f74(a925),f319(f319(f23(a925),x70111),x70112)),x70113),f319(f319(f23(a925),f319(f319(f74(a925),x70111),x70113)),x70112))+~P1(f319(f319(f226(a925),x70112),x70111))
% 28.73/28.52 [7012]E(f319(f319(f74(a925),f319(f319(f23(a925),x70121),x70122)),x70123),f319(f319(f23(a925),f319(f319(f74(a925),x70121),x70123)),x70122))+~P1(f319(f319(f226(a925),x70122),x70121))
% 28.73/28.52 [7026]~P1(f319(f319(f227(a925),x70261),x70263))+P1(f319(f319(f227(a925),f319(f319(f23(a925),x70261),x70262)),x70263))
% 28.73/28.52 [7053]~P4(x70531)+E(f162(x70531,x70532,f319(f319(f140(x70531,x70531,f5(x70531)),x70532),x70533)),x70533)
% 28.73/28.52 [7145]E(f319(f319(f23(a925),f319(f319(f74(a925),x71451),x71452)),f319(a104,x71453)),f319(f319(f23(a925),x71451),f319(a104,f319(f319(f23(a925),x71453),x71452))))+~P1(f319(f319(f226(a925),x71452),x71453))
% 28.73/28.52 [7146]~P126(x71461)+P1(f319(f319(f226(x71461),f2(x71461)),f319(f319(f236(x71461),f319(f69(x71461),x71462)),x71463)))
% 28.73/28.52 [7191]P15(x71911,x71912,x71913)+~P1(f319(f319(f226(f932(f924(x71911),a923)),x71913),x71912))
% 28.73/28.52 [7234]~P1(f319(f55(x72341),x72343))+P1(f319(f55(x72341),f319(f319(f93(f932(x72341,a923)),x72342),x72343)))
% 28.73/28.52 [7235]~P1(f319(f55(x72351),x72352))+P1(f319(f55(x72351),f319(f319(f93(f932(x72351,a923)),x72352),x72353)))
% 28.73/28.52 [7236]~P1(f319(f55(x72361),x72362))+P1(f319(f55(x72361),f319(f319(f23(f932(x72361,a923)),x72362),x72363)))
% 28.73/28.52 [7378]~P38(x73781,x73783)+P38(x73781,f319(f319(f93(f932(f931(x73781,x73781),a923)),x73782),x73783))
% 28.73/28.52 [7379]~P38(x73791,x73792)+P38(x73791,f319(f319(f93(f932(f931(x73791,x73791),a923)),x73792),x73793))
% 28.73/28.52 [7502]~P102(x75021)+E(f10(x75021,f319(f164(x75021),f319(f319(f143(x75021),x75022),x75023))),f319(f134(x75021,x75021,f93(x75021),x75022),x75023))
% 28.73/28.52 [7503]~P102(x75031)+E(f13(x75031,f319(f164(x75031),f319(f319(f143(x75031),x75032),x75033))),f319(f134(x75031,x75031,f102(x75031),x75032),x75033))
% 28.73/28.52 [7504]~P4(x75041)+E(f14(x75041,f319(f164(x75041),f319(f319(f143(x75041),x75042),x75043))),f319(f134(x75041,x75041,f224(x75041),x75042),x75043))
% 28.73/28.52 [7505]~P4(x75051)+E(f15(x75051,f319(f164(x75051),f319(f319(f143(x75051),x75052),x75053))),f319(f134(x75051,x75051,f225(x75051),x75052),x75053))
% 28.73/28.52 [7566]~P1(f319(f55(x75661),x75662))+P1(f319(f319(f226(a925),f319(f29(x75661),x75662)),f319(f29(x75661),f319(f319(f301(x75661),x75663),x75662))))
% 28.73/28.52 [7573]E(f319(f319(f102(f932(a925,a923)),f319(f294(a925,x75731),x75732)),f319(f294(a925,x75732),f319(f319(f74(a925),x75732),x75733))),f319(f294(a925,x75731),f319(f319(f74(a925),x75732),x75733)))+~P1(f319(f319(f226(a925),x75731),x75732))
% 28.73/28.52 [7580]P1(f319(f319(f226(a925),x75801),x75802))+~P1(f319(f319(f226(a925),f319(f319(f74(a925),x75803),x75801)),x75802))
% 28.73/28.52 [7581]P1(f319(f319(f226(a925),x75811),x75812))+~P1(f319(f319(f226(a925),f319(f319(f74(a925),x75811),x75813)),x75812))
% 28.73/28.52 [7582]P1(f319(f319(f226(a925),x75821),x75822))+~P1(f319(f319(f226(a925),f319(f319(f74(a925),x75823),x75821)),x75822))
% 28.73/28.52 [7583]P1(f319(f319(f226(a925),x75831),x75832))+~P1(f319(f319(f226(a925),f319(f319(f74(a925),x75831),x75833)),x75832))
% 28.73/28.52 [7584]P1(f319(f319(f227(a925),x75841),x75842))+~P1(f319(f319(f227(a925),f319(f319(f74(a925),x75841),x75843)),x75842))
% 28.73/28.52 [7622]~P4(x76221)+E(f11(x76221,f224(x76221),f319(f164(x76221),f319(f319(f143(x76221),x76222),x76223))),f319(f134(x76221,x76221,f224(x76221),x76222),x76223))
% 28.73/28.52 [7623]~P4(x76231)+E(f12(x76231,f225(x76231),f319(f164(x76231),f319(f319(f143(x76231),x76232),x76233))),f319(f134(x76231,x76231,f225(x76231),x76232),x76233))
% 28.73/28.52 [7627]~E(x76272,f180(f932(f931(x76271,x76271),a923)))+P1(f319(f319(f226(f932(f931(x76271,x76271),a923)),x76272),x76273))
% 28.73/28.52 [7726]E(f319(f319(f102(f932(x77261,a923)),x77262),f319(f319(f23(f932(x77261,a923)),x77263),x77262)),x77263)+~P1(f319(f319(f226(f932(x77261,a923)),x77262),x77263))
% 28.73/28.52 [7727]~P1(f319(f319(f226(a925),x77271),f319(f319(f74(a925),x77273),x77272)))+P1(f319(f319(f226(a925),f319(f319(f23(a925),x77271),x77272)),x77273))
% 28.73/28.52 [7728]~P1(f319(f319(f227(a925),x77281),f319(f319(f23(a925),x77283),x77282)))+P1(f319(f319(f227(a925),f319(f319(f74(a925),x77281),x77282)),x77283))
% 28.73/28.52 [7784]E(x77841,f105(x77842))+E(f319(f133(x77842),f319(f319(f319(f175(f926(x77842),f926(x77842)),x77843),f159(x77842)),x77841)),f319(f319(f156(x77842),x77841),f39(a925,x77843,f319(f181(f926(x77842)),x77841))))
% 28.73/28.52 [7793]E(f319(f319(f301(x77931),x77932),f319(f319(f23(f932(x77931,a923)),x77933),f319(f319(f301(x77931),x77932),f180(f932(x77931,a923))))),x77933)+~P1(f319(f319(f321(x77931),x77932),x77933))
% 28.73/28.52 [7954]P1(f319(f319(f226(a925),x79541),f319(f319(f74(a925),x79542),x79543)))+~P1(f319(f319(f226(a925),f319(f319(f23(a925),x79541),x79543)),x79542))
% 28.73/28.52 [7955]P1(f319(f319(f227(a925),x79551),f319(f319(f23(a925),x79552),x79553)))+~P1(f319(f319(f227(a925),f319(f319(f74(a925),x79551),x79553)),x79552))
% 28.73/28.52 [7980]P1(f319(f55(x79801),x79802))+~P1(f319(f55(x79801),f319(f319(f102(f932(x79801,a923)),x79803),x79802)))
% 28.73/28.52 [7981]P1(f319(f55(x79811),x79812))+~P1(f319(f55(x79811),f319(f319(f102(f932(x79811,a923)),x79812),x79813)))
% 28.73/28.52 [8055]~P47(x80551,x80553)+P1(f319(f319(f321(f931(x80551,x80551)),f319(f319(f244(x80551,x80551),x80552),x80552)),x80553))
% 28.73/28.52 [8191]E(f319(f319(f156(a925),f131(a925,f319(f294(a925,x81911),x81912))),x81913),f319(f319(f74(a925),x81911),x81913))+~P1(f319(f319(f227(a925),f319(f319(f74(a925),x81911),x81913)),x81912))
% 28.73/28.52 [8258]E(f319(f319(f167(a925),x82581),f131(a925,f319(f294(a925,x82582),x82583))),f131(a925,f319(f294(a925,x82582),f319(f319(f74(a925),x82582),x82581))))+~P1(f319(f319(f226(a925),f319(f319(f74(a925),x82582),x82581)),x82583))
% 28.73/28.52 [8315]~P99(x83151)+E(f319(f319(f236(x83151),x83152),f319(f95(a925),f319(f319(f74(a1),x83153),x83153))),f319(f319(f80(x83151,x83151),f319(f319(f236(x83151),x83152),f319(f95(a925),x83153))),f319(f319(f18(x83151,x83151,x83151),f75(x83151)),f5(x83151))))
% 28.73/28.52 [8582]E(f319(f319(f126(x85821),f319(f319(f167(x85821),x85822),x85823)),f319(f319(f143(x85821),f319(f319(f156(x85821),x85823),x85822)),f319(f319(f130(x85821),f319(a104,x85822)),x85823))),x85823)+~P1(f319(f319(f227(a925),x85822),f319(f181(f926(x85821)),x85823)))
% 28.73/28.52 [8589]P1(f319(f319(f226(f932(x85891,a923)),f307(x85891,x85892)),f307(x85891,x85893)))+~P1(f319(f319(f226(f932(x85891,f932(x85891,a923))),x85893),x85892))
% 28.73/28.52 [8590]~P60(x85901,x85902,x85903)+P60(x85901,x85902,f319(f319(f23(f932(f931(x85901,x85901),a923)),x85903),f299(x85901,f180(f932(f931(x85901,x85901),a923)))))
% 28.73/28.52 [8609]P1(f319(f319(f226(f932(x86091,a923)),f308(x86091,x86092)),f308(x86091,x86093)))+~P1(f319(f319(f226(f932(f931(x86091,x86091),a923)),x86093),x86092))
% 28.73/28.52 [8615]~P1(f319(f319(f227(f932(x86151,a923)),x86153),x86152))+P1(f319(f319(f321(x86151),f904(x86152,x86153,x86151)),f319(f319(f23(f932(x86151,a923)),x86152),x86153)))
% 28.73/28.52 [8617]~P131(x86171)+P1(f319(f319(f226(x86171),f2(x86171)),f319(f319(f74(x86171),f319(f319(f75(x86171),x86172),x86172)),f319(f319(f75(x86171),x86173),x86173))))
% 28.73/28.52 [8645]~P99(x86451)+E(f319(f319(f236(x86451),f319(f95(x86451),x86452)),f319(f95(a925),f319(f319(f74(a1),x86453),x86453))),f319(f319(f80(x86451,x86451),f319(f319(f236(x86451),f319(f95(x86451),x86452)),f319(f95(a925),x86453))),f319(f319(f18(x86451,x86451,x86451),f75(x86451)),f5(x86451))))
% 28.73/28.52 [8650]P1(f319(f319(f226(f932(x86501,a923)),f319(f273(x86501),x86502)),f319(f273(x86501),x86503)))+~P1(f319(f319(f226(f932(f931(x86501,x86501),a923)),x86502),x86503))
% 28.73/28.52 [8681]~P58(x86811,x86812)+~P1(f319(f319(f321(f931(x86811,x86811)),f319(f319(f244(x86811,x86811),x86813),x86813)),x86812))
% 28.73/28.52 [8682]~P38(x86821,x86822)+~P1(f319(f319(f321(f931(x86821,x86821)),f319(f319(f244(x86821,x86821),x86823),x86823)),x86822))
% 28.73/28.52 [8683]~P38(x86831,x86832)+~P1(f319(f319(f321(f931(x86831,x86831)),f319(f319(f244(x86831,x86831),x86833),x86833)),x86832))
% 28.73/28.52 [8726]~E(x87262,x87263)+P1(f319(f319(f321(f931(x87261,x87261)),f319(f319(f244(x87261,x87261),x87262),x87263)),f299(x87261,f180(f932(f931(x87261,x87261),a923)))))
% 28.73/28.52 [8743]P1(f319(f319(f226(f932(x87431,a923)),f32(f932(x87431,a923),x87432)),f32(f932(x87431,a923),x87433)))+~P1(f319(f319(f226(f932(f932(x87431,a923),a923)),x87433),x87432))
% 28.73/28.52 [8744]P1(f319(f319(f226(f932(x87441,a923)),f31(f932(x87441,a923),x87442)),f31(f932(x87441,a923),x87443)))+~P1(f319(f319(f226(f932(f932(x87441,a923),a923)),x87442),x87443))
% 28.73/28.52 [8798]~P9(x87981,x87983,x87982)+P1(f319(f319(f226(f932(f931(x87981,x87981),a923)),x87982),f319(f319(f246(x87981,x87981),x87983),f319(f16(f932(x87981,a923),x87981),x87983))))
% 28.73/28.52 [8799]~P57(x87991,x87993,x87992)+P1(f319(f319(f226(f932(f931(x87991,x87991),a923)),x87992),f319(f319(f246(x87991,x87991),x87993),f319(f16(f932(x87991,a923),x87991),x87993))))
% 28.73/28.52 [8849]~P92(x88491)+P1(f319(f319(f226(x88491),f319(f319(f23(x88491),f319(f69(x88491),x88492)),f319(f69(x88491),x88493))),f319(f69(x88491),f319(f319(f23(x88491),x88493),x88492))))
% 28.73/28.52 [8850]~P92(x88501)+P1(f319(f319(f226(x88501),f319(f319(f23(x88501),f319(f69(x88501),x88502)),f319(f69(x88501),x88503))),f319(f69(x88501),f319(f319(f23(x88501),x88502),x88503))))
% 28.73/28.52 [8882]P1(f319(f319(f226(f932(f931(x88821,x88821),a923)),f299(x88821,x88822)),f299(x88821,x88823)))+~P1(f319(f319(f226(f932(f931(x88821,x88821),a923)),x88822),x88823))
% 28.73/28.52 [8992]~P26(x89922,x89921,x89923,f234(f932(x89922,a923)))+E(f319(f66(x89921,x89922,x89922,f85(x89922,x89921,f234(f932(x89922,a923)),x89923)),x89923),f25(x89922))
% 28.73/28.52 [8993]~P26(x89932,x89931,x89933,f234(f932(x89932,a923)))+E(f319(f66(x89931,x89932,x89932,f85(x89932,x89931,f234(f932(x89932,a923)),x89933)),x89933),f25(x89932))
% 28.73/28.52 [9054]P60(x90541,x90542,x90543)+~P60(x90541,x90542,f319(f319(f23(f932(f931(x90541,x90541),a923)),x90543),f299(x90541,f180(f932(f931(x90541,x90541),a923)))))
% 28.73/28.52 [9074]P1(f319(f319(f226(f932(f931(f926(x90741),f926(x90741)),a923)),f149(x90741,x90742)),f149(x90741,x90743)))+~P1(f319(f319(f226(f932(f931(x90741,x90741),a923)),x90742),x90743))
% 28.73/28.52 [9075]P1(f319(f319(f226(f932(f931(f926(x90751),f926(x90751)),a923)),f150(x90751,x90752)),f150(x90751,x90753)))+~P1(f319(f319(f226(f932(f931(x90751,x90751),a923)),x90752),x90753))
% 28.73/28.52 [9096]~P57(x90961,x90963,x90962)+P1(f319(f319(f226(f932(f931(x90961,x90961),a923)),x90962),f319(f319(f281(x90961,x90961,x90961),f319(f278(x90961,x90961),x90962)),x90962)))
% 28.73/28.52 [9132]~P1(f319(f129(x91321),x91323))+P1(f319(f129(x91321),f319(f319(f130(x91321),f319(f181(f926(x91321)),f169(x91321,x91322,x91323))),x91323)))
% 28.73/28.52 [9151]~P1(f319(f129(x91511),x91512))+E(f319(f128(x91511,f319(f319(f7(x91511,f932(x91511,a923),a923),f321(x91511)),f319(f164(x91511),f168(x91511,x91512,x91513)))),x91512),f168(x91511,x91512,x91513))
% 28.73/28.52 [9206]E(x92061,x92062)+~P1(f319(f319(f321(f931(x92063,x92063)),f319(f319(f244(x92063,x92063),x92061),x92062)),f299(x92063,f180(f932(f931(x92063,x92063),a923)))))
% 28.73/28.52 [9290]P1(f319(f319(f321(x92901),x92902),f308(x92901,x92903)))+P1(f319(f319(f321(f931(x92901,x92901)),f319(f319(f244(x92901,x92901),f560(x92903,x92902,x92901)),x92902)),x92903))
% 28.73/28.52 [9291]P1(f319(f319(f321(x92911),x92912),f308(x92911,x92913)))+P1(f319(f319(f321(f931(x92911,x92911)),f319(f319(f244(x92911,x92911),f612(x92913,x92912,x92911)),x92912)),x92913))
% 28.73/28.52 [9292]P1(f319(f319(f321(x92921),x92922),f308(x92921,x92923)))+P1(f319(f319(f321(f931(x92921,x92921)),f319(f319(f244(x92921,x92921),f613(x92923,x92922,x92921)),x92922)),x92923))
% 28.73/28.52 [9328]P26(x93281,x93282,x93283,f234(f932(x93281,a923)))+~E(f319(f66(x93282,x93281,x93281,f85(x93281,x93282,f234(f932(x93281,a923)),x93283)),x93283),f25(x93281))
% 28.73/28.52 [9382]~P1(f319(f319(f321(f926(x93821)),x93823),f153(x93821,x93822)))+P1(f319(f152(x93821,f319(f319(f7(x93821,f932(x93821,a923),a923),f321(x93821)),x93822)),x93823))
% 28.73/28.52 [9407]P1(f319(x94073,x94072))+E(f319(f254(x94071),f319(f319(f18(x94071,a923,a923),f319(f319(f8(a923,f932(a923,a923),x94071),a317),f319(a316,x94072))),x94073)),f180(f932(x94071,a923)))
% 28.73/28.52 [9423]~P92(x94231)+P1(f319(f319(f226(x94231),f319(f69(x94231),f319(f319(f23(x94231),f319(f69(x94231),x94232)),f319(f69(x94231),x94233)))),f319(f69(x94231),f319(f319(f23(x94231),x94232),x94233))))
% 28.73/28.52 [9438]~P1(f319(x94383,x94382))+E(f319(f254(x94381),f319(f319(f18(x94381,a923,a923),f319(f319(f8(a923,f932(a923,a923),x94381),a317),f319(a316,x94382))),x94383)),f319(f319(f301(x94381),x94382),f180(f932(x94381,a923))))
% 28.73/28.52 [9447]~P1(f319(f319(f321(f932(x94471,a923)),x94473),f319(f300(x94471),x94472)))+P1(f319(f240(x94471,f319(f319(f7(x94471,f932(x94471,a923),a923),f321(x94471)),x94472)),x94473))
% 28.73/28.52 [9482]P38(x94821,x94822)+P1(f319(f319(f321(f931(x94821,x94821)),f319(f319(f244(x94821,x94821),f319(f568(x94822,x94821),f319(a104,x94823))),f319(f568(x94822,x94821),x94823))),x94822))
% 28.73/28.52 [9580]~P1(f319(f129(x95801),x95803))+P1(f319(f129(x95801),f319(f128(x95801,f319(f319(f8(a923,a923,x95801),a314),f319(a316,x95802))),x95803)))
% 28.73/28.52 [9624]P1(f319(f319(f321(f926(x96241)),x96242),f153(x96241,x96243)))+~P1(f319(f152(x96241,f319(f319(f7(x96241,f932(x96241,a923),a923),f321(x96241)),x96243)),x96242))
% 28.73/28.52 [9639]P1(f319(f319(f321(f932(x96391,a923)),x96392),f319(f300(x96391),x96393)))+~P1(f319(f240(x96391,f319(f319(f7(x96391,f932(x96391,a923),a923),f321(x96391)),x96393)),x96392))
% 28.73/28.52 [9701]P1(f319(f319(f321(x97011),f319(f260(x97011,x97012),x97013)),f319(f164(x97011),f319(f319(f146(f931(a91,x97011),x97011),f248(a91,x97011)),x97012))))+~P1(f319(f319(f227(a91),x97013),f319(f157(a91),f319(f319(f146(f931(a91,x97011),a91),f243(a91,x97011)),x97012))))
% 28.73/28.52 [9747]P1(f319(f319(f226(f932(f931(f926(x97471),f926(x97471)),a923)),f150(x97471,x97472)),f319(f319(f246(f926(x97471),f926(x97471)),f153(x97471,x97473)),f319(f16(f932(f926(x97471),a923),f926(x97471)),f153(x97471,x97473)))))+~P1(f319(f319(f226(f932(f931(x97471,x97471),a923)),x97472),f319(f319(f246(x97471,x97471),x97473),f319(f16(f932(x97471,a923),x97471),x97473))))
% 28.73/28.52 [9771]P1(f319(f319(f321(x97711),f319(f243(x97711,f931(a91,a91)),f319(f258(x97711,x97712),x97713))),f319(f164(x97711),f319(f319(f146(f931(a91,x97711),x97711),f248(a91,x97711)),x97712))))+~P1(f319(f319(f227(a91),f2(a91)),f319(f157(a91),f319(f319(f146(f931(a91,x97711),a91),f243(a91,x97711)),x97712))))
% 28.73/28.52 [9788]~P1(f319(f319(f226(f932(f931(x97881,x97881),a923)),x97882),f319(f319(f246(x97881,x97881),x97883),f319(f16(f932(x97881,a923),x97881),x97883))))+P1(f319(f319(f226(f932(f931(x97881,x97881),a923)),f319(f319(f281(x97881,x97881,x97881),x97882),f299(x97881,x97882))),f319(f319(f246(x97881,x97881),x97883),f319(f16(f932(x97881,a923),x97881),x97883))))
% 28.73/28.52 [10108]~P38(x101081,x101082)+~P1(f319(f319(f321(f931(x101081,x101081)),f319(f319(f244(x101081,x101081),f319(x101083,f319(a104,f569(x101082,x101081,x101083)))),f319(x101083,f569(x101082,x101081,x101083)))),x101082))
% 28.73/28.52 [10109]~P38(x101091,x101092)+~P1(f319(f319(f321(f931(x101091,x101091)),f319(f319(f244(x101091,x101091),f319(x101093,f319(a104,f620(x101093,x101092,x101091)))),f319(x101093,f620(x101093,x101092,x101091)))),x101092))
% 28.73/28.52 [10370]P1(f319(f319(f226(f932(f931(f932(x103701,a923),f932(x103701,a923)),a923)),f319(f319(f281(f932(x103701,a923),f932(x103701,a923),f932(x103701,a923)),f310(x103701,x103702)),f319(f319(f102(f932(f931(f932(x103701,a923),f932(x103701,a923)),a923)),f310(x103701,x103703)),f319(f319(f301(f931(f932(x103701,a923),f932(x103701,a923))),f319(f319(f244(f932(x103701,a923),f932(x103701,a923)),f180(f932(x103701,a923))),f180(f932(x103701,a923)))),f180(f932(f931(f932(x103701,a923),f932(x103701,a923)),a923)))))),f310(x103701,x103702)))+~P1(f319(f319(f226(f932(f931(x103701,x103701),a923)),f319(f319(f281(x103701,x103701,x103701),x103702),x103703)),x103702))
% 28.73/28.52 [10371]P1(f319(f319(f226(f932(f931(f932(x103711,a923),f932(x103711,a923)),a923)),f319(f319(f281(f932(x103711,a923),f932(x103711,a923),f932(x103711,a923)),f311(x103711,x103712)),f319(f319(f102(f932(f931(f932(x103711,a923),f932(x103711,a923)),a923)),f311(x103711,x103713)),f319(f319(f301(f931(f932(x103711,a923),f932(x103711,a923))),f319(f319(f244(f932(x103711,a923),f932(x103711,a923)),f180(f932(x103711,a923))),f180(f932(x103711,a923)))),f180(f932(f931(f932(x103711,a923),f932(x103711,a923)),a923)))))),f311(x103711,x103712)))+~P1(f319(f319(f226(f932(f931(x103711,x103711),a923)),f319(f319(f281(x103711,x103711,x103711),x103712),x103713)),x103712))
% 28.73/28.52 [7501]~P1(f319(f319(f226(a925),x75012),x75011))+E(f319(f319(f23(a925),f319(a104,f319(f319(f23(a925),x75011),x75012))),x75013),f319(f319(f23(a925),f319(a104,x75011)),f319(f319(f74(a925),x75012),x75013)))
% 28.73/28.52 [7541]~P65(x75411)+E(f319(f319(f74(x75411),f39(x75411,x75412,x75413)),f319(f319(f75(x75411),f319(f319(f30(x75411),x75412),x75413)),x75413)),x75412)
% 28.73/28.52 [7732]E(f319(f319(f75(a925),f319(f95(a925),x77321)),f319(f319(f75(a925),f319(f95(a925),x77322)),x77323)),f319(f319(f75(a925),f319(f95(a925),f319(f319(f75(a1),x77321),x77322))),x77323))+P1(f319(f319(f227(a1),x77321),a77))
% 28.73/28.52 [8200]~P1(f319(f319(f226(a925),x82003),x82002))+P1(f319(f319(f226(a925),x82001),f319(f319(f23(a925),f319(f319(f74(a925),x82002),x82001)),x82003)))
% 28.73/28.52 [8401]~P1(f319(f319(f226(a925),x84011),x84012))+E(f319(f319(f126(a925),f131(a925,f319(f294(a925,x84011),x84012))),f131(a925,f319(f294(a925,x84012),f319(f319(f74(a925),x84012),x84013)))),f131(a925,f319(f294(a925,x84011),f319(f319(f74(a925),x84012),x84013))))
% 28.73/28.52 [8658]~P1(f319(f55(x86581),x86582))+E(f319(a104,f319(f29(x86581),f319(f319(f23(f932(x86581,a923)),x86582),f319(f319(f301(x86581),x86583),f180(f932(x86581,a923)))))),f319(f29(x86581),f319(f319(f301(x86581),x86583),x86582)))
% 28.73/28.52 [8699]~P1(f319(f55(x86991),x86992))+E(f319(f319(f74(a925),f72(a925)),f319(f29(x86991),f319(f319(f23(f932(x86991,a923)),x86992),f319(f319(f301(x86991),x86993),f180(f932(x86991,a923)))))),f319(f29(x86991),f319(f319(f301(x86991),x86993),x86992)))
% 28.73/28.52 [8891]E(f319(f319(f23(a925),f319(f29(x88911),x88912)),f319(f29(x88911),f319(f319(f93(f932(x88911,a923)),x88912),x88913))),f319(f29(x88911),f319(f319(f23(f932(x88911,a923)),x88912),x88913)))+~P1(f319(f55(x88911),f319(f319(f93(f932(x88911,a923)),x88912),x88913)))
% 28.73/28.52 [9146]~P7(f319(x91462,f432(x91462,x91463,x91461)))+E(f319(f92(a1),f319(f319(f6(x91461,a925),f319(f319(f8(a1,a925,x91461),a96),x91462)),x91463)),f319(f319(f6(x91461,a1),x91462),x91463))
% 28.73/28.52 [9147]~P7(f319(x91472,f479(x91472,x91473,x91471)))+E(f319(f92(a1),f319(f319(f9(x91471,a925),f319(f319(f8(a1,a925,x91471),a96),x91472)),x91473)),f319(f319(f9(x91471,a1),x91472),x91473))
% 28.73/28.52 [9189]~P1(f319(f55(x91891),x91893))+P1(f319(f319(f226(a925),f319(f319(f23(a925),f319(f29(x91891),x91892)),f319(f29(x91891),x91893))),f319(f29(x91891),f319(f319(f23(f932(x91891,a923)),x91892),x91893))))
% 28.73/28.52 [9217]P1(f319(f319(f321(x92171),f432(x92172,x92173,x92171)),x92173))+E(f319(f92(a1),f319(f319(f6(x92171,a925),f319(f319(f8(a1,a925,x92171),a96),x92172)),x92173)),f319(f319(f6(x92171,a1),x92172),x92173))
% 28.73/28.52 [9218]P1(f319(f319(f321(x92181),f479(x92182,x92183,x92181)),x92183))+E(f319(f92(a1),f319(f319(f9(x92181,a925),f319(f319(f8(a1,a925,x92181),a96),x92182)),x92183)),f319(f319(f9(x92181,a1),x92182),x92183))
% 28.73/28.52 [9282]E(f79(x92821,f319(f319(f7(x92821,f932(x92821,a923),a923),f321(x92821)),f319(f319(f23(f932(x92821,a923)),x92822),f319(f319(f301(x92821),x92823),f180(f932(x92821,a923)))))),f239(x92821,x92823,x92822))+P1(f319(f319(f226(f932(x92821,a923)),x92822),f319(f319(f301(x92821),x92823),f180(f932(x92821,a923)))))
% 28.73/28.52 [9640]E(f319(f319(f146(f926(x96401),x96401),f319(f319(f7(f926(x96401),a925,x96401),f156(x96401)),x96402)),f319(f128(f926(x96401),f319(f319(f8(a925,a923,f926(x96401)),f319(f227(a925),x96402)),f181(f926(x96401)))),x96403)),f319(f319(f156(f926(x96401)),f171(x96401,x96403)),x96402))+~P1(f319(f319(f227(a925),x96402),f319(f181(f926(f926(x96401))),f171(x96401,x96403))))
% 28.73/28.52 [9721]E(f319(f128(x97211,x97212),x97213),f169(x97211,x97212,x97213))+P1(f319(f319(f321(x97211),f743(x97213,x97212,x97211)),f319(f164(x97211),f319(f319(f130(x97211),f319(f181(f926(x97211)),f169(x97211,x97212,x97213))),x97213))))
% 28.73/28.52 [9862]E(f319(f319(f130(x98621),f319(f181(f926(x98621)),f169(x98621,x98622,x98623))),x98623),f105(x98621))+~P1(f319(x98622,f319(f133(x98621),f319(f319(f130(x98621),f319(f181(f926(x98621)),f169(x98621,x98622,x98623))),x98623))))
% 28.73/28.52 [9962]~P1(f319(f319(f321(f931(x99621,x99621)),x99622),f299(x99621,x99623)))+P1(f319(f319(f321(f931(x99621,x99621)),x99622),f319(f319(f33(a925,f932(f931(x99621,x99621),a923)),f234(f932(a925,a923))),f319(f319(f7(a925,f932(f931(x99621,x99621),a923),f932(f931(x99621,x99621),a923)),f175(f931(x99621,x99621),a923)),x99623))))
% 28.73/28.52 [10029]~P1(f319(f319(f226(f932(x100291,a923)),f319(f319(f33(a925,f932(x100291,a923)),f319(f294(a925,f2(a925)),f411(x100293,x100292,x100291))),x100292)),x100293))+P1(f319(f319(f226(f932(x100291,a923)),f319(f319(f33(a925,f932(x100291,a923)),f234(f932(a925,a923))),x100292)),x100293))
% 28.73/28.52 [10079]~P1(f319(f319(f227(a1),f2(a1)),x100793))+P1(f319(f319(f227(a1),x100791),f319(f319(f74(a1),x100792),f319(f319(f75(a1),f319(f319(f74(a1),f319(f69(a1),f319(f319(f23(a1),x100792),x100791))),f72(a1))),x100793))))
% 28.73/28.52 [10095]~P38(x100951,f319(f319(f102(f932(f931(x100951,x100951),a923)),x100952),x100953))+P38(x100951,f319(f319(f102(f932(f931(x100951,x100951),a923)),f319(f319(f102(f932(f931(x100951,x100951),a923)),f319(f319(f281(x100951,x100951,x100951),x100952),x100952)),f319(f319(f281(x100951,x100951,x100951),x100953),x100952))),x100953))
% 28.73/28.52 [10170]P38(x101701,f319(f319(f102(f932(f931(x101701,x101701),a923)),x101702),x101703))+~P38(x101701,f319(f319(f102(f932(f931(x101701,x101701),a923)),f319(f319(f102(f932(f931(x101701,x101701),a923)),f319(f319(f281(x101701,x101701,x101701),x101702),x101702)),f319(f319(f281(x101701,x101701,x101701),x101703),x101702))),x101703))
% 28.73/28.52 [9724]~P145(x97241)+E(f319(f94(x97241),f319(a83,f319(f277(f931(a925,a925),f931(a925,a925),a100),f319(f319(f301(f931(a925,a925)),f319(f319(f244(a925,a925),x97242),x97243)),f180(f932(f931(a925,a925),a923)))))),f319(f319(f23(x97241),f319(f92(x97241),x97242)),f319(f92(x97241),x97243)))
% 28.73/28.52 [9808]P1(f319(x98083,x98082))+E(f319(f254(x98081),f319(f319(f18(x98081,a923,a923),f319(f319(f8(a923,f932(a923,a923),x98081),a317),f319(f319(f7(x98081,x98081,a923),a316),x98082))),x98083)),f180(f932(x98081,a923)))
% 28.73/28.52 [9810]~P1(f319(x98103,x98102))+E(f319(f254(x98101),f319(f319(f18(x98101,a923,a923),f319(f319(f8(a923,f932(a923,a923),x98101),a317),f319(f319(f7(x98101,x98101,a923),a316),x98102))),x98103)),f319(f319(f301(x98101),x98102),f180(f932(x98101,a923))))
% 28.73/28.52 [10058]E(x100581,x100582)+P1(f319(f319(f235(x100583,x100583,f319(f319(f8(f932(x100583,a923),f932(x100583,a923),x100583),f319(f8(a923,a923,x100583),a314)),a316)),x100581),x100582))
% 28.73/28.52 [10150]~E(x101501,x101502)+~P1(f319(f319(f235(x101503,x101503,f319(f319(f8(f932(x101503,a923),f932(x101503,a923),x101503),f319(f8(a923,a923,x101503),a314)),a316)),x101501),x101502))
% 28.73/28.52 [10162]~P1(f319(f55(x101621),x101623))+E(f319(f319(f58(x101621,f932(x101621,a923),f319(f319(f8(f932(x101621,a923),f932(f932(x101621,a923),f932(x101621,a923)),x101621),f319(f7(f932(x101621,a923),f932(x101621,a923),f932(x101621,a923)),f23(f932(x101621,a923)))),f319(f319(f7(x101621,f932(x101621,a923),f932(x101621,a923)),f301(x101621)),f180(f932(x101621,a923))))),x101622),x101623),f319(f319(f23(f932(x101621,a923)),x101622),x101623))
% 28.73/28.52 [10193]~P1(f319(f319(f227(a1),f2(a1)),x101933))+P1(f319(f319(f227(a1),f319(f319(f23(a1),x101931),f319(f319(f75(a1),f319(f319(f74(a1),f319(f69(a1),f319(f319(f23(a1),x101931),x101932))),f72(a1))),x101933))),x101932))
% 28.73/28.52 [10456]~P1(f319(f319(f321(x104561),x104563),f308(x104561,x104562)))+P1(f319(f307(x104561,f319(f319(f7(x104561,f932(f931(x104561,x104561),a923),f932(x104561,a923)),f319(f319(f8(f932(x104561,f932(f932(f931(x104561,x104561),a923),a923)),f932(f932(f931(x104561,x104561),a923),f932(x104561,a923)),x104561),f7(x104561,f932(f931(x104561,x104561),a923),a923)),f319(f319(f8(f932(x104561,f931(x104561,x104561)),f932(x104561,f932(f932(f931(x104561,x104561),a923),a923)),x104561),f319(f8(f931(x104561,x104561),f932(f932(f931(x104561,x104561),a923),a923),x104561),f321(f931(x104561,x104561)))),f244(x104561,x104561)))),x104562)),x104563))
% 28.73/28.52 [10469]P1(f319(f319(f321(x104691),x104692),f308(x104691,x104693)))+~P1(f319(f307(x104691,f319(f319(f7(x104691,f932(f931(x104691,x104691),a923),f932(x104691,a923)),f319(f319(f8(f932(x104691,f932(f932(f931(x104691,x104691),a923),a923)),f932(f932(f931(x104691,x104691),a923),f932(x104691,a923)),x104691),f7(x104691,f932(f931(x104691,x104691),a923),a923)),f319(f319(f8(f932(x104691,f931(x104691,x104691)),f932(x104691,f932(f932(f931(x104691,x104691),a923),a923)),x104691),f319(f8(f931(x104691,x104691),f932(f932(f931(x104691,x104691),a923),a923),x104691),f321(f931(x104691,x104691)))),f244(x104691,x104691)))),x104693)),x104692))
% 28.73/28.52 [10027]~P1(f319(f55(x100271),f319(f254(x100271),x100273)))+P1(f319(f55(x100271),f319(f254(x100271),f319(f319(f18(x100271,a923,a923),f319(f319(f8(a923,f932(a923,a923),x100271),a317),x100272)),x100273))))
% 28.73/28.52 [10028]~P1(f319(f55(x100281),f319(f254(x100281),x100282)))+P1(f319(f55(x100281),f319(f254(x100281),f319(f319(f18(x100281,a923,a923),f319(f319(f8(a923,f932(a923,a923),x100281),a317),x100282)),x100283))))
% 28.73/28.52 [10129]P1(f319(f55(x101291),f319(f254(x101291),x101292)))+~P1(f319(f55(x101291),f319(f254(x101291),f319(f319(f18(x101291,a923,a923),f319(f319(f8(a923,f932(a923,a923),x101291),a318),x101293)),x101292))))
% 28.73/28.52 [10130]P1(f319(f55(x101301),f319(f254(x101301),x101302)))+~P1(f319(f55(x101301),f319(f254(x101301),f319(f319(f18(x101301,a923,a923),f319(f319(f8(a923,f932(a923,a923),x101301),a318),x101302)),x101303))))
% 28.73/28.52 [10434]~P1(f319(f55(x104341),x104342))+P1(f319(f55(f926(x104341)),f319(f254(f926(x104341)),f319(f319(f18(f926(x104341),a923,a923),f319(f319(f8(a923,f932(a923,a923),f926(x104341)),a317),f319(f319(f7(f926(x104341),f932(x104341,a923),a923),f319(f319(f8(f932(x104341,a923),f932(f932(x104341,a923),a923),f926(x104341)),f226(f932(x104341,a923))),f164(x104341))),x104342))),f319(f319(f7(f926(x104341),a925,a923),f319(f319(f8(a925,f932(a925,a923),f926(x104341)),a316),f181(f926(x104341)))),x104343)))))
% 28.73/28.52 [10435]~P1(f319(f55(x104351),x104352))+P1(f319(f55(f926(x104351)),f319(f254(f926(x104351)),f319(f319(f18(f926(x104351),a923,a923),f319(f319(f8(a923,f932(a923,a923),f926(x104351)),a317),f319(f319(f7(f926(x104351),f932(x104351,a923),a923),f319(f319(f8(f932(x104351,a923),f932(f932(x104351,a923),a923),f926(x104351)),f226(f932(x104351,a923))),f164(x104351))),x104352))),f319(f319(f7(f926(x104351),a925,a923),f319(f319(f8(a925,f932(a925,a923),f926(x104351)),f226(a925)),f181(f926(x104351)))),x104353)))))
% 28.73/28.52 [10143]~P121(x101431)+E(f319(f319(f236(x101431),x101432),f319(f319(f75(a925),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),x101433)),f319(f319(f75(x101431),f319(f319(f236(x101431),x101432),x101433)),f319(f319(f236(x101431),x101432),x101433)))
% 28.73/28.52 [10173]~P87(x101731)+E(f319(f319(f236(x101731),f319(f319(f236(x101731),x101732),x101733)),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),f319(f319(f236(x101731),x101732),f319(f319(f75(a925),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),x101733)))
% 28.73/28.52 [10232]~P145(x102321)+E(f319(f319(f236(x102321),f319(f73(x102321),x102322)),f319(f319(f75(a925),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),x102323)),f319(f319(f236(x102321),x102322),f319(f319(f75(a925),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),x102323)))
% 28.73/28.52 [10378]~P126(x103781)+P1(f319(f319(f226(x103781),f2(x103781)),f319(f319(f74(x103781),f319(f319(f236(x103781),x103782),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))))),f319(f319(f236(x103781),x103783),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))))))
% 28.73/28.52 [10242]~P121(x102421)+E(f319(f319(f236(x102421),x102422),f319(a104,f319(f319(f75(a925),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),x102423))),f319(f319(f75(x102421),x102422),f319(f319(f75(x102421),f319(f319(f236(x102421),x102422),x102423)),f319(f319(f236(x102421),x102422),x102423))))
% 28.73/28.52 [10295]~P87(x102951)+E(f319(f319(f75(x102951),x102952),f319(f319(f236(x102951),f319(f319(f236(x102951),x102952),x102953)),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))))),f319(f319(f236(x102951),x102952),f319(a104,f319(f319(f75(a925),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),x102953))))
% 28.73/28.52 [10334]~P126(x103341)+P1(f319(f319(f226(x103341),f2(x103341)),f319(f319(f236(x103341),x103342),f319(f319(f75(a925),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),x103343))))
% 28.73/28.52 [10409]~P99(x104091)+E(f319(f319(f23(x104091),f319(f319(f74(x104091),f319(f319(f236(x104091),x104092),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))))),f319(f319(f236(x104091),x104093),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))))),f319(f319(f75(x104091),f319(f319(f75(x104091),f319(f95(x104091),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),x104092)),x104093)),f319(f319(f236(x104091),f319(f319(f23(x104091),x104092),x104093)),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))))
% 28.73/28.52 [10410]~P99(x104101)+E(f319(f319(f74(x104101),f319(f319(f74(x104101),f319(f319(f236(x104101),x104102),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))))),f319(f319(f236(x104101),x104103),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))))),f319(f319(f75(x104101),f319(f319(f75(x104101),f319(f95(x104101),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),x104102)),x104103)),f319(f319(f236(x104101),f319(f319(f74(x104101),x104102),x104103)),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))))
% 28.73/28.52 [7997]P26(x79971,x79972,x79973,x79974)+~E(f889(x79974,x79973,x79972,x79971),f890(x79974,x79973,x79972,x79971))
% 28.73/28.52 [8292]P35(x82921,x82922,x82923,x82924,f105(x82922))+~E(x82924,f105(x82921))
% 28.73/28.52 [8293]P35(x82931,x82932,x82933,f105(x82931),x82934)+~E(x82934,f105(x82932))
% 28.73/28.52 [8839]~P35(x88392,x88393,x88394,x88391,f105(x88393))+E(x88391,f105(x88392))
% 28.73/28.52 [8840]~P35(x88403,x88402,x88404,f105(x88403),x88401)+E(x88401,f105(x88402))
% 28.73/28.52 [5270]~P19(x52703,x52701,x52704)+E(f319(f319(x52701,x52702),x52702),x52702)
% 28.73/28.52 [5520]P1(f319(x55202,x55204))+E(f319(f128(x55201,x55202),f161(x55201,x55203,x55204)),f105(x55201))
% 28.73/28.52 [5556]~E(x55564,f180(f932(x55561,a923)))+E(f319(f302(x55561,x55562,x55563),x55564),f180(f932(x55562,a923)))
% 28.73/28.52 [5557]~E(x55574,f180(f932(x55571,a923)))+E(f319(f302(x55571,x55572,x55573),x55574),f180(f932(x55572,a923)))
% 28.73/28.52 [5800]~P1(f319(x58002,x58004))+E(f319(f128(x58001,x58002),f161(x58001,x58003,x58004)),f161(x58001,x58003,x58004))
% 28.73/28.52 [5828]~E(f319(f302(x58282,x58283,x58284),x58281),f180(f932(x58283,a923)))+E(x58281,f180(f932(x58282,a923)))
% 28.73/28.52 [5829]~E(f319(f302(x58292,x58293,x58294),x58291),f180(f932(x58293,a923)))+E(x58291,f180(f932(x58292,a923)))
% 28.73/28.52 [6017]~P8(x60171,x60173)+E(f263(x60171,x60172,f262(x60171,x60173),x60174),x60174)
% 28.73/28.52 [6126]~P4(x61262)+E(f319(f319(f140(x61261,x61262,x61263),x61264),f105(x61261)),f319(f319(f143(x61261),x61264),f105(x61261)))
% 28.73/28.52 [6483]~E(x64831,f180(f932(x64832,a923)))+~P1(f319(f56(x64832,x64833,x64831),x64834))
% 28.73/28.52 [6504]~P63(x65041,x65043,x65044,x65042)+P1(f319(f55(x65041),x65042))
% 28.73/28.52 [6505]~P63(x65051,x65053,x65054,x65052)+P1(f319(f55(x65051),x65052))
% 28.73/28.52 [6506]~P63(x65061,x65063,x65062,x65064)+P1(f319(f55(x65061),x65062))
% 28.73/28.52 [6507]~P63(x65071,x65073,x65072,x65074)+P1(f319(f55(x65071),x65072))
% 28.73/28.52 [6514]~P63(x65142,x65143,x65144,x65141)+~E(x65141,f180(f932(x65142,a923)))
% 28.73/28.52 [6515]~P63(x65152,x65153,x65154,x65151)+~E(x65151,f180(f932(x65152,a923)))
% 28.73/28.52 [6547]~P113(x65471)+E(f319(f319(f93(f932(x65471,a923)),f319(f294(x65471,x65472),x65473)),f295(x65471,x65473,x65474)),f180(f932(x65471,a923)))
% 28.73/28.52 [6574]~P1(f319(f319(x65743,x65744),x65742))+P1(f319(f319(f321(x65741),x65742),f287(x65741,x65743,x65744)))
% 28.73/28.52 [6575]~P1(f319(f319(x65753,x65754),x65752))+P1(f319(f319(f321(x65751),x65752),f286(x65751,x65753,x65754)))
% 28.73/28.52 [6576]~P1(f319(f319(x65763,x65762),x65764))+P1(f319(f319(f321(x65761),x65762),f290(x65761,x65763,x65764)))
% 28.73/28.52 [6577]~P1(f319(f319(x65773,x65772),x65774))+P1(f319(f319(f321(x65771),x65772),f288(x65771,x65773,x65774)))
% 28.73/28.52 [6642]~P52(x66424,x66421,x66422,x66423)+P1(f319(f319(x66421,x66422),x66423))
% 28.73/28.52 [6721]~P113(x67211)+E(f319(f319(f93(f932(x67211,a923)),f295(x67211,x67212,x67213)),f297(x67211,x67213,x67214)),f180(f932(x67211,a923)))
% 28.73/28.52 [6722]~P113(x67221)+E(f319(f319(f93(f932(x67221,a923)),f295(x67221,x67222,x67223)),f298(x67221,x67223,x67224)),f180(f932(x67221,a923)))
% 28.73/28.52 [6723]~P113(x67231)+E(f319(f319(f93(f932(x67231,a923)),f297(x67231,x67232,x67233)),f297(x67231,x67233,x67234)),f180(f932(x67231,a923)))
% 28.73/28.52 [6724]~P113(x67241)+E(f319(f319(f93(f932(x67241,a923)),f297(x67241,x67242,x67243)),f298(x67241,x67243,x67244)),f180(f932(x67241,a923)))
% 28.73/28.52 [6725]~P113(x67251)+E(f319(f319(f93(f932(x67251,a923)),f298(x67251,x67252,x67253)),f295(x67251,x67253,x67254)),f180(f932(x67251,a923)))
% 28.73/28.52 [6762]P1(f319(f319(x67621,x67622),f564(x67622,x67621)))+~P1(f319(f241(x67623,x67624,x67621),x67622))
% 28.73/28.52 [6766]~P52(x67661,x67662,x67663,x67664)+~P1(f319(f319(x67662,x67664),x67663))
% 28.73/28.52 [6846]~P4(x68462)+E(f319(f164(x68461),f142(x68461,x68462,x68463,x68464)),f319(f164(x68461),x68464))
% 28.73/28.52 [6897]~P149(x68971)+E(f182(x68971,x68972,f319(a104,x68973),x68974),f182(x68971,x68972,x68973,f319(x68972,x68974)))
% 28.73/28.52 [6960]~P1(f319(f319(f321(x69604),x69603),f287(x69604,x69601,x69602)))+P1(f319(f319(x69601,x69602),x69603))
% 28.73/28.52 [6961]~P1(f319(f319(f321(x69614),x69613),f286(x69614,x69611,x69612)))+P1(f319(f319(x69611,x69612),x69613))
% 28.73/28.52 [6962]~P1(f319(f319(f321(x69624),x69622),f290(x69624,x69621,x69623)))+P1(f319(f319(x69621,x69622),x69623))
% 28.73/28.52 [6963]~P1(f319(f319(f321(x69634),x69632),f288(x69634,x69631,x69633)))+P1(f319(f319(x69631,x69632),x69633))
% 28.73/28.52 [7038]E(f319(f29(f933(x70381,x70382)),f305(x70381,x70382,x70383,x70384)),f2(a925))+P1(f319(f55(x70382),x70384))
% 28.73/28.52 [7039]E(f319(f29(f933(x70391,x70392)),f305(x70391,x70392,x70393,x70394)),f2(a925))+P1(f319(f55(x70391),x70393))
% 28.73/28.52 [7242]~P16(x72424,x72421,x72422)+E(f319(f66(x72421,x72421,x72421,f319(x72422,x72423)),f319(x72422,x72423)),f319(x72422,x72423))
% 28.73/28.52 [7486]E(f269(x74861,x74862,x74863,x74864),f319(f244(f932(a91,f932(a923,f929(f927(x74861)))),f931(a91,a91)),f35(x74861)))+~P1(f319(f319(f226(a91),x74863),f2(a91)))
% 28.73/28.52 [8121]~E(x81212,x81213)+P1(f319(f319(f321(f931(x81211,x81211)),f319(f319(f244(x81211,x81211),x81212),x81213)),f299(x81211,x81214)))
% 28.73/28.52 [8150]~P26(x81501,x81502,x81503,f234(f932(x81501,a923)))+E(f319(f71(x81501,x81502,f234(f932(x81501,a923)),x81503),f319(x81503,x81504)),x81504)
% 28.73/28.52 [8151]~P26(x81511,x81512,x81513,f234(f932(x81511,a923)))+E(f319(f85(x81511,x81512,f234(f932(x81511,a923)),x81513),f319(x81513,x81514)),x81514)
% 28.73/28.52 [8241]~P1(f319(f319(f321(f926(x82411)),f319(f319(f143(x82411),x82414),x82412)),f153(x82411,x82413)))+P1(f319(f319(f321(f926(x82411)),x82412),f153(x82411,x82413)))
% 28.73/28.52 [8242]~P1(f319(f319(f321(f926(x82421)),f319(f319(f126(x82421),x82424),x82422)),f153(x82421,x82423)))+P1(f319(f319(f321(f926(x82421)),x82422),f153(x82421,x82423)))
% 28.73/28.52 [8243]~P1(f319(f319(f321(f926(x82431)),f319(f319(f126(x82431),x82432),x82434)),f153(x82431,x82433)))+P1(f319(f319(f321(f926(x82431)),x82432),f153(x82431,x82433)))
% 28.73/28.52 [8254]~P4(x82541)+P14(x82541,f319(f319(f146(x82542,x82541),x82543),f142(x82542,x82541,x82543,x82544)))
% 28.73/28.52 [8357]P26(x83574,x83573,x83571,x83572)+E(f319(x83571,f889(x83572,x83571,x83573,x83574)),f319(x83571,f890(x83572,x83571,x83573,x83574)))
% 28.73/28.52 [8466]~P26(x84662,x84661,x84664,x84663)+P26(x84661,x84662,f71(x84662,x84661,x84663,x84664),f319(f302(x84662,x84661,x84664),x84663))
% 28.73/28.52 [8607]P38(f931(x86072,x86074),f272(x86072,x86074,x86071,x86073))+P1(f319(x86071,f566(x86072,x86073,x86074,x86071)))
% 28.73/28.52 [8727]E(x87271,x87272)+~P1(f319(f319(f321(f931(x87273,x87273)),f319(f319(f244(x87273,x87273),x87271),x87272)),f255(x87273,x87274)))
% 28.73/28.52 [8788]~P1(f319(f55(f933(x87883,x87881)),f305(x87883,x87881,x87884,x87882)))+P1(f319(f55(x87881),x87882))
% 28.73/28.52 [8789]~P1(f319(f55(f933(x87891,x87893)),f305(x87891,x87893,x87892,x87894)))+P1(f319(f55(x87891),x87892))
% 28.73/28.52 [8790]~P1(f319(f55(f933(x87903,x87901)),f305(x87903,x87901,x87904,x87902)))+P1(f319(f55(x87901),x87902))
% 28.73/28.52 [8791]~P1(f319(f55(f933(x87911,x87913)),f305(x87911,x87913,x87912,x87914)))+P1(f319(f55(x87911),x87912))
% 28.73/28.52 [8800]~P26(x88001,x88002,x88003,x88004)+P27(x88001,x88002,x88003,x88004,f319(f302(x88001,x88002,x88003),x88004))
% 28.73/28.52 [8802]P12(x88021,x88022,x88023,x88024)+~E(f319(x88024,f858(x88022,x88024,x88023,x88021)),f319(x88024,f859(x88022,x88024,x88023,x88021)))
% 28.73/28.52 [8892]~P27(x88922,x88923,x88924,x88921,f180(f932(x88923,a923)))+E(x88921,f180(f932(x88922,a923)))
% 28.73/28.52 [8893]~P27(x88933,x88932,x88934,f180(f932(x88933,a923)),x88931)+E(x88931,f180(f932(x88932,a923)))
% 28.73/28.52 [8985]P38(f931(x89851,x89852),f272(x89851,x89852,x89853,x89854))+~P38(x89852,f319(x89854,f566(x89851,x89854,x89852,x89853)))
% 28.73/28.52 [9560]E(f319(f319(f151(x95601,x95602),f692(x95603,x95604,x95602,x95601)),f693(x95603,x95604,x95602,x95601)),x95604)+~P1(f319(f319(f321(f931(f926(x95601),f926(x95601))),f319(f319(f244(f926(x95601),f926(x95601)),x95602),x95604)),f149(x95601,x95603)))
% 28.73/28.52 [9565]~P1(f319(f319(f321(f931(f926(x95651),f926(x95651))),f319(f319(f244(f926(x95651),f926(x95651)),x95652),x95653)),f137(x95651,x95654)))+P1(f319(f319(f321(f931(f926(x95651),f926(x95651))),f319(f319(f244(f926(x95651),f926(x95651)),x95652),x95653)),f139(x95651,x95654)))
% 28.73/28.52 [9677]P1(f319(f55(x96771),x96772))+~P1(f319(f319(f321(f931(f932(x96771,a923),f932(x96771,a923))),f319(f319(f244(f932(x96771,a923),f932(x96771,a923)),x96773),x96772)),f311(x96771,x96774)))
% 28.73/28.52 [9678]P1(f319(f55(x96781),x96782))+~P1(f319(f319(f321(f931(f932(x96781,a923),f932(x96781,a923))),f319(f319(f244(f932(x96781,a923),f932(x96781,a923)),x96782),x96783)),f311(x96781,x96784)))
% 28.73/28.52 [9681]~E(x96811,f180(f932(x96812,a923)))+~P1(f319(f319(f321(f931(f932(x96812,a923),f932(x96812,a923))),f319(f319(f244(f932(x96812,a923),f932(x96812,a923)),x96813),x96811)),f311(x96812,x96814)))
% 28.73/28.52 [10345]P12(x103451,x103452,x103453,x103454)+~P1(f319(f319(f249(x103451,x103451,a923),f319(f319(f7(x103451,f932(x103451,x103452),f932(x103451,a923)),f319(f319(f8(f932(x103452,a923),f932(f932(x103451,x103452),f932(x103451,a923)),x103451),f8(x103452,a923,x103451)),f319(f319(f8(x103452,f932(x103452,a923),x103451),a316),x103454))),x103454)),f601(x103454,x103453,x103452,x103451)))
% 28.73/28.52 [5169]~E(x51694,f105(x51691))+E(f319(f319(f146(x51691,x51692),x51693),x51694),f105(x51692))
% 28.73/28.52 [5170]~E(x51702,f105(x51701))+E(f319(f319(f151(x51701,x51702),x51703),x51704),f105(x51701))
% 28.73/28.52 [5171]~E(x51714,f105(x51711))+E(f319(f319(f146(x51711,x51712),x51713),x51714),f105(x51712))
% 28.73/28.52 [5409]E(x54091,f105(x54092))+~E(f319(f319(f146(x54092,x54093),x54094),x54091),f105(x54093))
% 28.73/28.52 [5410]E(x54101,f105(x54102))+~E(f319(f319(f146(x54102,x54103),x54104),x54101),f105(x54103))
% 28.73/28.52 [5411]E(x54111,f105(x54112))+~E(f319(f319(f151(x54112,x54111),x54113),x54114),f105(x54112))
% 28.73/28.52 [5447]E(x54471,x54472)+~E(f319(f319(f126(x54473),x54474),x54471),f319(f319(f126(x54473),x54474),x54472))
% 28.73/28.52 [5448]E(x54481,x54482)+~E(f319(f319(f126(x54483),x54481),x54484),f319(f319(f126(x54483),x54482),x54484))
% 28.73/28.52 [5594]P1(f319(x55943,x55942))+E(f162(x55941,x55942,f319(f128(x55941,x55943),x55944)),f319(f128(x55941,x55943),x55944))
% 28.73/28.52 [5596]~P1(f319(x55962,x55963))+P34(x55961,x55962,f319(f319(f143(x55961),x55963),x55964))
% 28.73/28.52 [5605]E(x56051,x56052)+~E(f131(a925,f319(f294(a925,x56051),x56053)),f319(f319(f143(a925),x56052),x56054))
% 28.73/28.52 [5653]~P28(x56532,x56533)+P28(x56531,f319(f319(f67(x56532,x56531),x56533),x56534))
% 28.73/28.52 [5654]~P38(x56542,x56543)+P38(x56541,f319(f319(f280(x56542,x56541),x56543),x56544))
% 28.73/28.52 [5655]~P39(x56552,x56553)+P39(x56551,f319(f319(f280(x56552,x56551),x56553),x56554))
% 28.73/28.52 [5656]~P56(x56562,x56563)+P56(x56561,f319(f319(f280(x56562,x56561),x56563),x56564))
% 28.73/28.52 [5784]~P34(x57841,x57842,x57844)+P34(x57841,x57842,f319(f319(f143(x57841),x57843),x57844))
% 28.73/28.52 [5785]~P34(x57851,x57852,x57854)+P34(x57851,x57852,f319(f319(f126(x57851),x57853),x57854))
% 28.73/28.52 [5786]~P34(x57861,x57862,x57863)+P34(x57861,x57862,f319(f319(f126(x57861),x57863),x57864))
% 28.73/28.52 [5873]~E(x58731,f105(x58732))+~E(f319(f319(f126(x58732),x58733),f319(f319(f143(x58732),x58734),f105(x58732))),x58731)
% 28.73/28.52 [5898]~P32(x58983,x58981,f319(f319(f143(x58983),x58982),x58984))+P1(f319(x58981,x58982))
% 28.73/28.52 [5908]E(f106(x59081,x59082),x59083)+~E(f319(f319(f126(x59081),x59083),f319(f319(f143(x59081),x59084),f105(x59081))),x59082)
% 28.73/28.52 [5909]E(f136(x59091,x59092),x59093)+~E(f319(f319(f126(x59091),x59094),f319(f319(f143(x59091),x59093),f105(x59091))),x59092)
% 28.73/28.52 [6019]~E(f131(a925,f319(f294(a925,x60191),x60192)),f319(f319(f143(a925),x60193),x60194))+P1(f319(f319(f227(a925),x60191),x60192))
% 28.73/28.52 [6028]P32(x60281,x60282,x60283)+~P32(x60281,x60282,f319(f319(f143(x60281),x60284),x60283))
% 28.73/28.52 [6029]P32(x60291,x60292,x60293)+~P32(x60291,x60292,f319(f319(f126(x60291),x60294),x60293))
% 28.73/28.52 [6030]P32(x60301,x60302,x60303)+~P32(x60301,x60302,f319(f319(f126(x60301),x60303),x60304))
% 28.73/28.52 [6116]~E(f319(f95(a925),x61164),f2(a925))+E(f319(f319(f156(x61161),f319(f319(f143(x61161),x61162),x61163)),f319(f95(a925),x61164)),x61162)
% 28.73/28.52 [6233]E(x62331,f319(f319(f126(x62332),f319(f160(x62332),x62333)),f319(f319(f143(x62332),x62334),f105(x62332))))+~E(f319(f160(x62332),x62331),f319(f319(f143(x62332),x62334),x62333))
% 28.73/28.52 [6404]~P113(x64041)+E(f319(f319(f93(f932(x64041,a923)),f319(f294(x64041,x64042),x64043)),f319(f294(x64041,x64043),x64044)),f180(f932(x64041,a923)))
% 28.73/28.52 [6416]E(f319(f319(f156(x64161),f161(x64161,x64162,x64163)),x64164),x64163)+~P1(f319(f319(f227(a925),x64164),x64162))
% 28.73/28.52 [6443]~P79(x64431)+E(f319(f157(x64431),f319(f319(f146(a1,x64431),x64432),f170(x64433,x64434))),f319(f319(f6(a1,x64431),x64432),f319(f164(a1),f170(x64433,x64434))))
% 28.73/28.52 [6444]~P79(x64441)+E(f319(f319(f6(a1,x64441),x64442),f319(f164(a1),f170(x64443,x64444))),f319(f157(x64441),f319(f319(f146(a1,x64441),x64442),f170(x64443,x64444))))
% 28.73/28.52 [6587]~E(x65872,f319(f319(f126(x65871),f319(f160(x65871),x65874)),f319(f319(f143(x65871),x65873),f105(x65871))))+E(f319(f160(x65871),x65872),f319(f319(f143(x65871),x65873),x65874))
% 28.73/28.52 [6605]~P21(x66052,x66053,x66054,x66051)+E(f319(x66051,f180(f932(x66052,a923))),f25(x66053))
% 28.73/28.52 [6631]~P113(x66311)+E(f319(f319(f93(f932(x66311,a923)),f298(x66311,x66312,x66313)),f319(f294(x66311,x66313),x66314)),f180(f932(x66311,a923)))
% 28.73/28.52 [6847]E(x68471,f180(f932(x68472,a923)))+~E(f305(x68473,x68472,x68474,x68471),f180(f932(f933(x68473,x68472),a923)))
% 28.73/28.52 [6848]E(x68481,f180(f932(x68482,a923)))+~E(f305(x68482,x68483,x68481,x68484),f180(f932(f933(x68482,x68483),a923)))
% 28.73/28.52 [6920]~P4(x69202)+E(f319(f181(f926(x69201)),f142(x69201,x69202,x69203,x69204)),f319(f181(f926(x69201)),x69204))
% 28.73/28.52 [6931]~P1(f319(f242(x69313,x69314,x69311),x69312))+P1(f319(f319(x69311,f565(x69312,x69311)),x69312))
% 28.73/28.52 [6956]E(f319(f95(a925),x69561),f2(a925))+E(f319(f319(f156(x69562),f319(f319(f143(x69562),x69563),x69564)),f319(f95(a925),x69561)),f319(f319(f156(x69562),x69564),f319(f319(f23(a925),f319(f95(a925),x69561)),f72(a925))))
% 28.73/28.52 [6972]~P1(f319(f55(x69722),x69724))+P1(f319(f55(x69721),f319(f302(x69722,x69721,x69723),x69724)))
% 28.73/28.52 [7204]~P26(x72042,x72041,x72043,x72044)+E(f319(f29(x72041),f319(f302(x72042,x72041,x72043),x72044)),f319(f29(x72042),x72044))
% 28.73/28.52 [7222]E(f319(f302(x72221,x72222,x72223),f319(f303(x72221,x72222,x72223),x72224)),x72224)+~E(f319(f302(x72221,x72222,x72223),f234(f932(x72221,a923))),f234(f932(x72222,a923)))
% 28.73/28.52 [7635]~P26(x76351,x76352,x76353,f234(f932(x76351,a923)))+E(f319(f303(x76351,x76352,x76353),f319(f302(x76351,x76352,x76353),x76354)),x76354)
% 28.73/28.52 [7915]E(x79151,x79152)+~P1(f319(f319(f321(x79153),x79151),f319(f164(x79153),f161(x79153,x79154,x79152))))
% 28.73/28.52 [7924]~E(x79241,f2(a925))+~P1(f319(f319(f321(x79242),x79243),f319(f164(x79242),f161(x79242,x79241,x79244))))
% 28.73/28.52 [7957]P1(f319(x79571,x79572))+~P1(f319(f319(f321(x79573),x79572),f319(f164(x79573),f169(x79573,x79571,x79574))))
% 28.73/28.52 [8067]~P1(f319(f319(f321(f926(x80671)),f319(f319(f143(x80671),x80672),x80674)),f153(x80671,x80673)))+P1(f319(f319(f321(x80671),x80672),x80673))
% 28.73/28.52 [8196]~P1(f319(f319(f321(x81961),x81962),f319(f164(x81961),f168(x81961,x81963,x81964))))+P1(f319(f319(f321(x81961),x81962),f319(f164(x81961),x81963)))
% 28.73/28.52 [8197]~P1(f319(f319(f321(x81971),x81972),f319(f164(x81971),f168(x81971,x81973,x81974))))+P1(f319(f319(f321(x81971),x81972),f319(f164(x81971),x81973)))
% 28.73/28.52 [8198]~P1(f319(f319(f321(x81981),x81982),f319(f164(x81981),f162(x81981,x81984,x81983))))+P1(f319(f319(f321(x81981),x81982),f319(f164(x81981),x81983)))
% 28.73/28.52 [8199]~P1(f319(f319(f321(x81991),x81992),f319(f164(x81991),f169(x81991,x81994,x81993))))+P1(f319(f319(f321(x81991),x81992),f319(f164(x81991),x81993)))
% 28.73/28.52 [8209]E(f319(f181(f926(x82091)),x82092),x82093)+~P1(f319(f319(f321(f926(x82091)),x82092),f319(f164(f926(x82091)),f49(x82091,x82093,x82094))))
% 28.73/28.52 [8306]P1(f319(x83063,x83062))+E(f319(f128(x83061,f319(f319(f8(a923,a923,x83061),a314),f319(a316,x83062))),f319(f128(x83061,x83063),x83064)),f319(f128(x83061,x83063),x83064))
% 28.73/28.52 [8417]E(f319(f319(f156(x84171),f169(x84171,x84172,x84173)),x84174),f319(f319(f156(x84171),x84173),x84174))+~P1(f319(f319(f227(a925),x84174),f319(f181(f926(x84171)),f169(x84171,x84172,x84173))))
% 28.73/28.52 [8504]~P79(x85041)+E(f319(f319(f6(a925,x85041),f319(f319(f8(a925,x85041,a925),x85042),a104)),f319(f294(a925,x85043),x85044)),f319(f319(f6(a925,x85041),x85042),f319(f294(a925,f319(a104,x85043)),f319(a104,x85044))))
% 28.73/28.52 [8514]~P79(x85141)+E(f319(f319(f6(a925,x85141),f319(f319(f8(a925,x85141,a925),x85142),a104)),f295(a925,x85143,x85144)),f319(f319(f6(a925,x85141),x85142),f295(a925,f319(a104,x85143),f319(a104,x85144))))
% 28.73/28.52 [8643]~P26(x86431,x86433,x86434,f234(f932(x86431,a923)))+P26(x86431,f932(x86432,x86433),f319(f319(f8(x86433,f932(x86432,x86433),x86431),f16(x86433,x86432)),x86434),f234(f932(x86431,a923)))
% 28.73/28.52 [8732]~P26(x87322,x87321,x87324,x87323)+E(f319(f302(x87321,x87322,f71(x87322,x87321,x87323,x87324)),f319(f302(x87322,x87321,x87324),x87323)),x87323)
% 28.73/28.52 [8792]~P1(f319(f319(f321(f931(x87921,x87921)),f319(f319(f244(x87921,x87921),x87922),x87924)),f255(x87921,x87923)))+P1(f319(f319(f321(x87921),x87922),x87923))
% 28.73/28.52 [8915]~P26(x89152,x89151,x89153,f234(f932(x89152,a923)))+E(f319(f302(x89151,x89152,f85(x89152,x89151,f234(f932(x89152,a923)),x89153)),f319(f302(x89152,x89151,x89153),x89154)),x89154)
% 28.73/28.52 [8916]~P26(x89162,x89161,x89163,f234(f932(x89162,a923)))+E(f319(f302(x89161,x89162,f85(x89162,x89161,f234(f932(x89162,a923)),x89163)),f319(f302(x89162,x89161,x89163),x89164)),x89164)
% 28.73/28.52 [8991]~P27(x89911,x89912,x89913,x89914,f234(f932(x89912,a923)))+E(f319(f302(x89911,x89912,x89913),f234(f932(x89911,a923))),f234(f932(x89912,a923)))
% 28.73/28.52 [9025]~E(f319(f319(f6(x90251,a925),x90254),x90253),f319(a104,x90252))+P1(f319(f319(f321(x90251),f466(x90252,x90253,x90254,x90251)),x90253))
% 28.73/28.52 [9046]~E(f319(f319(f6(x90464,a925),x90461),x90463),f319(a104,x90462))+P1(f319(f319(f227(a925),f2(a925)),f319(x90461,f466(x90462,x90463,x90461,x90464))))
% 28.73/28.52 [9057]~P1(f319(f55(x90572),x90574))+P1(f319(f319(f226(a925),f319(f29(x90571),f319(f302(x90572,x90571,x90573),x90574))),f319(f29(x90572),x90574)))
% 28.73/28.52 [9058]E(f319(f319(f244(x90581,x90582),f661(x90583,x90584,x90582,x90581)),f662(x90583,x90584,x90582,x90581)),x90584)+~P1(f319(f319(f321(f931(x90581,x90582)),x90584),f319(f278(x90582,x90581),x90583)))
% 28.73/28.52 [9066]P26(x90661,x90662,x90663,x90664)+P1(f319(f319(f321(x90661),f889(x90664,x90663,x90662,x90661)),x90664))
% 28.73/28.52 [9067]P26(x90671,x90672,x90673,x90674)+P1(f319(f319(f321(x90671),f890(x90674,x90673,x90672,x90671)),x90674))
% 28.73/28.52 [9136]P12(x91361,x91362,x91363,x91364)+P1(f319(f319(f321(f931(x91361,x91361)),f601(x91364,x91363,x91362,x91361)),x91363))
% 28.73/28.52 [9194]P1(f319(x91941,x91942))+~P1(f319(x91941,f319(f319(f244(x91943,x91944),f533(x91944,x91943,x91941)),f534(x91944,x91943,x91941))))
% 28.73/28.52 [9211]E(f319(f181(f926(x92111)),x92112),f319(f181(f926(x92111)),x92113))+~P1(f319(f319(f321(f931(f926(x92111),f926(x92111))),f319(f319(f244(f926(x92111),f926(x92111)),x92112),x92113)),f137(x92111,x92114)))
% 28.73/28.52 [9212]E(f319(f181(f926(x92121)),x92122),f319(f181(f926(x92121)),x92123))+~P1(f319(f319(f321(f931(f926(x92121),f926(x92121))),f319(f319(f244(f926(x92121),f926(x92121)),x92122),x92123)),f149(x92121,x92124)))
% 28.73/28.52 [9213]E(f319(f181(f926(x92131)),x92132),f319(f181(f926(x92131)),x92133))+~P1(f319(f319(f321(f931(f926(x92131),f926(x92131))),f319(f319(f244(f926(x92131),f926(x92131)),x92132),x92133)),f150(x92131,x92134)))
% 28.73/28.52 [9214]E(f319(f181(f926(x92141)),x92142),f319(f181(f926(x92141)),x92143))+~P1(f319(f319(f321(f931(f926(x92141),f926(x92141))),f319(f319(f244(f926(x92141),f926(x92141)),x92142),x92143)),f150(x92141,x92144)))
% 28.73/28.52 [9215]E(f319(f181(f926(x92151)),x92152),f319(f181(f926(x92151)),x92153))+~P1(f319(f319(f321(f931(f926(x92151),f926(x92151))),f319(f319(f244(f926(x92151),f926(x92151)),x92152),x92153)),f150(x92151,x92154)))
% 28.73/28.52 [9286]P1(f319(f319(f226(a925),f147(x92861,x92862,x92863)),f147(x92861,x92864,x92863)))+P1(f319(f319(f321(x92861),f690(x92864,x92862,x92863,x92861)),f319(f164(x92861),x92863)))
% 28.73/28.52 [9289]E(f319(f181(f926(x92891)),x92892),f319(f181(f926(x92891)),x92893))+~P1(f319(f319(f321(f931(f926(x92891),f926(x92891))),f319(f319(f244(f926(x92891),f926(x92891)),x92892),x92893)),f299(f926(x92891),f149(x92891,x92894))))
% 28.73/28.52 [9530]~P26(x95301,x95302,x95303,x95304)+~P1(f319(f319(f227(a925),f319(f29(x95302),f319(f302(x95301,x95302,x95303),x95304))),f319(f29(x95301),x95304)))
% 28.73/28.52 [9578]~P1(f319(f319(f321(f931(f926(x95781),f926(x95781))),f319(f319(f244(f926(x95781),f926(x95781)),x95782),x95783)),f149(x95781,x95784)))+P1(f319(f319(f321(f931(f926(x95781),f926(x95781))),f319(f319(f244(f926(x95781),f926(x95781)),x95782),x95783)),f150(x95781,f299(x95781,x95784))))
% 28.73/28.52 [9582]~P1(f319(f319(f321(f931(f926(x95821),f926(x95821))),f319(f319(f244(f926(x95821),f926(x95821)),x95822),x95823)),f150(x95821,x95824)))+P1(f319(f319(f321(f931(f926(x95821),f926(x95821))),f319(f319(f244(f926(x95821),f926(x95821)),x95822),x95823)),f299(f926(x95821),f149(x95821,x95824))))
% 28.73/28.52 [9598]P1(f319(f319(f321(f931(x95981,x95981)),f319(f319(f244(x95981,x95981),x95982),x95983)),f299(x95981,x95984)))+~P1(f319(f319(f321(f931(x95981,x95981)),f319(f319(f244(x95981,x95981),x95982),x95983)),f319(f319(f281(x95981,x95981,x95981),x95984),f299(x95981,x95984))))
% 28.73/28.52 [9789]E(f319(f319(f126(x97891),f705(x97892,x97893,x97894,x97891)),f319(f319(f143(x97891),f706(x97892,x97893,x97894,x97891)),f708(x97892,x97893,x97894,x97891))),x97894)+~P1(f319(f319(f321(f931(f926(x97891),f926(x97891))),f319(f319(f244(f926(x97891),f926(x97891)),x97894),x97893)),f149(x97891,x97892)))
% 28.73/28.52 [9790]E(f319(f319(f126(x97901),f705(x97902,x97903,x97904,x97901)),f319(f319(f143(x97901),f707(x97902,x97903,x97904,x97901)),f708(x97902,x97903,x97904,x97901))),x97903)+~P1(f319(f319(f321(f931(f926(x97901),f926(x97901))),f319(f319(f244(f926(x97901),f926(x97901)),x97904),x97903)),f149(x97901,x97902)))
% 28.73/28.52 [9869]P1(f319(f319(f321(f931(x98691,x98691)),f319(f319(f244(x98691,x98691),x98692),f640(x98693,x98694,x98692,x98691))),f299(x98691,x98693)))+~P1(f319(f319(f321(f931(x98691,x98691)),f319(f319(f244(x98691,x98691),x98692),x98694)),f319(f319(f281(x98691,x98691,x98691),x98693),f299(x98691,x98693))))
% 28.73/28.52 [9941]P1(f319(f319(f226(a925),f147(x99411,x99412,x99413)),f147(x99411,x99414,x99413)))+~P1(f319(f319(f227(a925),f319(x99412,f690(x99414,x99412,x99413,x99411))),f319(x99414,f690(x99414,x99412,x99413,x99411))))
% 28.73/28.52 [10023]P1(f319(f319(f321(f931(x100231,x100231)),f319(f319(f244(x100231,x100231),f649(x100232,x100233,x100234,x100231)),x100233)),f299(x100231,x100232)))+~P1(f319(f319(f321(f931(x100231,x100231)),f319(f319(f244(x100231,x100231),x100234),x100233)),f319(f319(f281(x100231,x100231,x100231),x100232),f299(x100231,x100232))))
% 28.73/28.52 [5429]~E(x54292,x54293)+E(f162(x54291,x54292,f319(f319(f143(x54291),x54293),x54294)),x54294)
% 28.73/28.52 [5441]~E(x54412,f2(a925))+E(f319(f319(f167(x54411),x54412),f319(f319(f143(x54411),x54413),x54414)),f105(x54411))
% 28.73/28.52 [5550]P1(f319(x55502,x55503))+E(f169(x55501,x55502,f319(f319(f143(x55501),x55503),x55504)),f105(x55501))
% 28.73/28.52 [5616]~P67(x56162)+E(f319(f319(f73(f932(x56161,x56162)),x56163),x56164),f319(f73(x56162),f319(x56163,x56164)))
% 28.73/28.52 [5617]~P67(x56172)+E(f319(f319(f73(f932(x56171,x56172)),x56173),x56174),f319(f73(x56172),f319(x56173,x56174)))
% 28.73/28.52 [5630]~E(x56302,f2(a925))+E(f319(f319(f130(x56301),x56302),f319(f319(f143(x56301),x56303),x56304)),f319(f319(f143(x56301),x56303),x56304))
% 28.73/28.52 [5631]P1(f319(x56312,x56313))+E(f319(f128(x56311,x56312),f319(f319(f143(x56311),x56313),x56314)),f319(f128(x56311,x56312),x56314))
% 28.73/28.52 [5767]~E(x57672,x57674)+P1(f319(f319(f319(f301(x57671),x57672),x57673),x57674))
% 28.73/28.52 [5775]E(x57751,f105(x57752))+E(f136(x57753,f319(f319(f146(x57752,x57753),x57754),x57751)),f319(x57754,f136(x57752,x57751)))
% 28.73/28.52 [5789]~E(x57891,f57(x57892,x57894))+E(f319(x57891,f319(f319(f301(x57892),x57893),f180(f932(x57892,a923)))),x57893)
% 28.73/28.52 [5805]~E(f319(f95(a925),x58052),f2(a925))+E(f319(f319(f167(x58051),f319(f95(a925),x58052)),f319(f319(f143(x58051),x58053),x58054)),f105(x58051))
% 28.73/28.52 [5824]E(x58241,f105(x58242))+E(f319(f133(x58243),f319(f319(f146(x58242,x58243),x58244),x58241)),f319(x58244,f319(f133(x58242),x58241)))
% 28.73/28.52 [5928]~P1(f319(x59283,x59284))+P1(f319(f319(f319(f301(x59281),x59282),x59283),x59284))
% 28.73/28.52 [6031]~E(f319(f95(a925),x60312),f2(a925))+E(f319(f319(f130(x60311),f319(f95(a925),x60312)),f319(f319(f143(x60311),x60313),x60314)),f319(f319(f143(x60311),x60313),x60314))
% 28.73/28.52 [6048]~P20(x60482,x60484,x60481)+E(f319(x60481,f319(f319(f301(x60482),x60483),f180(f932(x60482,a923)))),x60483)
% 28.73/28.52 [6074]~E(x60742,x60743)+P1(f319(f319(f321(x60741),x60742),f319(f319(f301(x60741),x60743),x60744)))
% 28.73/28.52 [6075]~E(x60752,x60753)+P1(f319(f319(f321(x60751),x60752),f319(f319(f301(x60751),x60753),x60754)))
% 28.73/28.52 [6080]~P102(x60801)+E(f319(f319(f102(x60801),x60802),f319(f319(f102(x60801),x60803),x60804)),f319(f319(f102(x60801),x60803),f319(f319(f102(x60801),x60802),x60804)))
% 28.73/28.52 [6081]~P107(x60811)+E(f319(f319(f102(x60811),x60812),f319(f319(f102(x60811),x60813),x60814)),f319(f319(f102(x60811),x60813),f319(f319(f102(x60811),x60812),x60814)))
% 28.73/28.52 [6082]~P107(x60821)+E(f319(f319(f102(x60821),x60822),f319(f319(f102(x60821),x60823),x60824)),f319(f319(f102(x60821),x60823),f319(f319(f102(x60821),x60822),x60824)))
% 28.73/28.52 [6083]~P102(x60831)+E(f319(f319(f93(x60831),x60832),f319(f319(f93(x60831),x60833),x60834)),f319(f319(f93(x60831),x60833),f319(f319(f93(x60831),x60832),x60834)))
% 28.73/28.52 [6084]~P108(x60841)+E(f319(f319(f93(x60841),x60842),f319(f319(f93(x60841),x60843),x60844)),f319(f319(f93(x60841),x60843),f319(f319(f93(x60841),x60842),x60844)))
% 28.73/28.52 [6085]~P108(x60851)+E(f319(f319(f93(x60851),x60852),f319(f319(f93(x60851),x60853),x60854)),f319(f319(f93(x60851),x60853),f319(f319(f93(x60851),x60852),x60854)))
% 28.73/28.52 [6086]~P121(x60861)+E(f319(f319(f75(x60861),x60862),f319(f319(f75(x60861),x60863),x60864)),f319(f319(f75(x60861),x60863),f319(f319(f75(x60861),x60862),x60864)))
% 28.73/28.52 [6087]~P121(x60871)+E(f319(f319(f74(x60871),x60872),f319(f319(f74(x60871),x60873),x60874)),f319(f319(f74(x60871),x60873),f319(f319(f74(x60871),x60872),x60874)))
% 28.73/28.52 [6088]~P4(x60881)+E(f319(f319(f224(x60881),x60882),f319(f319(f224(x60881),x60883),x60884)),f319(f319(f224(x60881),x60883),f319(f319(f224(x60881),x60882),x60884)))
% 28.73/28.52 [6089]~P4(x60891)+E(f319(f319(f224(x60891),x60892),f319(f319(f224(x60891),x60893),x60894)),f319(f319(f224(x60891),x60893),f319(f319(f224(x60891),x60892),x60894)))
% 28.73/28.52 [6090]~P4(x60901)+E(f319(f319(f225(x60901),x60902),f319(f319(f225(x60901),x60903),x60904)),f319(f319(f225(x60901),x60903),f319(f319(f225(x60901),x60902),x60904)))
% 28.73/28.52 [6091]~P4(x60911)+E(f319(f319(f225(x60911),x60912),f319(f319(f225(x60911),x60913),x60914)),f319(f319(f225(x60911),x60913),f319(f319(f225(x60911),x60912),x60914)))
% 28.73/28.52 [6098]E(x60981,x60982)+E(f162(x60983,x60981,f319(f319(f143(x60983),x60982),x60984)),f319(f319(f143(x60983),x60982),f162(x60983,x60981,x60984)))
% 28.73/28.52 [6113]~P1(f319(x61132,x61133))+E(f319(f128(x61131,x61132),f319(f319(f143(x61131),x61133),x61134)),f319(f319(f143(x61131),x61133),f319(f128(x61131,x61132),x61134)))
% 28.73/28.52 [6207]~E(x62074,f180(f932(x62071,a923)))+E(f319(f302(x62071,x62072,f319(f16(x62072,x62071),x62073)),x62074),f180(f932(x62072,a923)))
% 28.73/28.52 [6253]~P1(f319(x62532,x62533))+E(f169(x62531,x62532,f319(f319(f143(x62531),x62533),x62534)),f319(f319(f143(x62531),x62533),f169(x62531,x62532,x62534)))
% 28.73/28.52 [6315]E(x63151,f180(f932(x63152,a923)))+E(f319(f319(f33(x63152,f932(x63153,a923)),x63151),f319(f16(f932(x63153,a923),x63152),x63154)),x63154)
% 28.73/28.52 [6316]E(x63161,f180(f932(x63162,a923)))+E(f319(f319(f34(x63162,f932(x63163,a923)),x63161),f319(f16(f932(x63163,a923),x63162),x63164)),x63164)
% 28.73/28.52 [6325]~E(x63254,f180(f932(x63252,a923)))+E(f319(f319(f246(x63251,x63252),x63253),f319(f16(f932(x63252,a923),x63251),x63254)),f180(f932(f931(x63251,x63252),a923)))
% 28.73/28.52 [6326]~E(x63263,f180(f932(x63261,a923)))+E(f319(f319(f246(x63261,x63262),x63263),f319(f16(f932(x63262,a923),x63261),x63264)),f180(f932(f931(x63261,x63262),a923)))
% 28.73/28.52 [6377]E(x63771,f2(a925))+E(f319(f319(f130(x63772),x63771),f319(f319(f143(x63772),x63773),x63774)),f319(f319(f130(x63772),f319(f319(f23(a925),x63771),f72(a925))),x63774))
% 28.73/28.52 [6398]E(x63981,f180(f932(x63982,a923)))+E(f319(f302(x63982,x63983,f319(f16(x63983,x63982),x63984)),x63981),f319(f319(f301(x63983),x63984),f180(f932(x63983,a923))))
% 28.73/28.52 [6401]E(f319(f303(x64011,x64012,f319(f16(x64012,x64011),x64013)),x64014),f180(f932(x64011,a923)))+P1(f319(f319(f321(x64012),x64013),x64014))
% 28.73/28.52 [6467]~E(x64673,f180(f932(x64671,a923)))+E(f319(f319(f33(x64671,f932(x64672,a923)),x64673),f319(f16(f932(x64672,a923),x64671),x64674)),f180(f932(x64672,a923)))
% 28.73/28.52 [6468]~E(x64683,f180(f932(x64681,a923)))+E(f319(f319(f34(x64681,f932(x64682,a923)),x64683),f319(f16(f932(x64682,a923),x64681),x64684)),f234(f932(x64682,a923)))
% 28.73/28.52 [6470]~P65(x64701)+E(f39(x64701,f319(f319(f75(x64701),x64702),x64703),f319(f319(f75(x64701),x64702),x64704)),f319(f319(f75(x64701),x64702),f39(x64701,x64703,x64704)))
% 28.73/28.52 [6641]E(f319(f303(x66411,x66412,f319(f16(x66412,x66411),x66413)),x66414),f234(f932(x66411,a923)))+~P1(f319(f319(f321(x66412),x66413),x66414))
% 28.73/28.52 [6663]~P1(f319(f319(f321(x66631),x66632),x66634))+P1(f319(f319(f321(x66631),x66632),f319(f319(f301(x66631),x66633),x66634)))
% 28.73/28.52 [6664]~P1(f319(f319(f321(x66641),x66642),x66644))+P1(f319(f319(f321(x66641),x66642),f319(f319(f301(x66641),x66643),x66644)))
% 28.73/28.52 [6665]~P1(f319(f319(f321(x66651),x66652),x66654))+P1(f319(f319(f321(x66651),x66652),f319(f319(f301(x66651),x66653),x66654)))
% 28.73/28.52 [6670]P1(f319(x66701,x66702))+~P1(f319(f152(x66703,x66701),f319(f319(f143(x66703),x66702),x66704)))
% 28.73/28.52 [6679]~E(x66793,f319(f319(f23(a925),f319(f181(f926(x66791)),x66792)),f72(a925)))+E(f106(x66791,f319(f319(f151(x66791,x66792),x66793),x66794)),f106(x66791,x66792))
% 28.73/28.52 [6699]~P4(x66991)+E(f319(f319(f93(f932(x66991,a923)),f319(f293(x66991),x66992)),f295(x66991,x66993,x66994)),f295(x66991,x66993,f319(f319(f224(x66991),x66992),x66994)))
% 28.73/28.52 [6700]~P4(x67001)+E(f319(f319(f93(f932(x67001,a923)),f319(f275(x67001),x67002)),f295(x67001,x67003,x67004)),f295(x67001,f319(f319(f225(x67001),x67002),x67003),x67004))
% 28.73/28.52 [6715]E(f319(f319(f93(f932(x67151,a923)),x67152),f319(f319(f301(x67151),x67153),x67154)),f319(f319(f93(f932(x67151,a923)),x67152),x67154))+P1(f319(f319(f321(x67151),x67153),x67152))
% 28.73/28.52 [6716]E(f319(f319(f93(f932(x67161,a923)),x67162),f319(f319(f301(x67161),x67163),x67164)),f319(f319(f93(f932(x67161,a923)),x67162),x67164))+P1(f319(f319(f321(x67161),x67163),x67162))
% 28.73/28.52 [6728]E(f162(x67281,x67282,f319(f319(f126(x67281),x67283),x67284)),f319(f319(f126(x67281),x67283),f162(x67281,x67282,x67284)))+P1(f319(f319(f321(x67281),x67282),f319(f164(x67281),x67283)))
% 28.73/28.52 [6733]~P87(x67331)+E(f319(f319(f75(x67331),f319(f319(f236(x67331),x67332),x67333)),f319(f319(f236(x67331),x67332),x67334)),f319(f319(f236(x67331),x67332),f319(f319(f74(a925),x67333),x67334)))
% 28.73/28.52 [6734]~P121(x67341)+E(f319(f319(f75(x67341),f319(f319(f236(x67341),x67342),x67343)),f319(f319(f236(x67341),x67342),x67344)),f319(f319(f236(x67341),x67342),f319(f319(f74(a925),x67343),x67344)))
% 28.73/28.52 [6771]~P106(x67711)+E(f319(f319(f93(x67711),f319(f319(f102(x67711),x67712),x67713)),f319(f319(f102(x67711),x67712),x67714)),f319(f319(f102(x67711),x67712),f319(f319(f93(x67711),x67713),x67714)))
% 28.73/28.52 [6772]~P106(x67721)+E(f319(f319(f102(x67721),f319(f319(f93(x67721),x67722),x67723)),f319(f319(f93(x67721),x67722),x67724)),f319(f319(f93(x67721),x67722),f319(f319(f102(x67721),x67723),x67724)))
% 28.73/28.52 [6773]~P121(x67731)+E(f319(f319(f74(x67731),f319(f319(f75(x67731),x67732),x67733)),f319(f319(f75(x67731),x67732),x67734)),f319(f319(f75(x67731),x67732),f319(f319(f74(x67731),x67733),x67734)))
% 28.73/28.52 [6774]~P4(x67741)+E(f319(f319(f225(x67741),f319(f319(f224(x67741),x67742),x67743)),f319(f319(f224(x67741),x67742),x67744)),f319(f319(f224(x67741),x67742),f319(f319(f225(x67741),x67743),x67744)))
% 28.73/28.52 [6775]~P4(x67751)+E(f319(f319(f224(x67751),f319(f319(f225(x67751),x67752),x67753)),f319(f319(f225(x67751),x67752),x67754)),f319(f319(f225(x67751),x67752),f319(f319(f224(x67751),x67753),x67754)))
% 28.73/28.52 [6810]~P65(x68101)+E(f39(x68101,f319(f319(f75(x68101),x68102),x68103),f319(f319(f75(x68101),x68104),x68103)),f319(f319(f75(x68101),f39(x68101,x68102,x68104)),x68103))
% 28.73/28.52 [6813]~E(f319(f181(f926(x68131)),x68133),f319(f181(f926(x68132)),x68134))+E(f319(f319(f146(f931(x68131,x68132),x68132),f248(x68131,x68132)),f319(f319(f173(x68131,x68132),x68133),x68134)),x68134)
% 28.73/28.52 [6814]~E(f319(f181(f926(x68141)),x68143),f319(f181(f926(x68142)),x68144))+E(f319(f319(f146(f931(x68141,x68142),x68141),f243(x68141,x68142)),f319(f319(f173(x68141,x68142),x68143),x68144)),x68143)
% 28.73/28.52 [6819]P1(f319(f152(x68191,x68192),x68193))+~P1(f319(f152(x68191,x68192),f319(f319(f143(x68191),x68194),x68193)))
% 28.73/28.52 [6820]P1(f319(f152(x68201,x68202),x68203))+~P1(f319(f152(x68201,x68202),f319(f319(f126(x68201),x68204),x68203)))
% 28.73/28.52 [6821]P1(f319(f152(x68211,x68212),x68213))+~P1(f319(f152(x68211,x68212),f319(f319(f126(x68211),x68213),x68214)))
% 28.73/28.52 [6826]~P66(x68261)+E(f39(x68261,f319(f319(f23(x68261),x68262),f39(x68261,x68263,x68264)),x68264),f39(x68261,f319(f319(f23(x68261),x68262),x68263),x68264))
% 28.73/28.52 [6827]~P65(x68271)+E(f39(x68271,f319(f319(f75(x68271),x68272),f39(x68271,x68273,x68274)),x68274),f39(x68271,f319(f319(f75(x68271),x68272),x68273),x68274))
% 28.73/28.52 [6828]~P65(x68281)+E(f39(x68281,f319(f319(f74(x68281),x68282),f39(x68281,x68283,x68284)),x68284),f39(x68281,f319(f319(f74(x68281),x68282),x68283),x68284))
% 28.73/28.52 [6829]~P65(x68291)+E(f39(x68291,f319(f319(f74(x68291),x68292),f39(x68291,x68293,x68294)),x68294),f39(x68291,f319(f319(f74(x68291),x68292),x68293),x68294))
% 28.73/28.52 [6911]~P4(x69111)+E(f319(f319(f93(f932(x69111,a923)),f295(x69111,x69112,x69113)),f319(f293(x69111),x69114)),f295(x69111,x69112,f319(f319(f224(x69111),x69113),x69114)))
% 28.73/28.52 [6912]~P4(x69121)+E(f319(f319(f93(f932(x69121,a923)),f295(x69121,x69122,x69123)),f319(f275(x69121),x69124)),f295(x69121,f319(f319(f225(x69121),x69122),x69124),x69123))
% 28.73/28.52 [6915]~E(f319(f181(f926(x69151)),x69153),f319(f181(f926(x69152)),x69154))+E(f319(f319(f173(x69151,x69152),f319(f160(x69151),x69153)),f319(f160(x69152),x69154)),f319(f160(f931(x69151,x69152)),f319(f319(f173(x69151,x69152),x69153),x69154)))
% 28.73/28.52 [6928]E(x69281,f319(f319(f23(a925),f319(f181(f926(x69282)),x69283)),f72(a925)))+E(f106(x69282,f319(f319(f151(x69282,x69283),x69281),x69284)),f319(f319(f151(x69282,f106(x69282,x69283)),x69281),x69284))
% 28.73/28.52 [6943]~P1(f319(f129(x69432),x69434))+P1(f319(f129(f931(x69431,x69432)),f319(f319(f173(x69431,x69432),x69433),x69434)))
% 28.73/28.52 [6944]~P1(f319(f129(x69441),x69443))+P1(f319(f129(f931(x69441,x69442)),f319(f319(f173(x69441,x69442),x69443),x69444)))
% 28.73/28.52 [7207]E(f319(f319(f30(a925),x72071),x72072),x72073)+~P1(f319(f42(x72071,x72072),f319(f319(f244(a925,a925),x72073),x72074)))
% 28.73/28.52 [7230]E(f39(a925,x72301,x72302),x72303)+~P1(f319(f42(x72301,x72302),f319(f319(f244(a925,a925),x72304),x72303)))
% 28.73/28.52 [7233]P1(f319(f129(x72331),x72332))+~P1(f319(f129(x72333),f319(f319(f146(x72331,x72333),x72334),x72332)))
% 28.73/28.52 [7317]E(f162(x73171,x73172,f319(f319(f126(x73171),x73173),x73174)),f319(f319(f126(x73171),f162(x73171,x73172,x73173)),x73174))+~P1(f319(f319(f321(x73171),x73172),f319(f164(x73171),x73173)))
% 28.73/28.52 [7383]E(f319(f95(a925),x73831),f2(a925))+E(f319(f319(f130(x73832),f319(f95(a925),x73831)),f319(f319(f143(x73832),x73833),x73834)),f319(f319(f130(x73832),f319(f319(f23(a925),f319(f95(a925),x73831)),f72(a925))),x73834))
% 28.73/28.52 [7410]~P66(x74101)+E(f39(x74101,f319(f319(f23(x74101),f39(x74101,x74102,x74103)),x74104),x74103),f39(x74101,f319(f319(f23(x74101),x74102),x74104),x74103))
% 28.73/28.52 [7411]~P65(x74111)+E(f39(x74111,f319(f319(f75(x74111),f39(x74111,x74112,x74113)),x74114),x74113),f39(x74111,f319(f319(f75(x74111),x74112),x74114),x74113))
% 28.73/28.52 [7412]~P65(x74121)+E(f39(x74121,f319(f319(f74(x74121),f39(x74121,x74122,x74123)),x74124),x74123),f39(x74121,f319(f319(f74(x74121),x74122),x74124),x74123))
% 28.73/28.52 [7413]~P65(x74131)+E(f39(x74131,f319(f319(f75(x74131),f39(x74131,x74132,x74133)),x74134),x74133),f39(x74131,f319(f319(f75(x74131),x74132),x74134),x74133))
% 28.73/28.52 [7414]~P65(x74141)+E(f39(x74141,f319(f319(f74(x74141),f39(x74141,x74142,x74143)),x74144),x74143),f39(x74141,f319(f319(f74(x74141),x74142),x74144),x74143))
% 28.73/28.52 [7606]~E(x76061,f319(f319(f143(x76062),x76063),x76064))+~P1(f319(f319(f226(a925),f319(f181(f926(x76062)),x76061)),f319(f181(f926(x76062)),x76064)))
% 28.73/28.52 [7806]P26(x78061,x78062,x78063,f319(f164(x78061),x78064))+~P1(f319(f129(x78062),f319(f319(f146(x78061,x78062),x78063),x78064)))
% 28.73/28.52 [7881]~P1(f319(f319(f226(f932(x78811,a923)),x78812),x78814))+P1(f319(f319(f226(f932(x78811,a923)),x78812),f319(f319(f301(x78811),x78813),x78814)))
% 28.73/28.52 [7916]~P66(x79161)+E(f39(x79161,f319(f319(f23(x79161),f39(x79161,x79162,x79163)),f39(x79161,x79164,x79163)),x79163),f39(x79161,f319(f319(f23(x79161),x79162),x79164),x79163))
% 28.73/28.52 [7917]~P65(x79171)+E(f39(x79171,f319(f319(f75(x79171),f39(x79171,x79172,x79173)),f39(x79171,x79174,x79173)),x79173),f39(x79171,f319(f319(f75(x79171),x79172),x79174),x79173))
% 28.73/28.52 [7918]~P65(x79181)+E(f39(x79181,f319(f319(f74(x79181),f39(x79181,x79182,x79183)),f39(x79181,x79184,x79183)),x79183),f39(x79181,f319(f319(f74(x79181),x79182),x79184),x79183))
% 28.73/28.52 [8020]~E(f319(x80204,f783(x80204,x80203,x80201,x80202)),f234(f932(x80202,a923)))+E(f319(f319(f34(x80201,f932(x80202,a923)),x80203),x80204),f234(f932(x80202,a923)))
% 28.73/28.52 [8021]~E(f319(x80214,f881(x80214,x80213,x80211,x80212)),f180(f932(x80212,a923)))+E(f319(f319(f33(x80211,f932(x80212,a923)),x80213),x80214),f180(f932(x80212,a923)))
% 28.73/28.52 [8022]~E(f319(x80224,f877(x80224,x80223,x80222,x80221)),f180(f932(x80222,a923)))+E(f319(f319(f33(x80221,f932(x80222,a923)),x80223),x80224),f180(f932(x80222,a923)))
% 28.73/28.52 [8023]~E(f319(x80234,f790(x80234,x80233,x80232,x80231)),f234(f932(x80232,a923)))+E(f319(f319(f34(x80231,f932(x80232,a923)),x80233),x80234),f234(f932(x80232,a923)))
% 28.73/28.52 [8418]P1(f319(x84181,x84182))+~P1(f319(f319(f321(x84183),x84182),f319(f319(f93(f932(x84183,a923)),x84184),f319(f254(x84183),x84181))))
% 28.73/28.52 [8455]~P1(f319(f319(f226(f932(x84551,a923)),x84553),x84554))+P1(f319(f319(f226(f932(x84551,a923)),f319(f319(f301(x84551),x84552),x84553)),f319(f319(f301(x84551),x84552),x84554)))
% 28.73/28.52 [8465]E(f319(x84651,f895(x84651,x84652,x84653)),x84653)+~P1(f319(f319(f321(x84654),x84653),f319(f302(x84652,x84654,x84651),f234(f932(x84652,a923)))))
% 28.73/28.52 [8500]P1(f319(f319(f321(x85001),x85002),x85003))+~P1(f319(f319(f321(x85001),x85002),f319(f319(f93(f932(x85001,a923)),x85003),f319(f254(x85001),x85004))))
% 28.73/28.52 [8636]P1(f319(x86362,x86363))+E(f319(f319(f130(x86361),f319(f181(f926(x86361)),f169(x86361,x86362,f319(f319(f143(x86361),x86363),x86364)))),f319(f319(f143(x86361),x86363),x86364)),f319(f319(f143(x86361),x86363),x86364))
% 28.73/28.52 [8746]~P1(f319(f319(f227(a925),f319(x87464,x87462)),f319(x87464,x87463)))+P1(f319(f319(f321(f931(x87461,x87461)),f319(f319(f244(x87461,x87461),x87462),x87463)),f319(f319(f280(a925,x87461),a232),x87464)))
% 28.73/28.52 [8843]~P1(f319(x88432,f761(x88434,x88432,x88433,x88431)))+E(f169(x88431,x88432,f319(f319(f126(x88431),x88433),x88434)),f319(f319(f126(x88431),x88433),f169(x88431,x88432,x88434)))
% 28.73/28.52 [8920]P26(f926(x89201),f926(x89202),f319(f146(x89201,x89202),x89203),x89204)+~P26(x89201,x89202,x89203,f31(f932(x89201,a923),f319(f302(f926(x89201),f932(x89201,a923),f164(x89201)),x89204)))
% 28.73/28.52 [8995]~P1(f319(x89952,x89953))+E(f319(f319(f130(x89951),f319(f181(f926(x89951)),f169(x89951,x89952,f319(f319(f143(x89951),x89953),x89954)))),f319(f319(f143(x89951),x89953),x89954)),f319(f319(f130(x89951),f319(f181(f926(x89951)),f169(x89951,x89952,x89954))),x89954))
% 28.73/28.52 [9037]~E(x90372,x90373)+E(f319(f128(x90371,f319(f319(f8(a923,a923,x90371),a314),f319(a316,x90372))),f319(f319(f143(x90371),x90373),x90374)),f319(f128(x90371,f319(f319(f8(a923,a923,x90371),a314),f319(a316,x90372))),x90374))
% 28.73/28.52 [9047]E(f319(f319(f34(x90471,f932(x90472,a923)),x90473),x90474),f234(f932(x90472,a923)))+P1(f319(f319(f321(x90471),f783(x90474,x90473,x90471,x90472)),x90473))
% 28.73/28.52 [9048]E(f319(f319(f33(x90481,f932(x90482,a923)),x90483),x90484),f180(f932(x90482,a923)))+P1(f319(f319(f321(x90481),f881(x90484,x90483,x90481,x90482)),x90483))
% 28.73/28.52 [9049]E(f319(f319(f33(x90491,f932(x90492,a923)),x90493),x90494),f180(f932(x90492,a923)))+P1(f319(f319(f321(x90491),f877(x90494,x90493,x90492,x90491)),x90493))
% 28.73/28.52 [9050]E(f319(f319(f34(x90501,f932(x90502,a923)),x90503),x90504),f234(f932(x90502,a923)))+P1(f319(f319(f321(x90501),f790(x90504,x90503,x90502,x90501)),x90503))
% 28.73/28.52 [9088]P1(f319(f319(f227(a925),f319(x90881,x90882)),f319(x90881,x90883)))+~P1(f319(f319(f321(f931(x90884,x90884)),f319(f319(f244(x90884,x90884),x90882),x90883)),f319(f319(f280(a925,x90884),a232),x90881)))
% 28.73/28.52 [9115]E(f169(x91151,x91152,f319(f319(f126(x91151),x91153),x91154)),f319(f319(f126(x91151),x91153),f169(x91151,x91152,x91154)))+P1(f319(f319(f321(x91151),f761(x91154,x91152,x91153,x91151)),f319(f164(x91151),x91153)))
% 28.73/28.52 [9170]~P27(x91701,x91702,x91703,f234(f932(x91701,a923)),f234(f932(x91702,a923)))+E(f319(f302(x91701,x91702,x91703),f319(f73(f932(x91701,a923)),x91704)),f319(f73(f932(x91702,a923)),f319(f302(x91701,x91702,x91703),x91704)))
% 28.73/28.52 [9275]P1(f319(f319(f321(x92751),f522(x92752,x92753,x92754,x92751)),x92753))+~P1(f319(f319(f321(f932(x92751,a923)),x92754),f319(f319(f54(x92751),x92753),x92752)))
% 28.73/28.52 [9278]E(x92781,x92782)+~P1(f319(f319(f321(f931(x92783,x92783)),f319(f319(f244(x92783,x92783),x92781),x92782)),f319(f319(f175(f931(x92783,x92783),a923),f2(a925)),x92784)))
% 28.73/28.52 [9360]E(f319(f277(x93601,x93601,x93602),f319(f319(f301(x93601),f522(x93602,x93603,x93604,x93601)),f180(f932(x93601,a923)))),x93604)+~P1(f319(f319(f321(f932(x93601,a923)),x93604),f319(f319(f54(x93601),x93603),x93602)))
% 28.73/28.52 [9365]~P1(f319(f319(f321(f931(x93651,x93651)),f319(f319(f244(x93651,x93651),x93653),x93652)),f299(x93651,x93654)))+P1(f319(f319(f321(f931(x93651,x93651)),f319(f319(f244(x93651,x93651),x93652),x93653)),f299(x93651,f319(f278(x93651,x93651),x93654))))
% 28.73/28.52 [9378]~P65(x93781)+E(f319(f319(f74(x93781),f319(f319(f74(x93781),f319(f319(f75(x93781),x93782),f319(f319(f30(x93781),x93783),x93782))),f39(x93781,x93783,x93782))),x93784),f319(f319(f74(x93781),x93783),x93784))
% 28.73/28.52 [9391]~P1(f319(f319(f321(x93911),x93913),x93914))+P1(f319(f319(f321(f932(x93911,a923)),f319(f277(x93911,x93911,x93912),f319(f319(f301(x93911),x93913),f180(f932(x93911,a923))))),f319(f319(f54(x93911),x93914),x93912)))
% 28.73/28.52 [9403]P1(f319(f319(f321(f931(x94031,x94031)),f319(f319(f244(x94031,x94031),x94032),x94033)),f299(x94031,x94034)))+~P1(f319(f319(f321(f931(x94031,x94031)),f319(f319(f244(x94031,x94031),x94033),x94032)),f299(x94031,f319(f278(x94031,x94031),x94034))))
% 28.73/28.52 [9489]E(f319(f319(f151(x94891,f319(f160(x94891),x94892)),f319(f319(f23(a925),f319(f319(f23(a925),f319(f181(f926(x94891)),x94892)),x94893)),f72(a925))),x94894),f319(f160(x94891),f319(f319(f151(x94891,x94892),x94893),x94894)))+~P1(f319(f319(f227(a925),x94893),f319(f181(f926(x94891)),x94892)))
% 28.73/28.52 [9493]~P1(f319(x94932,f753(x94934,x94932,x94933,x94931)))+E(f319(f319(f130(x94931),f319(f181(f926(x94931)),f169(x94931,x94932,f319(f319(f126(x94931),x94933),x94934)))),f319(f319(f126(x94931),x94933),x94934)),f319(f319(f130(x94931),f319(f181(f926(x94931)),f169(x94931,x94932,x94934))),x94934))
% 28.73/28.52 [9538]~P26(x95382,x95381,x95383,f234(f932(x95382,a923)))+P1(f319(f319(f226(f932(x95381,a923)),f319(f302(x95382,x95381,x95383),f319(f73(f932(x95382,a923)),x95384))),f319(f73(f932(x95381,a923)),f319(f302(x95382,x95381,x95383),x95384))))
% 28.73/28.52 [9551]~P6(x95511)+E(f319(f134(x95511,x95512,f319(f7(x95512,x95511,x95511),f319(f319(f8(x95511,f932(x95511,x95511),x95512),f102(x95511)),x95513)),f180(x95511)),x95514),f319(f319(f33(x95512,x95511),f319(f164(x95512),x95514)),x95513))
% 28.73/28.52 [9552]~P6(x95521)+E(f319(f134(x95521,x95522,f319(f7(x95522,x95521,x95521),f319(f319(f8(x95521,f932(x95521,x95521),x95522),f93(x95521)),x95523)),f234(x95521)),x95524),f319(f319(f34(x95522,x95521),f319(f164(x95522),x95524)),x95523))
% 28.73/28.52 [9562]E(f319(f319(f130(x95621),f319(f181(f926(x95621)),f169(x95621,x95622,f319(f319(f126(x95621),x95623),x95624)))),f319(f319(f126(x95621),x95623),x95624)),f319(f319(f130(x95621),f319(f181(f926(x95621)),f169(x95621,x95622,x95624))),x95624))+P1(f319(f319(f321(x95621),f753(x95624,x95622,x95623,x95621)),f319(f164(x95621),x95623)))
% 28.73/28.52 [9632]~P1(f319(f319(f321(f931(f926(x96324),f926(x96324))),f319(f319(f244(f926(x96324),f926(x96324)),x96323),x96322)),f149(x96324,x96321)))+P1(f319(f319(f227(a925),f692(x96321,x96322,x96323,x96324)),f319(f181(f926(x96324)),x96323)))
% 28.73/28.52 [9633]~P65(x96331)+E(f319(f319(f74(x96331),f319(f319(f74(x96331),f319(f319(f75(x96331),f319(f319(f30(x96331),x96332),x96333)),x96333)),f39(x96331,x96332,x96333))),x96334),f319(f319(f74(x96331),x96332),x96334))
% 28.73/28.52 [9663]~P1(f319(f319(f321(f931(f926(x96631),f926(x96631))),f319(f319(f244(f926(x96631),f926(x96631)),x96632),x96633)),f319(f278(f926(x96631),f926(x96631)),f149(x96631,x96634))))+P1(f319(f319(f321(f931(f926(x96631),f926(x96631))),f319(f319(f244(f926(x96631),f926(x96631)),x96632),x96633)),f149(x96631,f319(f278(x96631,x96631),x96634))))
% 28.73/28.52 [9664]P1(f319(f319(f321(f931(f926(x96641),f926(x96641))),f319(f319(f244(f926(x96641),f926(x96641)),x96642),x96643)),f319(f278(f926(x96641),f926(x96641)),f149(x96641,x96644))))+~P1(f319(f319(f321(f931(f926(x96641),f926(x96641))),f319(f319(f244(f926(x96641),f926(x96641)),x96642),x96643)),f149(x96641,f319(f278(x96641,x96641),x96644))))
% 28.73/28.52 [9704]~P1(f319(f319(f321(x97041),x97043),f319(f256(x97041,x97042),x97044)))+P1(f319(f319(f321(f931(x97041,x97042)),f319(f319(f244(x97041,x97042),x97043),f573(x97044,x97042,x97043,x97041))),x97044))
% 28.73/28.52 [9705]~P1(f319(f319(f321(x97051),x97053),f319(f256(x97051,x97052),x97054)))+P1(f319(f319(f321(f931(x97051,x97052)),f319(f319(f244(x97051,x97052),x97053),f575(x97054,x97052,x97053,x97051))),x97054))
% 28.73/28.52 [9864]~P1(f319(f319(f321(f931(x98641,x98641)),f319(f319(f244(x98641,x98641),x98642),x98644)),f319(f319(f281(x98641,x98641,x98641),x98643),f299(x98641,x98643))))+P1(f319(f319(f321(f931(x98641,x98641)),f319(f319(f244(x98641,x98641),x98642),f649(x98643,x98644,x98642,x98641))),x98643))
% 28.73/28.52 [10038]P12(x100381,x100382,x100383,x100384)+P1(f319(f319(f321(f931(x100381,x100381)),f319(f319(f244(x100381,x100381),f859(x100382,x100384,x100383,x100381)),f858(x100382,x100384,x100383,x100381))),x100383))
% 28.73/28.52 [10046]~P1(f319(f319(f321(f931(x100462,x100461)),x100464),f319(f278(x100461,x100462),x100463)))+P1(f319(f319(f321(f931(x100461,x100462)),f319(f319(f244(x100461,x100462),f662(x100463,x100464,x100461,x100462)),f661(x100463,x100464,x100461,x100462))),x100463))
% 28.73/28.52 [10071]~P1(f319(f319(f321(f931(f926(x100711),f926(x100711))),f319(f319(f244(f926(x100711),f926(x100711)),x100714),x100713)),f149(x100711,x100712)))+P1(f319(f319(f321(f931(x100711,x100711)),f319(f319(f244(x100711,x100711),f706(x100712,x100713,x100714,x100711)),f707(x100712,x100713,x100714,x100711))),x100712))
% 28.73/28.52 [10164]~P1(f319(f319(f321(f931(f926(x101641),f926(x101641))),f319(f319(f244(f926(x101641),f926(x101641)),x101642),x101644)),f149(x101641,x101643)))+P1(f319(f319(f321(f931(x101641,x101641)),f319(f319(f244(x101641,x101641),f319(f319(f156(x101641),x101642),f692(x101643,x101644,x101642,x101641))),f693(x101643,x101644,x101642,x101641))),x101643))
% 28.73/28.52 [10184]~P1(f319(f55(x101842),x101844))+E(f319(f319(f319(f59(f932(x101841,a923),x101842,f102(f932(x101841,a923))),f319(f319(f7(x101842,f932(x101841,a923),f932(x101841,a923)),f319(f319(f8(x101841,f932(f932(x101841,a923),f932(x101841,a923)),x101842),f301(x101841)),x101843)),f180(f932(x101841,a923)))),f180(f932(x101841,a923))),x101844),f319(f302(x101842,x101841,x101843),x101844))
% 28.73/28.52 [10299]~P26(x102991,x102992,x102993,f234(f932(x102991,a923)))+P1(f319(f319(f226(f932(x102991,a923)),f319(f303(x102991,x102992,x102993),f319(f319(f301(x102992),x102994),f180(f932(x102992,a923))))),f319(f319(f301(x102991),f79(x102991,f319(f319(f7(x102991,x102992,a923),f319(f319(f8(x102992,f932(x102992,a923),x102991),a316),x102993)),x102994))),f180(f932(x102991,a923)))))
% 28.73/28.52 [5835]~E(f319(f319(f126(x58351),x58352),x58354),x58353)+E(f319(f319(f167(x58351),f319(f181(f926(x58351)),x58352)),x58353),x58352)
% 28.73/28.52 [5836]~E(f319(f319(f126(x58362),x58363),x58361),x58364)+E(x58361,f319(f319(f130(x58362),f319(f181(f926(x58362)),x58363)),x58364))
% 28.73/28.52 [5847]~E(x58474,f2(a925))+E(f319(f319(f156(x58471),f319(f319(f143(x58471),x58472),x58473)),x58474),x58472)
% 28.73/28.52 [6390]~P121(x63901)+E(f319(f319(f236(x63901),f319(f319(f236(x63901),x63902),x63903)),x63904),f319(f319(f236(x63901),x63902),f319(f319(f75(a925),x63903),x63904)))
% 28.73/28.52 [6391]~P87(x63911)+E(f319(f319(f236(x63911),f319(f319(f236(x63911),x63912),x63913)),x63914),f319(f319(f236(x63911),x63912),f319(f319(f75(a925),x63913),x63914)))
% 28.73/28.52 [6399]E(x63991,f2(a925))+E(f319(f319(f156(x63992),f319(f319(f143(x63992),x63993),x63994)),x63991),f319(f319(f156(x63992),x63994),f319(f319(f23(a925),x63991),f72(a925))))
% 28.73/28.52 [6425]~P121(x64251)+E(f319(f319(f75(x64251),f319(f319(f75(x64251),x64252),x64253)),x64254),f319(f319(f75(x64251),x64252),f319(f319(f75(x64251),x64253),x64254)))
% 28.73/28.52 [6426]~P124(x64261)+E(f319(f319(f283(x64261),f319(f319(f75(x64261),x64262),x64263)),x64264),f319(f319(f75(x64261),x64262),f319(f319(f283(x64261),x64263),x64264)))
% 28.73/28.52 [6427]~P121(x64271)+E(f319(f319(f74(x64271),f319(f319(f74(x64271),x64272),x64273)),x64274),f319(f319(f74(x64271),x64272),f319(f319(f74(x64271),x64273),x64274)))
% 28.73/28.52 [6428]~P102(x64281)+E(f319(f319(f102(x64281),f319(f319(f102(x64281),x64282),x64283)),x64284),f319(f319(f102(x64281),x64282),f319(f319(f102(x64281),x64283),x64284)))
% 28.73/28.52 [6429]~P107(x64291)+E(f319(f319(f102(x64291),f319(f319(f102(x64291),x64292),x64293)),x64294),f319(f319(f102(x64291),x64292),f319(f319(f102(x64291),x64293),x64294)))
% 28.73/28.52 [6430]~P107(x64301)+E(f319(f319(f102(x64301),f319(f319(f102(x64301),x64302),x64303)),x64304),f319(f319(f102(x64301),x64302),f319(f319(f102(x64301),x64303),x64304)))
% 28.73/28.52 [6431]~P102(x64311)+E(f319(f319(f93(x64311),f319(f319(f93(x64311),x64312),x64313)),x64314),f319(f319(f93(x64311),x64312),f319(f319(f93(x64311),x64313),x64314)))
% 28.73/28.52 [6432]~P108(x64321)+E(f319(f319(f93(x64321),f319(f319(f93(x64321),x64322),x64323)),x64324),f319(f319(f93(x64321),x64322),f319(f319(f93(x64321),x64323),x64324)))
% 28.73/28.52 [6433]~P108(x64331)+E(f319(f319(f93(x64331),f319(f319(f93(x64331),x64332),x64333)),x64334),f319(f319(f93(x64331),x64332),f319(f319(f93(x64331),x64333),x64334)))
% 28.73/28.52 [6434]~P76(x64341)+E(f319(f319(f75(x64341),f319(f319(f75(x64341),x64342),x64343)),x64344),f319(f319(f75(x64341),x64342),f319(f319(f75(x64341),x64343),x64344)))
% 28.73/28.52 [6435]~P121(x64351)+E(f319(f319(f75(x64351),f319(f319(f75(x64351),x64352),x64353)),x64354),f319(f319(f75(x64351),x64352),f319(f319(f75(x64351),x64353),x64354)))
% 28.73/28.52 [6437]~P121(x64371)+E(f319(f319(f74(x64371),f319(f319(f74(x64371),x64372),x64373)),x64374),f319(f319(f74(x64371),x64372),f319(f319(f74(x64371),x64373),x64374)))
% 28.73/28.52 [6438]~P77(x64381)+E(f319(f319(f74(x64381),f319(f319(f74(x64381),x64382),x64383)),x64384),f319(f319(f74(x64381),x64382),f319(f319(f74(x64381),x64383),x64384)))
% 28.73/28.52 [6439]~P4(x64391)+E(f319(f319(f224(x64391),f319(f319(f224(x64391),x64392),x64393)),x64394),f319(f319(f224(x64391),x64392),f319(f319(f224(x64391),x64393),x64394)))
% 28.73/28.52 [6440]~P4(x64401)+E(f319(f319(f224(x64401),f319(f319(f224(x64401),x64402),x64403)),x64404),f319(f319(f224(x64401),x64402),f319(f319(f224(x64401),x64403),x64404)))
% 28.73/28.52 [6441]~P4(x64411)+E(f319(f319(f225(x64411),f319(f319(f225(x64411),x64412),x64413)),x64414),f319(f319(f225(x64411),x64412),f319(f319(f225(x64411),x64413),x64414)))
% 28.73/28.52 [6442]~P4(x64421)+E(f319(f319(f225(x64421),f319(f319(f225(x64421),x64422),x64423)),x64424),f319(f319(f225(x64421),x64422),f319(f319(f225(x64421),x64423),x64424)))
% 28.73/28.52 [6451]~P65(x64511)+E(f39(x64511,f319(f319(f74(x64511),x64512),f319(f319(f75(x64511),x64513),x64514)),x64514),f39(x64511,x64512,x64514))
% 28.73/28.52 [6452]~P65(x64521)+E(f39(x64521,f319(f319(f74(x64521),x64522),f319(f319(f75(x64521),x64523),x64524)),x64523),f39(x64521,x64522,x64523))
% 28.73/28.52 [6588]E(f319(f319(f156(x65881),f319(f319(f167(x65881),x65882),x65883)),x65884),f319(f319(f156(x65881),x65883),x65884))+~P1(f319(f319(f227(a925),x65884),x65882))
% 28.73/28.52 [6767]~E(x67672,x67674)+P1(f319(f319(f164(x67671),f319(f319(f143(x67671),x67672),x67673)),x67674))
% 28.73/28.52 [6769]~P121(x67691)+E(f319(f319(f75(x67691),f319(f319(f75(x67691),x67692),x67693)),x67694),f319(f319(f75(x67691),f319(f319(f75(x67691),x67692),x67694)),x67693))
% 28.73/28.52 [6770]~P121(x67701)+E(f319(f319(f74(x67701),f319(f319(f74(x67701),x67702),x67703)),x67704),f319(f319(f74(x67701),f319(f319(f74(x67701),x67702),x67704)),x67703))
% 28.73/28.52 [6832]~P149(x68322)+E(f319(f319(f6(x68321,x68322),f319(f16(x68322,x68321),x68323)),x68324),f319(f319(f75(x68322),f319(f92(x68322),f319(f29(x68321),x68324))),x68323))
% 28.73/28.52 [7003]E(f319(f319(f93(f932(x70031,a923)),f319(f319(f301(x70031),x70032),x70033)),x70034),f319(f319(f93(f932(x70031,a923)),x70033),x70034))+P1(f319(f319(f321(x70031),x70032),x70034))
% 28.73/28.52 [7004]E(f319(f319(f93(f932(x70041,a923)),f319(f319(f301(x70041),x70042),x70043)),x70044),f319(f319(f93(f932(x70041,a923)),x70043),x70044))+P1(f319(f319(f321(x70041),x70042),x70044))
% 28.73/28.52 [7075]~P106(x70751)+E(f319(f319(f93(x70751),f319(f319(f102(x70751),x70752),x70753)),f319(f319(f102(x70751),x70754),x70753)),f319(f319(f102(x70751),f319(f319(f93(x70751),x70752),x70754)),x70753))
% 28.73/28.52 [7076]~P106(x70761)+E(f319(f319(f102(x70761),f319(f319(f93(x70761),x70762),x70763)),f319(f319(f93(x70761),x70764),x70763)),f319(f319(f93(x70761),f319(f319(f102(x70761),x70762),x70764)),x70763))
% 28.73/28.52 [7077]~P68(x70771)+E(f319(f319(f224(x70771),f319(f319(f23(x70771),x70772),x70773)),f319(f319(f23(x70771),x70774),x70773)),f319(f319(f23(x70771),f319(f319(f224(x70771),x70772),x70774)),x70773))
% 28.73/28.52 [7078]~P68(x70781)+E(f319(f319(f225(x70781),f319(f319(f23(x70781),x70782),x70783)),f319(f319(f23(x70781),x70784),x70783)),f319(f319(f23(x70781),f319(f319(f225(x70781),x70782),x70784)),x70783))
% 28.73/28.52 [7079]~P121(x70791)+E(f319(f319(f74(x70791),f319(f319(f75(x70791),x70792),x70793)),f319(f319(f75(x70791),x70794),x70793)),f319(f319(f75(x70791),f319(f319(f74(x70791),x70792),x70794)),x70793))
% 28.73/28.52 [7080]~P122(x70801)+E(f319(f319(f74(x70801),f319(f319(f75(x70801),x70802),x70803)),f319(f319(f75(x70801),x70804),x70803)),f319(f319(f75(x70801),f319(f319(f74(x70801),x70802),x70804)),x70803))
% 28.73/28.52 [7081]~P90(x70811)+E(f319(f319(f224(x70811),f319(f319(f74(x70811),x70812),x70813)),f319(f319(f74(x70811),x70814),x70813)),f319(f319(f74(x70811),f319(f319(f224(x70811),x70812),x70814)),x70813))
% 28.73/28.52 [7082]~P90(x70821)+E(f319(f319(f225(x70821),f319(f319(f74(x70821),x70822),x70823)),f319(f319(f74(x70821),x70824),x70823)),f319(f319(f74(x70821),f319(f319(f225(x70821),x70822),x70824)),x70823))
% 28.73/28.52 [7083]~P4(x70831)+E(f319(f319(f225(x70831),f319(f319(f224(x70831),x70832),x70833)),f319(f319(f224(x70831),x70834),x70833)),f319(f319(f224(x70831),f319(f319(f225(x70831),x70832),x70834)),x70833))
% 28.73/28.52 [7084]~P4(x70841)+E(f319(f319(f224(x70841),f319(f319(f225(x70841),x70842),x70843)),f319(f319(f225(x70841),x70844),x70843)),f319(f319(f225(x70841),f319(f319(f224(x70841),x70842),x70844)),x70843))
% 28.73/28.52 [7085]~P78(x70851)+E(f319(f319(f75(x70851),f319(f319(f236(x70851),x70852),x70853)),f319(f319(f236(x70851),x70854),x70853)),f319(f319(f236(x70851),f319(f319(f75(x70851),x70852),x70854)),x70853))
% 28.73/28.52 [7086]~P121(x70861)+E(f319(f319(f75(x70861),f319(f319(f236(x70861),x70862),x70863)),f319(f319(f236(x70861),x70864),x70863)),f319(f319(f236(x70861),f319(f319(f75(x70861),x70862),x70864)),x70863))
% 28.73/28.52 [7087]~P72(x70871)+E(f319(f319(f283(x70871),f319(f319(f236(x70871),x70872),x70873)),f319(f319(f236(x70871),x70874),x70873)),f319(f319(f236(x70871),f319(f319(f283(x70871),x70872),x70874)),x70873))
% 28.73/28.52 [7088]~P124(x70881)+E(f319(f319(f23(x70881),f319(f319(f283(x70881),x70882),x70883)),f319(f319(f283(x70881),x70884),x70883)),f319(f319(f283(x70881),f319(f319(f23(x70881),x70882),x70884)),x70883))
% 28.73/28.52 [7089]~P124(x70891)+E(f319(f319(f74(x70891),f319(f319(f283(x70891),x70892),x70893)),f319(f319(f283(x70891),x70894),x70893)),f319(f319(f283(x70891),f319(f319(f74(x70891),x70892),x70894)),x70893))
% 28.73/28.52 [7090]~P121(x70901)+E(f319(f319(f74(x70901),f319(f319(f75(x70901),x70902),x70903)),f319(f319(f75(x70901),x70904),x70903)),f319(f319(f75(x70901),f319(f319(f74(x70901),x70902),x70904)),x70903))
% 28.73/28.52 [7122]E(f319(f319(f151(x71221,x71222),x71223),x71224),x71222)+~P1(f319(f319(f226(a925),f319(f181(f926(x71221)),x71222)),x71223))
% 28.73/28.52 [7147]~P1(f319(x71473,x71474))+P1(f319(f319(f319(f102(f932(x71471,a923)),x71472),x71473),x71474))
% 28.73/28.52 [7148]~P1(f319(x71483,x71484))+P1(f319(f319(f319(f102(f932(x71481,a923)),x71482),x71483),x71484))
% 28.73/28.52 [7149]~P1(f319(x71492,x71494))+P1(f319(f319(f319(f102(f932(x71491,a923)),x71492),x71493),x71494))
% 28.73/28.52 [7150]~P1(f319(x71502,x71504))+P1(f319(f319(f319(f102(f932(x71501,a923)),x71502),x71503),x71504))
% 28.73/28.52 [7168]E(f319(f319(f156(x71681),f319(f319(f126(x71681),x71682),x71683)),x71684),f319(f319(f156(x71681),x71682),x71684))+~P1(f319(f319(f227(a925),x71684),f319(f181(f926(x71681)),x71682)))
% 28.73/28.52 [7178]E(f319(f319(f23(f932(x71781,a923)),f319(f319(f301(x71781),x71782),x71783)),x71784),f319(f319(f23(f932(x71781,a923)),x71783),x71784))+~P1(f319(f319(f321(x71781),x71782),x71784))
% 28.73/28.52 [7179]E(f319(f319(f23(f932(x71791,a923)),f319(f319(f301(x71791),x71792),x71793)),x71794),f319(f319(f23(f932(x71791,a923)),x71793),x71794))+~P1(f319(f319(f321(x71791),x71792),x71794))
% 28.73/28.52 [7220]~E(f131(a925,f319(f294(a925,x72201),x72202)),f319(f319(f143(a925),x72204),x72203))+E(f131(a925,f319(f294(a925,f319(f319(f74(a925),x72201),f72(a925))),x72202)),x72203)
% 28.73/28.52 [7241]~P1(f319(f319(f164(x72411),x72413),x72414))+P1(f319(f319(f164(x72411),f319(f319(f143(x72411),x72412),x72413)),x72414))
% 28.73/28.52 [7291]E(x72911,f2(a925))+E(f319(f319(f143(x72912),x72913),f319(f319(f167(x72912),f319(f319(f23(a925),x72911),f72(a925))),x72914)),f319(f319(f167(x72912),x72911),f319(f319(f143(x72912),x72913),x72914)))
% 28.73/28.52 [7394]E(f319(f319(f156(x73941),x73942),f319(f319(f23(a925),x73943),f319(f181(f926(x73941)),x73944))),f319(f319(f156(x73941),f319(f319(f126(x73941),x73944),x73942)),x73943))+P1(f319(f319(f227(a925),x73943),f319(f181(f926(x73941)),x73944)))
% 28.73/28.52 [7422]E(f319(f319(f93(f932(x74221,a923)),x74222),f319(f319(f301(x74221),x74223),x74224)),f319(f319(f301(x74221),x74223),f319(f319(f93(f932(x74221,a923)),x74222),x74224)))+~P1(f319(f319(f321(x74221),x74223),x74222))
% 28.73/28.52 [7423]E(f319(f319(f93(f932(x74231,a923)),x74232),f319(f319(f301(x74231),x74233),x74234)),f319(f319(f301(x74231),x74233),f319(f319(f93(f932(x74231,a923)),x74232),x74234)))+~P1(f319(f319(f321(x74231),x74233),x74232))
% 28.73/28.52 [7462]E(f319(f319(f156(x74621),f319(f319(f151(x74621,x74622),x74623),x74624)),x74623),x74624)+~P1(f319(f319(f227(a925),x74623),f319(f181(f926(x74621)),x74622)))
% 28.73/28.52 [7484]E(x74841,f180(f932(x74842,a923)))+E(f319(f302(f931(x74843,x74842),x74843,f243(x74843,x74842)),f319(f319(f246(x74843,x74842),x74844),f319(f16(f932(x74842,a923),x74843),x74841))),x74844)
% 28.73/28.52 [7485]E(x74851,f180(f932(x74852,a923)))+E(f319(f302(f931(x74852,x74853),x74853,f248(x74852,x74853)),f319(f319(f246(x74852,x74853),x74851),f319(f16(f932(x74853,a923),x74852),x74854))),x74854)
% 28.73/28.52 [7557]E(f319(f319(f23(f932(x75571,a923)),f319(f319(f301(x75571),x75572),x75573)),x75574),f319(f319(f301(x75571),x75572),f319(f319(f23(f932(x75571,a923)),x75573),x75574)))+P1(f319(f319(f321(x75571),x75572),x75574))
% 28.73/28.52 [7592]~E(x75924,f180(f932(x75922,a923)))+E(f319(f302(f931(x75921,x75922),x75921,f243(x75921,x75922)),f319(f319(f246(x75921,x75922),x75923),f319(f16(f932(x75922,a923),x75921),x75924))),f180(f932(x75921,a923)))
% 28.73/28.52 [7593]~E(x75933,f180(f932(x75931,a923)))+E(f319(f302(f931(x75931,x75932),x75932,f248(x75931,x75932)),f319(f319(f246(x75931,x75932),x75933),f319(f16(f932(x75932,a923),x75931),x75934))),f180(f932(x75932,a923)))
% 28.73/28.52 [7642]~P1(f319(f319(f321(x76421),x76422),x76424))+P1(f319(f319(f321(x76421),x76422),f319(f319(f102(f932(x76421,a923)),x76423),x76424)))
% 28.73/28.52 [7643]~P1(f319(f319(f321(x76431),x76432),x76434))+P1(f319(f319(f321(x76431),x76432),f319(f319(f102(f932(x76431,a923)),x76433),x76434)))
% 28.73/28.52 [7644]~P1(f319(f319(f321(x76441),x76442),x76444))+P1(f319(f319(f321(x76441),x76442),f319(f319(f102(f932(x76441,a923)),x76443),x76444)))
% 28.73/28.52 [7645]~P1(f319(f319(f321(x76451),x76452),x76453))+P1(f319(f319(f321(x76451),x76452),f319(f319(f102(f932(x76451,a923)),x76453),x76454)))
% 28.73/28.52 [7646]~P1(f319(f319(f321(x76461),x76462),x76463))+P1(f319(f319(f321(x76461),x76462),f319(f319(f102(f932(x76461,a923)),x76463),x76464)))
% 28.73/28.52 [7647]~P1(f319(f319(f321(x76471),x76472),x76473))+P1(f319(f319(f321(x76471),x76472),f319(f319(f102(f932(x76471,a923)),x76473),x76474)))
% 28.73/28.52 [7664]E(f319(f319(f93(f932(x76641,a923)),f319(f319(f301(x76641),x76642),x76643)),x76644),f319(f319(f301(x76641),x76642),f319(f319(f93(f932(x76641,a923)),x76643),x76644)))+~P1(f319(f319(f321(x76641),x76642),x76644))
% 28.73/28.52 [7665]E(f319(f319(f93(f932(x76651,a923)),f319(f319(f301(x76651),x76652),x76653)),x76654),f319(f319(f301(x76651),x76652),f319(f319(f93(f932(x76651,a923)),x76653),x76654)))+~P1(f319(f319(f321(x76651),x76652),x76654))
% 28.73/28.52 [7936]P1(f319(x79361,x79362))+~P1(f319(f319(f319(f93(f932(x79363,a923)),x79364),x79361),x79362))
% 28.73/28.52 [7937]P1(f319(x79371,x79372))+~P1(f319(f319(f319(f93(f932(x79373,a923)),x79371),x79374),x79372))
% 28.73/28.52 [7938]P1(f319(x79381,x79382))+~P1(f319(f319(f319(f93(f932(x79383,a923)),x79384),x79381),x79382))
% 28.73/28.52 [7939]P1(f319(x79391,x79392))+~P1(f319(f319(f319(f93(f932(x79393,a923)),x79391),x79394),x79392))
% 28.73/28.52 [7940]E(f319(f319(f6(x79401,a925),x79402),f319(f319(f23(f932(x79401,a923)),x79403),f319(f319(f301(x79401),x79404),f180(f932(x79401,a923))))),f319(f319(f6(x79401,a925),x79402),x79403))+P1(f319(f319(f321(x79401),x79404),x79403))
% 28.73/28.52 [7945]~P79(x79451)+E(f319(f157(x79451),f319(f319(f146(a925,x79451),x79452),f131(a925,f319(f294(a925,x79453),x79454)))),f319(f319(f6(a925,x79451),x79452),f319(f164(a925),f131(a925,f319(f294(a925,x79453),x79454)))))
% 28.73/28.52 [7946]~P79(x79461)+E(f319(f319(f6(a925,x79461),x79462),f319(f164(a925),f131(a925,f319(f294(a925,x79463),x79464)))),f319(f157(x79461),f319(f319(f146(a925,x79461),x79462),f131(a925,f319(f294(a925,x79463),x79464)))))
% 28.73/28.52 [8060]~E(x80603,x80604)+P1(f319(f56(x80601,x80602,f319(f319(f301(x80601),x80603),f180(f932(x80601,a923)))),x80604))
% 28.73/28.52 [8157]P1(f319(f319(f321(x81571),x81572),f319(f164(x81571),x81573)))+~P1(f319(f319(f321(x81571),x81572),f319(f164(x81571),f319(f319(f167(x81571),x81574),x81573))))
% 28.73/28.52 [8158]P1(f319(f319(f321(x81581),x81582),f319(f164(x81581),x81583)))+~P1(f319(f319(f321(x81581),x81582),f319(f164(x81581),f319(f319(f130(x81581),x81584),x81583))))
% 28.73/28.52 [8228]P1(f319(f319(f321(x82281),x82282),x82283))+~P1(f319(f319(f321(x82281),x82282),f319(f319(f93(f932(x82281,a923)),x82284),x82283)))
% 28.73/28.52 [8229]P1(f319(f319(f321(x82291),x82292),x82293))+~P1(f319(f319(f321(x82291),x82292),f319(f319(f93(f932(x82291,a923)),x82294),x82293)))
% 28.73/28.52 [8230]P1(f319(f319(f321(x82301),x82302),x82303))+~P1(f319(f319(f321(x82301),x82302),f319(f319(f93(f932(x82301,a923)),x82304),x82303)))
% 28.73/28.52 [8231]P1(f319(f319(f321(x82311),x82312),x82313))+~P1(f319(f319(f321(x82311),x82312),f319(f319(f93(f932(x82311,a923)),x82313),x82314)))
% 28.73/28.52 [8232]P1(f319(f319(f321(x82321),x82322),x82323))+~P1(f319(f319(f321(x82321),x82322),f319(f319(f93(f932(x82321,a923)),x82323),x82324)))
% 28.73/28.52 [8233]P1(f319(f319(f321(x82331),x82332),x82333))+~P1(f319(f319(f321(x82331),x82332),f319(f319(f93(f932(x82331,a923)),x82333),x82334)))
% 28.73/28.52 [8234]P1(f319(f319(f321(x82341),x82342),x82343))+~P1(f319(f319(f321(x82341),x82342),f319(f319(f23(f932(x82341,a923)),x82343),x82344)))
% 28.73/28.52 [8235]P1(f319(f319(f321(x82351),x82352),x82353))+~P1(f319(f319(f321(x82351),x82352),f319(f319(f23(f932(x82351,a923)),x82353),x82354)))
% 28.73/28.52 [8236]P1(f319(f319(f321(x82361),x82362),x82363))+~P1(f319(f319(f321(x82361),x82362),f319(f319(f23(f932(x82361,a923)),x82363),x82364)))
% 28.73/28.52 [8251]E(f319(f319(f126(x82511),f319(f319(f167(x82511),x82512),x82513)),f319(f319(f143(x82511),x82514),f319(f319(f130(x82511),f319(a104,x82512)),x82513))),f319(f319(f151(x82511,x82513),x82512),x82514))+~P1(f319(f319(f227(a925),x82512),f319(f181(f926(x82511)),x82513)))
% 28.73/28.52 [8274]P1(f319(f319(f321(x82741),x82742),x82743))+~P1(f319(f319(f226(f932(x82741,a923)),f319(f319(f301(x82741),x82742),x82744)),x82743))
% 28.73/28.52 [8309]~P1(f319(f319(f321(x83091),x83092),x83093))+~P1(f319(f319(f321(x83091),x83092),f319(f319(f23(f932(x83091,a923)),x83094),x83093)))
% 28.73/28.52 [8310]~P1(f319(f319(f321(x83101),x83102),x83103))+~P1(f319(f319(f321(x83101),x83102),f319(f319(f23(f932(x83101,a923)),x83104),x83103)))
% 28.73/28.52 [8311]~P1(f319(f319(f321(x83111),x83112),x83113))+~P1(f319(f319(f321(x83111),x83112),f319(f319(f23(f932(x83111,a923)),x83114),x83113)))
% 28.73/28.52 [8344]~P1(f319(f319(f227(a925),x83444),f319(f181(f926(x83441)),x83443)))+P1(f319(f319(f321(x83441),x83442),f319(f164(x83441),f319(f319(f151(x83441,x83443),x83444),x83442))))
% 28.73/28.52 [8387]E(f319(f95(a925),x83871),f2(a925))+E(f319(f319(f143(x83872),x83873),f319(f319(f167(x83872),f319(f319(f23(a925),f319(f95(a925),x83871)),f72(a925))),x83874)),f319(f319(f167(x83872),f319(f95(a925),x83871)),f319(f319(f143(x83872),x83873),x83874)))
% 28.73/28.52 [8397]E(f319(f319(f156(x83971),f319(f319(f130(x83971),x83972),x83973)),x83974),f319(f319(f156(x83971),x83973),f319(f319(f74(a925),x83972),x83974)))+~P1(f319(f319(f226(a925),f319(f319(f74(a925),x83972),x83974)),f319(f181(f926(x83971)),x83973)))
% 28.73/28.52 [8406]~P149(x84062)+E(f319(f319(f6(x84061,x84062),f319(f319(f8(a925,x84062,x84061),f92(x84062)),x84063)),x84064),f319(f92(x84062),f319(f319(f6(x84061,a925),x84063),x84064)))
% 28.73/28.52 [8407]~P145(x84072)+E(f319(f319(f6(x84071,x84072),f319(f319(f8(a1,x84072,x84071),f94(x84072)),x84073)),x84074),f319(f94(x84072),f319(f319(f6(x84071,a1),x84073),x84074)))
% 28.73/28.52 [8457]~P75(x84572)+E(f319(f319(f9(x84571,x84572),f319(f319(f8(x84572,x84572,x84571),f69(x84572)),x84573)),x84574),f319(f69(x84572),f319(f319(f9(x84571,x84572),x84573),x84574)))
% 28.73/28.52 [8458]~P70(x84582)+E(f319(f319(f6(x84581,x84582),f319(f319(f8(x84582,x84582,x84581),f73(x84582)),x84583)),x84584),f319(f73(x84582),f319(f319(f6(x84581,x84582),x84583),x84584)))
% 28.73/28.52 [8460]E(f319(f319(f6(x84601,a925),x84602),f319(f319(f23(f932(x84601,a923)),x84603),f319(f319(f301(x84601),x84604),f180(f932(x84601,a923))))),f319(f319(f23(a925),f319(f319(f6(x84601,a925),x84602),x84603)),f319(x84602,x84604)))+~P1(f319(f319(f321(x84601),x84604),x84603))
% 28.73/28.52 [8480]P1(f319(f319(f226(f932(x84801,a923)),x84802),x84803))+~P1(f319(f319(f226(f932(x84801,a923)),f319(f319(f301(x84801),x84804),x84802)),x84803))
% 28.73/28.52 [8604]~E(f319(f302(x86042,x86043,x86041),f234(f932(x86042,a923))),f234(f932(x86043,a923)))+E(f319(x86041,f319(f85(x86042,x86043,f234(f932(x86042,a923)),x86041),x86044)),x86044)
% 28.73/28.52 [8605]~E(f319(f302(x86052,x86053,x86051),f234(f932(x86052,a923))),f234(f932(x86053,a923)))+E(f319(x86051,f319(f85(x86052,x86053,f234(f932(x86052,a923)),x86051),x86054)),x86054)
% 28.73/28.52 [8690]P38(x86901,x86902)+~P38(x86901,f319(f319(f301(f931(x86901,x86901)),f319(f319(f244(x86901,x86901),x86903),x86904)),x86902))
% 28.73/28.52 [8691]P62(x86911,x86912)+~P62(x86911,f319(f319(f301(f931(x86911,x86911)),f319(f319(f244(x86911,x86911),x86913),x86914)),x86912))
% 28.73/28.52 [8696]~P4(x86961)+E(f319(f319(f140(x86961,x86961,f5(x86961)),x86962),f319(f319(f140(x86961,x86961,f5(x86961)),x86963),x86964)),f319(f319(f140(x86961,x86961,f5(x86961)),x86963),f319(f319(f140(x86961,x86961,f5(x86961)),x86962),x86964)))
% 28.73/28.52 [8711]E(x87111,x87112)+~P1(f319(f56(x87113,x87114,f319(f319(f301(x87113),x87111),f180(f932(x87113,a923)))),x87112))
% 28.73/28.52 [8723]E(f319(f319(f126(x87231),f319(f319(f167(x87231),x87232),x87233)),f319(f319(f167(x87231),x87234),f319(f319(f130(x87231),x87232),x87233))),f319(f319(f167(x87231),f319(f319(f74(a925),x87232),x87234)),x87233))+~P1(f319(f319(f226(a925),f319(f319(f74(a925),x87232),x87234)),f319(f181(f926(x87231)),x87233)))
% 28.73/28.52 [8761]P1(f319(f55(x87611),x87612))+~E(x87612,f319(f302(a925,x87611,x87613),f319(f254(a925),f319(f319(f7(a925,a925,a923),f227(a925)),x87614))))
% 28.73/28.52 [8762]P1(f319(f55(x87621),x87622))+~E(x87622,f319(f302(a925,x87621,x87623),f319(f254(a925),f319(f319(f7(a925,a925,a923),f227(a925)),x87624))))
% 28.73/28.52 [8782]~P95(x87821)+E(f319(f134(x87821,x87821,f74(x87821),f319(f319(f74(x87821),x87822),x87823)),x87824),f319(f319(f74(x87821),x87822),f319(f134(x87821,x87821,f74(x87821),x87823),x87824)))
% 28.73/28.52 [8819]P1(f319(f319(f226(f932(x88191,a923)),f319(f256(x88191,x88192),x88193)),f319(f256(x88191,x88192),x88194)))+~P1(f319(f319(f226(f932(f931(x88191,x88192),a923)),x88193),x88194))
% 28.73/28.52 [8831]~P1(f319(f319(f226(a925),x88312),x88314))+P1(f319(f319(f226(f932(x88311,a923)),f319(f164(x88311),f319(f319(f167(x88311),x88312),x88313))),f319(f164(x88311),f319(f319(f167(x88311),x88314),x88313))))
% 28.73/28.52 [8832]~P1(f319(f319(f226(a925),x88324),x88322))+P1(f319(f319(f226(f932(x88321,a923)),f319(f164(x88321),f319(f319(f130(x88321),x88322),x88323))),f319(f164(x88321),f319(f319(f130(x88321),x88324),x88323))))
% 28.73/28.52 [8889]~P1(f319(f55(x88891),f319(f319(f23(f932(x88891,a923)),x88892),x88894)))+P1(f319(f55(x88891),f319(f319(f23(f932(x88891,a923)),x88892),f319(f319(f301(x88891),x88893),x88894))))
% 28.73/28.52 [8930]P1(f319(f319(f321(f931(x89301,x89301)),x89302),f299(x89301,x89303)))+~P1(f319(f319(f321(f931(x89301,x89301)),x89302),f319(f319(f175(f931(x89301,x89301),a923),x89304),x89303)))
% 28.73/28.52 [8931]P1(f319(f319(f321(f931(x89311,x89311)),x89312),f299(x89311,x89313)))+~P1(f319(f319(f321(f931(x89311,x89311)),x89312),f319(f319(f175(f931(x89311,x89311),a923),x89314),x89313)))
% 28.73/28.52 [9018]~P1(f319(f55(x90181),f319(f319(f23(f932(x90181,a923)),x90182),f319(f319(f301(x90181),x90184),x90183))))+P1(f319(f55(x90181),f319(f319(f23(f932(x90181,a923)),x90182),x90183)))
% 28.73/28.52 [9093]P1(f319(f319(f321(f931(x90931,x90932)),f319(f319(f244(x90931,x90932),x90933),x90934)),f180(f932(f931(x90931,x90932),a923))))+~P1(f319(f319(f180(f932(x90931,f932(x90932,a923))),x90933),x90934))
% 28.73/28.52 [9235]~P102(x92351)+P1(f319(f319(f226(x92351),f319(f319(f102(x92351),x92352),f319(f319(f93(x92351),x92353),x92354))),f319(f319(f93(x92351),f319(f319(f102(x92351),x92352),x92353)),f319(f319(f102(x92351),x92352),x92354))))
% 28.73/28.52 [9236]~P4(x92361)+P1(f319(f319(f226(x92361),f319(f319(f225(x92361),x92362),f319(f319(f224(x92361),x92363),x92364))),f319(f319(f224(x92361),f319(f319(f225(x92361),x92362),x92363)),f319(f319(f225(x92361),x92362),x92364))))
% 28.73/28.52 [9253]~P1(f319(f319(f321(f931(x92531,x92532)),f319(f319(f244(x92531,x92532),x92533),x92534)),f180(f932(f931(x92531,x92532),a923))))+P1(f319(f319(f180(f932(x92531,f932(x92532,a923))),x92533),x92534))
% 28.73/28.52 [9386]E(x93861,x93862)+~P1(f319(f319(f321(f931(x93863,x93863)),f319(f319(f244(x93863,x93863),x93861),x93862)),f319(f164(f931(x93863,x93863)),f319(f319(f173(x93863,x93863),x93864),x93864))))
% 28.73/28.52 [9417]~P1(f319(f319(f321(f931(x94171,x94171)),f319(f319(f244(x94171,x94171),x94173),x94172)),f299(x94171,x94174)))+~P38(x94171,f319(f319(f301(f931(x94171,x94171)),f319(f319(f244(x94171,x94171),x94172),x94173)),x94174))
% 28.73/28.52 [9418]~P1(f319(f319(f321(f931(x94181,x94181)),f319(f319(f244(x94181,x94181),x94183),x94182)),f299(x94181,x94184)))+~P62(x94181,f319(f319(f301(f931(x94181,x94181)),f319(f319(f244(x94181,x94181),x94182),x94183)),x94184))
% 28.73/28.52 [9422]E(x94221,x94222)+E(f319(f128(x94223,f319(f319(f8(a923,a923,x94223),a314),f319(a316,x94221))),f319(f319(f143(x94223),x94222),x94224)),f319(f319(f143(x94223),x94222),f319(f128(x94223,f319(f319(f8(a923,a923,x94223),a314),f319(a316,x94221))),x94224)))
% 28.73/28.52 [9432]P1(f319(f319(f321(x94321),x94322),f319(f164(x94321),x94323)))+~P1(f319(f319(f321(f931(x94321,x94321)),f319(f319(f244(x94321,x94321),x94322),x94324)),f319(f164(f931(x94321,x94321)),f319(f319(f173(x94321,x94321),x94323),x94323))))
% 28.73/28.52 [9453]~P27(x94532,x94531,x94533,f234(f932(x94532,a923)),f234(f932(x94531,a923)))+E(f319(f302(x94531,x94532,f85(x94532,x94531,f234(f932(x94532,a923)),x94533)),x94534),f319(f303(x94532,x94531,x94533),x94534))
% 28.73/28.52 [9468]~P102(x94681)+P1(f319(f319(f226(x94681),f319(f319(f102(x94681),f319(f319(f93(x94681),x94682),x94683)),f319(f319(f93(x94681),x94682),x94684))),f319(f319(f93(x94681),x94682),f319(f319(f102(x94681),x94683),x94684))))
% 28.73/28.52 [9469]~P4(x94691)+P1(f319(f319(f226(x94691),f319(f319(f225(x94691),f319(f319(f224(x94691),x94692),x94693)),f319(f319(f224(x94691),x94692),x94694))),f319(f319(f224(x94691),x94692),f319(f319(f225(x94691),x94693),x94694))))
% 28.73/28.52 [9507]P1(f319(f319(f321(f931(x95071,x95071)),f319(f319(f244(x95071,x95071),x95072),x95073)),f319(f319(f281(x95071,x95071,x95071),x95074),f299(x95071,x95074))))+~P1(f319(f319(f321(f931(x95071,x95071)),f319(f319(f244(x95071,x95071),x95072),x95073)),x95074))
% 28.73/28.52 [9532]~P27(x95322,x95321,x95324,f234(f932(x95322,a923)),f234(f932(x95321,a923)))+E(f319(f254(x95321),f319(f319(f8(x95322,a923,x95321),x95323),f85(x95322,x95321,f234(f932(x95322,a923)),x95324))),f319(f302(x95322,x95321,x95324),f319(f254(x95322),x95323)))
% 28.73/28.52 [9546]~E(f319(f302(x95462,x95461,x95463),f234(f932(x95462,a923))),f234(f932(x95461,a923)))+P1(f319(f319(f226(f932(x95461,a923)),f319(f73(f932(x95461,a923)),f319(f302(x95462,x95461,x95463),x95464))),f319(f302(x95462,x95461,x95463),f319(f73(f932(x95462,a923)),x95464))))
% 28.73/28.52 [9877]P1(f319(f319(f321(f931(x98771,x98771)),f319(f319(f244(x98771,x98771),x98772),x98773)),f319(f278(x98771,x98771),f319(f319(f281(x98771,x98771,x98771),x98774),f299(x98771,x98774)))))+~P1(f319(f319(f321(f931(x98771,x98771)),f319(f319(f244(x98771,x98771),x98772),x98773)),f319(f319(f281(x98771,x98771,x98771),f319(f278(x98771,x98771),x98774)),f299(x98771,f319(f278(x98771,x98771),x98774)))))
% 28.73/28.52 [9878]~P1(f319(f319(f321(f931(x98781,x98781)),f319(f319(f244(x98781,x98781),x98782),x98783)),f319(f278(x98781,x98781),f319(f319(f281(x98781,x98781,x98781),x98784),f299(x98781,x98784)))))+P1(f319(f319(f321(f931(x98781,x98781)),f319(f319(f244(x98781,x98781),x98782),x98783)),f319(f319(f281(x98781,x98781,x98781),f319(f278(x98781,x98781),x98784)),f299(x98781,f319(f278(x98781,x98781),x98784)))))
% 28.73/28.52 [9899]~P1(f319(f319(f321(x98992),x98994),f319(f276(x98991,x98992),x98993)))+P1(f319(f319(f321(f931(x98991,x98992)),f319(f319(f244(x98991,x98992),f572(x98993,x98991,x98994,x98992)),x98994)),x98993))
% 28.73/28.52 [9900]~P1(f319(f319(f321(x99002),x99004),f319(f276(x99001,x99002),x99003)))+P1(f319(f319(f321(f931(x99001,x99002)),f319(f319(f244(x99001,x99002),f574(x99003,x99001,x99004,x99002)),x99004)),x99003))
% 28.73/28.52 [9928]~P1(f319(f319(f321(x99281),x99284),f319(f319(f102(f932(x99281,a923)),x99282),x99283)))+P1(f319(f319(f319(f102(f932(x99281,a923)),f319(f319(f7(x99281,f932(x99281,a923),a923),f321(x99281)),x99282)),f319(f319(f7(x99281,f932(x99281,a923),a923),f321(x99281)),x99283)),x99284))
% 28.73/28.52 [9929]~P1(f319(f319(f321(x99291),x99294),f319(f319(f93(f932(x99291,a923)),x99292),x99293)))+P1(f319(f319(f319(f93(f932(x99291,a923)),f319(f319(f7(x99291,f932(x99291,a923),a923),f321(x99291)),x99292)),f319(f319(f7(x99291,f932(x99291,a923),a923),f321(x99291)),x99293)),x99294))
% 28.73/28.52 [10021]~P1(f319(f319(f321(f931(x100211,x100211)),f319(f319(f244(x100211,x100211),x100214),x100213)),f319(f319(f281(x100211,x100211,x100211),x100212),f299(x100211,x100212))))+P1(f319(f319(f321(f931(x100211,x100211)),f319(f319(f244(x100211,x100211),f640(x100212,x100213,x100214,x100211)),x100213)),x100212))
% 28.73/28.52 [10059]P1(f319(f319(f321(x100591),x100592),f319(f319(f102(f932(x100591,a923)),x100593),x100594)))+~P1(f319(f319(f319(f102(f932(x100591,a923)),f319(f319(f7(x100591,f932(x100591,a923),a923),f321(x100591)),x100593)),f319(f319(f7(x100591,f932(x100591,a923),a923),f321(x100591)),x100594)),x100592))
% 28.73/28.52 [10060]P1(f319(f319(f321(x100601),x100602),f319(f319(f93(f932(x100601,a923)),x100603),x100604)))+~P1(f319(f319(f319(f93(f932(x100601,a923)),f319(f319(f7(x100601,f932(x100601,a923),a923),f321(x100601)),x100603)),f319(f319(f7(x100601,f932(x100601,a923),a923),f321(x100601)),x100604)),x100602))
% 28.73/28.52 [10350]P33(x103501,f319(f319(f7(x103501,f932(f931(x103501,x103501),a923),f932(x103501,a923)),f319(f319(f8(f932(x103501,f932(f932(f931(x103501,x103501),a923),a923)),f932(f932(f931(x103501,x103501),a923),f932(x103501,a923)),x103501),f7(x103501,f932(f931(x103501,x103501),a923),a923)),f319(f319(f8(f932(x103501,f931(x103501,x103501)),f932(x103501,f932(f932(f931(x103501,x103501),a923),a923)),x103501),f319(f8(f931(x103501,x103501),f932(f932(f931(x103501,x103501),a923),a923),x103501),f321(f931(x103501,x103501)))),f244(x103501,x103501)))),x103502),x103503,x103504)+~P1(f319(f319(f321(f931(f926(x103501),f926(x103501))),f319(f319(f244(f926(x103501),f926(x103501)),x103503),x103504)),f150(x103501,x103502)))
% 28.73/28.52 [10354]P63(x103541,f319(f319(f7(x103541,f932(f931(x103541,x103541),a923),f932(x103541,a923)),f319(f319(f8(f932(x103541,f932(f932(f931(x103541,x103541),a923),a923)),f932(f932(f931(x103541,x103541),a923),f932(x103541,a923)),x103541),f7(x103541,f932(f931(x103541,x103541),a923),a923)),f319(f319(f8(f932(x103541,f931(x103541,x103541)),f932(x103541,f932(f932(f931(x103541,x103541),a923),a923)),x103541),f319(f8(f931(x103541,x103541),f932(f932(f931(x103541,x103541),a923),a923),x103541),f321(f931(x103541,x103541)))),f244(x103541,x103541)))),x103542),x103543,x103544)+~P1(f319(f319(f321(f931(f932(x103541,a923),f932(x103541,a923))),f319(f319(f244(f932(x103541,a923),f932(x103541,a923)),x103543),x103544)),f311(x103541,x103542)))
% 28.73/28.52 [10388]E(x103881,x103882)+~E(f319(f319(f7(x103883,f932(f931(x103883,x103884),a923),f932(x103884,a923)),f319(f319(f8(f932(x103884,f932(f932(f931(x103883,x103884),a923),a923)),f932(f932(f931(x103883,x103884),a923),f932(x103884,a923)),x103883),f7(x103884,f932(f931(x103883,x103884),a923),a923)),f319(f319(f8(f932(x103884,f931(x103883,x103884)),f932(x103884,f932(f932(f931(x103883,x103884),a923),a923)),x103883),f319(f8(f931(x103883,x103884),f932(f932(f931(x103883,x103884),a923),a923),x103884),f321(f931(x103883,x103884)))),f244(x103883,x103884)))),x103881),f319(f319(f7(x103883,f932(f931(x103883,x103884),a923),f932(x103884,a923)),f319(f319(f8(f932(x103884,f932(f932(f931(x103883,x103884),a923),a923)),f932(f932(f931(x103883,x103884),a923),f932(x103884,a923)),x103883),f7(x103884,f932(f931(x103883,x103884),a923),a923)),f319(f319(f8(f932(x103884,f931(x103883,x103884)),f932(x103884,f932(f932(f931(x103883,x103884),a923),a923)),x103883),f319(f8(f931(x103883,x103884),f932(f932(f931(x103883,x103884),a923),a923),x103884),f321(f931(x103883,x103884)))),f244(x103883,x103884)))),x103882))
% 28.73/28.52 [10391]~P33(x103911,f319(f319(f7(x103911,f932(f931(x103911,x103911),a923),f932(x103911,a923)),f319(f319(f8(f932(x103911,f932(f932(f931(x103911,x103911),a923),a923)),f932(f932(f931(x103911,x103911),a923),f932(x103911,a923)),x103911),f7(x103911,f932(f931(x103911,x103911),a923),a923)),f319(f319(f8(f932(x103911,f931(x103911,x103911)),f932(x103911,f932(f932(f931(x103911,x103911),a923),a923)),x103911),f319(f8(f931(x103911,x103911),f932(f932(f931(x103911,x103911),a923),a923),x103911),f321(f931(x103911,x103911)))),f244(x103911,x103911)))),x103914),x103912,x103913)+P1(f319(f319(f321(f931(f926(x103911),f926(x103911))),f319(f319(f244(f926(x103911),f926(x103911)),x103912),x103913)),f150(x103911,x103914)))
% 28.73/28.52 [10392]~P63(x103921,f319(f319(f7(x103921,f932(f931(x103921,x103921),a923),f932(x103921,a923)),f319(f319(f8(f932(x103921,f932(f932(f931(x103921,x103921),a923),a923)),f932(f932(f931(x103921,x103921),a923),f932(x103921,a923)),x103921),f7(x103921,f932(f931(x103921,x103921),a923),a923)),f319(f319(f8(f932(x103921,f931(x103921,x103921)),f932(x103921,f932(f932(f931(x103921,x103921),a923),a923)),x103921),f319(f8(f931(x103921,x103921),f932(f932(f931(x103921,x103921),a923),a923),x103921),f321(f931(x103921,x103921)))),f244(x103921,x103921)))),x103924),x103922,x103923)+P1(f319(f319(f321(f931(f932(x103921,a923),f932(x103921,a923))),f319(f319(f244(f932(x103921,a923),f932(x103921,a923)),x103922),x103923)),f311(x103921,x103924)))
% 28.73/28.52 [7714]~P99(x77141)+E(f319(f319(f75(x77141),f319(f95(x77141),x77142)),f319(f319(f75(x77141),f319(f95(x77141),x77143)),x77144)),f319(f319(f75(x77141),f319(f95(x77141),f319(f319(f75(a1),x77142),x77143))),x77144))
% 28.73/28.52 [7715]~P99(x77151)+E(f319(f319(f74(x77151),f319(f95(x77151),x77152)),f319(f319(f23(x77151),f319(f95(x77151),x77153)),x77154)),f319(f319(f23(x77151),f319(f95(x77151),f319(f319(f74(a1),x77152),x77153))),x77154))
% 28.73/28.52 [7716]~P99(x77161)+E(f319(f319(f74(x77161),f319(f95(x77161),x77162)),f319(f319(f74(x77161),f319(f95(x77161),x77163)),x77164)),f319(f319(f74(x77161),f319(f95(x77161),f319(f319(f74(a1),x77162),x77163))),x77164))
% 28.73/28.52 [7756]~P149(x77561)+E(f319(f157(x77561),f319(f319(f146(x77562,x77561),f319(f16(x77561,x77562),x77563)),x77564)),f319(f319(f75(x77561),f319(f92(x77561),f319(f181(f926(x77562)),x77564))),x77563))
% 28.73/28.52 [7994]E(f319(f260(x79941,f319(f319(f143(f931(a91,x79941)),x79942),x79943)),x79944),f319(f248(a91,x79941),x79942))+~P1(f319(f319(f227(a91),x79944),f319(f243(a91,x79941),x79942)))
% 28.73/28.52 [8035]~P99(x80351)+E(f319(f319(f74(x80351),f319(f95(x80351),x80352)),f319(f319(f23(x80351),x80353),f319(f95(x80351),x80354))),f319(f319(f74(x80351),f319(f95(x80351),f319(f319(f74(a1),x80352),f319(f73(a1),x80354)))),x80353))
% 28.73/28.52 [8171]E(f319(f260(x81711,x81712),f319(f319(f23(a91),x81713),f319(f243(a91,x81711),x81714))),f319(f260(x81711,f319(f319(f143(f931(a91,x81711)),x81714),x81712)),x81713))+P1(f319(f319(f227(a91),x81713),f319(f243(a91,x81711),x81714)))
% 28.73/28.52 [8611]~P1(f319(f319(f321(x86111),x86112),f319(f164(x86111),f106(x86111,x86114))))+P1(f319(f319(f321(x86111),x86112),f319(f164(x86111),f106(x86111,f319(f319(f126(x86111),x86113),x86114)))))
% 28.73/28.52 [8612]~P1(f319(f319(f321(x86121),x86122),f319(f164(x86121),f106(x86121,x86123))))+P1(f319(f319(f321(x86121),x86122),f319(f164(x86121),f106(x86121,f319(f319(f126(x86121),x86123),x86124)))))
% 28.73/28.52 [8631]E(f319(f319(f102(f932(x86311,a923)),f319(f319(f93(f932(x86311,a923)),x86312),x86313)),x86314),f319(f319(f93(f932(x86311,a923)),x86312),f319(f319(f102(f932(x86311,a923)),x86313),x86314)))+~P1(f319(f319(f226(f932(x86311,a923)),x86314),x86312))
% 28.73/28.52 [8945]~E(f319(f319(f102(f932(x89451,a923)),f319(f319(f93(f932(x89451,a923)),x89453),x89454)),x89452),f319(f319(f93(f932(x89451,a923)),x89453),f319(f319(f102(f932(x89451,a923)),x89454),x89452)))+P1(f319(f319(f226(f932(x89451,a923)),x89452),x89453))
% 28.73/28.52 [9240]~P1(f319(f319(f226(f932(x92401,a923)),x92402),f319(f319(f102(f932(x92401,a923)),x92403),x92404)))+P1(f319(f319(f226(f932(x92401,a923)),f319(f319(f23(f932(x92401,a923)),x92402),x92403)),x92404))
% 28.73/28.52 [9357]~E(f319(f302(x93571,x93572,x93573),f234(f932(x93571,a923))),f234(f932(x93572,a923)))+E(f319(f302(x93571,x93572,x93573),f319(f302(x93572,x93571,f85(x93571,x93572,f234(f932(x93571,a923)),x93573)),x93574)),x93574)
% 28.73/28.52 [9362]P1(f319(f319(f226(f932(x93621,a923)),x93622),f319(f319(f102(f932(x93621,a923)),x93623),x93624)))+~P1(f319(f319(f226(f932(x93621,a923)),f319(f319(f23(f932(x93621,a923)),x93622),x93623)),x93624))
% 28.73/28.52 [9449]~P92(x94491)+E(f319(f69(x94491),f319(f319(f6(x94492,x94491),f319(f319(f8(x94491,x94491,x94492),f69(x94491)),x94493)),x94494)),f319(f319(f6(x94492,x94491),f319(f319(f8(x94491,x94491,x94492),f69(x94491)),x94493)),x94494))
% 28.73/28.52 [9623]~P92(x96231)+P1(f319(f319(f226(x96231),f2(x96231)),f319(f319(f6(x96232,x96231),f319(f319(f8(x96231,x96231,x96232),f69(x96231)),x96233)),x96234)))
% 28.73/28.52 [9627]~P70(x96271)+E(f319(f157(x96271),f319(f319(f146(x96272,x96271),f319(f66(x96271,x96271,x96272,f73(x96271)),x96273)),x96274)),f319(f73(x96271),f319(f157(x96271),f319(f319(f146(x96272,x96271),x96273),x96274))))
% 28.73/28.52 [9770]~P92(x97701)+P1(f319(f319(f226(x97701),f319(f69(x97701),f319(f319(f6(x97702,x97701),x97703),x97704))),f319(f319(f6(x97702,x97701),f319(f319(f8(x97701,x97701,x97702),f69(x97701)),x97703)),x97704)))
% 28.73/28.52 [9801]~E(f319(f319(f74(a925),x98011),x98014),f319(f319(f74(a925),x98013),x98012))+P1(f319(f319(f321(f931(f931(a925,a925),f931(a925,a925))),f319(f319(f244(f931(a925,a925),f931(a925,a925)),f319(f319(f244(a925,a925),x98011),x98012)),f319(f319(f244(a925,a925),x98013),x98014))),a100))
% 28.73/28.52 [9802]~P1(f319(f319(f227(a925),x98021),x98023))+P1(f319(f319(f321(f931(f931(a925,a925),f931(a925,a925))),f319(f319(f244(f931(a925,a925),f931(a925,a925)),f319(f319(f244(a925,a925),x98021),x98022)),f319(f319(f244(a925,a925),x98023),x98024))),a26))
% 28.73/28.52 [9803]~P1(f319(f319(f227(a925),x98031),x98033))+P1(f319(f319(f321(f931(f931(a925,a925),f931(a925,a925))),f319(f319(f244(f931(a925,a925),f931(a925,a925)),f319(f319(f244(a925,a925),x98031),x98032)),f319(f319(f244(a925,a925),x98033),x98034))),a64))
% 28.73/28.52 [9958]E(f319(f319(f74(a925),x99581),x99582),f319(f319(f74(a925),x99583),x99584))+~P1(f319(f319(f321(f931(f931(a925,a925),f931(a925,a925))),f319(f319(f244(f931(a925,a925),f931(a925,a925)),f319(f319(f244(a925,a925),x99581),x99584)),f319(f319(f244(a925,a925),x99583),x99582))),a100))
% 28.73/28.52 [9994]E(f319(f319(f156(x99941),f319(f319(f130(x99941),f319(f181(f926(x99941)),f169(x99941,x99942,x99943))),x99943)),x99944),f319(f319(f156(x99941),x99943),f319(f319(f74(a925),x99944),f319(f181(f926(x99941)),f169(x99941,x99942,x99943)))))+~P1(f319(f319(f227(a925),x99944),f319(f181(f926(x99941)),f319(f319(f130(x99941),f319(f181(f926(x99941)),f169(x99941,x99942,x99943))),x99943))))
% 28.73/28.52 [10012]~P1(f319(f319(f321(x100122),x100124),f319(f319(f33(x100121,f932(x100122,a923)),f234(f932(x100121,a923))),x100123)))+P1(f319(f319(f319(f33(x100121,f932(x100122,a923)),f234(f932(x100121,a923))),f319(f319(f8(f932(x100122,a923),f932(x100122,a923),x100121),f319(f7(x100122,f932(x100122,a923),a923),f321(x100122))),x100123)),x100124))
% 28.73/28.52 [10013]~P1(f319(f319(f321(x100132),x100134),f319(f319(f34(x100131,f932(x100132,a923)),f234(f932(x100131,a923))),x100133)))+P1(f319(f319(f319(f34(x100131,f932(x100132,a923)),f234(f932(x100131,a923))),f319(f319(f8(f932(x100132,a923),f932(x100132,a923),x100131),f319(f7(x100132,f932(x100132,a923),a923),f321(x100132))),x100133)),x100134))
% 28.73/28.52 [10088]~P1(f319(f43(x100881,x100882),f319(f319(f244(a1,a1),x100884),x100883)))+P1(f319(f43(f319(f73(a1),x100881),x100882),f319(f319(f244(a1,a1),f319(f319(f319(f86(a1),f319(f319(a316,x100883),f2(a1))),f319(f73(a1),x100884)),f319(f319(f23(a1),f319(f73(a1),x100884)),f72(a1)))),f319(f319(f319(f86(a1),f319(f319(a316,x100883),f2(a1))),f2(a1)),f319(f319(f23(a1),x100882),x100883)))))
% 28.73/28.52 [10100]P1(f319(f319(f321(x101001),x101002),f319(f319(f33(x101003,f932(x101001,a923)),f234(f932(x101003,a923))),x101004)))+~P1(f319(f319(f319(f33(x101003,f932(x101001,a923)),f234(f932(x101003,a923))),f319(f319(f8(f932(x101001,a923),f932(x101001,a923),x101003),f319(f7(x101001,f932(x101001,a923),a923),f321(x101001))),x101004)),x101002))
% 28.73/28.52 [10101]P1(f319(f319(f321(x101011),x101012),f319(f319(f34(x101013,f932(x101011,a923)),f234(f932(x101013,a923))),x101014)))+~P1(f319(f319(f319(f34(x101013,f932(x101011,a923)),f234(f932(x101013,a923))),f319(f319(f8(f932(x101011,a923),f932(x101011,a923),x101013),f319(f7(x101011,f932(x101011,a923),a923),f321(x101011))),x101014)),x101012))
% 28.73/28.52 [10113]E(f319(f319(f33(a925,f932(x101131,a923)),f234(f932(a925,a923))),x101132),f319(f319(f33(a925,f932(x101131,a923)),f234(f932(a925,a923))),x101133))+~E(f319(f319(f33(a925,f932(x101131,a923)),f319(f294(a925,f2(a925)),f412(x101132,x101134,x101133,x101131))),x101133),f319(f319(f33(a925,f932(x101131,a923)),f319(f294(a925,f2(a925)),f319(f319(f74(a925),f412(x101132,x101134,x101133,x101131)),x101134))),x101132))
% 28.73/28.52 [10467]~P1(f319(f319(f226(f932(f931(x104671,x104672),a923)),x104673),x104674))+P1(f319(f319(f226(f932(x104671,f932(x104672,a923))),f319(f319(f7(x104671,f932(f931(x104671,x104672),a923),f932(x104672,a923)),f319(f319(f8(f932(x104672,f932(f932(f931(x104671,x104672),a923),a923)),f932(f932(f931(x104671,x104672),a923),f932(x104672,a923)),x104671),f7(x104672,f932(f931(x104671,x104672),a923),a923)),f319(f319(f8(f932(x104672,f931(x104671,x104672)),f932(x104672,f932(f932(f931(x104671,x104672),a923),a923)),x104671),f319(f8(f931(x104671,x104672),f932(f932(f931(x104671,x104672),a923),a923),x104672),f321(f931(x104671,x104672)))),f244(x104671,x104672)))),x104673)),f319(f319(f7(x104671,f932(f931(x104671,x104672),a923),f932(x104672,a923)),f319(f319(f8(f932(x104672,f932(f932(f931(x104671,x104672),a923),a923)),f932(f932(f931(x104671,x104672),a923),f932(x104672,a923)),x104671),f7(x104672,f932(f931(x104671,x104672),a923),a923)),f319(f319(f8(f932(x104672,f931(x104671,x104672)),f932(x104672,f932(f932(f931(x104671,x104672),a923),a923)),x104671),f319(f8(f931(x104671,x104672),f932(f932(f931(x104671,x104672),a923),a923),x104672),f321(f931(x104671,x104672)))),f244(x104671,x104672)))),x104674)))
% 28.73/28.52 [10483]P1(f319(f319(f226(f932(f931(x104831,x104832),a923)),x104833),x104834))+~P1(f319(f319(f226(f932(x104831,f932(x104832,a923))),f319(f319(f7(x104831,f932(f931(x104831,x104832),a923),f932(x104832,a923)),f319(f319(f8(f932(x104832,f932(f932(f931(x104831,x104832),a923),a923)),f932(f932(f931(x104831,x104832),a923),f932(x104832,a923)),x104831),f7(x104832,f932(f931(x104831,x104832),a923),a923)),f319(f319(f8(f932(x104832,f931(x104831,x104832)),f932(x104832,f932(f932(f931(x104831,x104832),a923),a923)),x104831),f319(f8(f931(x104831,x104832),f932(f932(f931(x104831,x104832),a923),a923),x104832),f321(f931(x104831,x104832)))),f244(x104831,x104832)))),x104833)),f319(f319(f7(x104831,f932(f931(x104831,x104832),a923),f932(x104832,a923)),f319(f319(f8(f932(x104832,f932(f932(f931(x104831,x104832),a923),a923)),f932(f932(f931(x104831,x104832),a923),f932(x104832,a923)),x104831),f7(x104832,f932(f931(x104831,x104832),a923),a923)),f319(f319(f8(f932(x104832,f931(x104831,x104832)),f932(x104832,f932(f932(f931(x104831,x104832),a923),a923)),x104831),f319(f8(f931(x104831,x104832),f932(f932(f931(x104831,x104832),a923),a923),x104832),f321(f931(x104831,x104832)))),f244(x104831,x104832)))),x104834)))
% 28.73/28.52 [9496]~P1(f319(f319(f321(f931(x94961,x94961)),x94962),f299(x94961,x94964)))+P1(f319(f319(f321(f931(x94961,x94961)),x94962),f299(x94961,f319(f319(f102(f932(f931(x94961,x94961),a923)),x94963),x94964))))
% 28.73/28.52 [9497]~P1(f319(f319(f321(f931(x94971,x94971)),x94972),f299(x94971,x94973)))+P1(f319(f319(f321(f931(x94971,x94971)),x94972),f299(x94971,f319(f319(f102(f932(f931(x94971,x94971),a923)),x94973),x94974))))
% 28.73/28.52 [10202]~P1(f319(f319(f226(a925),f319(f319(f74(a925),x102021),x102024)),f319(f319(f74(a925),x102023),x102022)))+P1(f319(f319(f226(a1),f319(a83,f319(f277(f931(a925,a925),f931(a925,a925),a100),f319(f319(f301(f931(a925,a925)),f319(f319(f244(a925,a925),x102021),x102022)),f180(f932(f931(a925,a925),a923)))))),f319(a83,f319(f277(f931(a925,a925),f931(a925,a925),a100),f319(f319(f301(f931(a925,a925)),f319(f319(f244(a925,a925),x102023),x102024)),f180(f932(f931(a925,a925),a923)))))))
% 28.73/28.52 [10203]~P1(f319(f319(f227(a925),f319(f319(f74(a925),x102031),x102034)),f319(f319(f74(a925),x102033),x102032)))+P1(f319(f319(f227(a1),f319(a83,f319(f277(f931(a925,a925),f931(a925,a925),a100),f319(f319(f301(f931(a925,a925)),f319(f319(f244(a925,a925),x102031),x102032)),f180(f932(f931(a925,a925),a923)))))),f319(a83,f319(f277(f931(a925,a925),f931(a925,a925),a100),f319(f319(f301(f931(a925,a925)),f319(f319(f244(a925,a925),x102033),x102034)),f180(f932(f931(a925,a925),a923)))))))
% 28.73/28.52 [10293]P1(f319(f319(f226(a925),f319(f319(f74(a925),x102931),x102932)),f319(f319(f74(a925),x102933),x102934)))+~P1(f319(f319(f226(a1),f319(a83,f319(f277(f931(a925,a925),f931(a925,a925),a100),f319(f319(f301(f931(a925,a925)),f319(f319(f244(a925,a925),x102931),x102934)),f180(f932(f931(a925,a925),a923)))))),f319(a83,f319(f277(f931(a925,a925),f931(a925,a925),a100),f319(f319(f301(f931(a925,a925)),f319(f319(f244(a925,a925),x102933),x102932)),f180(f932(f931(a925,a925),a923)))))))
% 28.73/28.52 [10294]P1(f319(f319(f227(a925),f319(f319(f74(a925),x102941),x102942)),f319(f319(f74(a925),x102943),x102944)))+~P1(f319(f319(f227(a1),f319(a83,f319(f277(f931(a925,a925),f931(a925,a925),a100),f319(f319(f301(f931(a925,a925)),f319(f319(f244(a925,a925),x102941),x102944)),f180(f932(f931(a925,a925),a923)))))),f319(a83,f319(f277(f931(a925,a925),f931(a925,a925),a100),f319(f319(f301(f931(a925,a925)),f319(f319(f244(a925,a925),x102943),x102942)),f180(f932(f931(a925,a925),a923)))))))
% 28.73/28.52 [10336]P1(f319(f319(f226(f932(x103361,a923)),f319(f319(f33(a925,f932(x103361,a923)),f234(f932(a925,a923))),x103362)),f319(f319(f33(a925,f932(x103361,a923)),f234(f932(a925,a923))),x103363)))+~P1(f319(f319(f226(f932(x103361,a923)),f319(f319(f33(a925,f932(x103361,a923)),f319(f294(a925,f2(a925)),f369(x103363,x103364,x103362,x103361))),x103362)),f319(f319(f33(a925,f932(x103361,a923)),f319(f294(a925,f2(a925)),f319(f319(f74(a925),f369(x103363,x103364,x103362,x103361)),x103364))),x103363)))
% 28.73/28.52 [10395]P1(f319(f319(f226(a91),x103954),f2(a91)))+E(f319(f319(f251(f931(a91,a91),f931(x103951,f932(a928,a315)),f931(a91,a91),f931(f932(a91,f932(a923,f929(f927(x103951)))),f931(a91,a91))),f319(x103952,x103953)),f319(f319(f8(f932(f932(a91,f932(a923,f929(f927(x103951)))),f932(f931(a91,a91),f931(f932(a91,f932(a923,f929(f927(x103951)))),f931(a91,a91)))),f932(f931(a91,a91),f931(f932(a91,f932(a923,f929(f927(x103951)))),f931(a91,a91))),f931(x103951,f932(a928,a315))),f319(f251(f931(a91,a91),f932(a91,f932(a923,f929(f927(x103951)))),f931(a91,a91),f931(f932(a91,f932(a923,f929(f927(x103951)))),f931(a91,a91))),f269(x103951,x103952,f319(f319(f23(a91),x103954),f72(a91)),x103953))),f319(f319(f8(f932(f932(a91,f932(a923,f929(f927(x103951)))),f932(a91,f932(a923,f929(f927(x103951))))),f932(f932(a91,f932(a923,f929(f927(x103951)))),f932(f931(a91,a91),f931(f932(a91,f932(a923,f929(f927(x103951)))),f931(a91,a91)))),f931(x103951,f932(a928,a315))),f319(f8(f932(a91,f932(a923,f929(f927(x103951)))),f932(f931(a91,a91),f931(f932(a91,f932(a923,f929(f927(x103951)))),f931(a91,a91))),f932(a91,f932(a923,f929(f927(x103951))))),f244(f932(a91,f932(a923,f929(f927(x103951)))),f931(a91,a91)))),f319(f319(f8(f932(a91,f932(a923,f929(f927(x103951)))),f932(f932(a91,f932(a923,f929(f927(x103951)))),f932(a91,f932(a923,f929(f927(x103951))))),f931(x103951,f932(a928,a315))),f38(x103951)),f319(f319(f8(x103951,f932(a91,f932(a923,f929(f927(x103951)))),f931(x103951,f932(a928,a315))),f36(x103951)),f243(x103951,f932(a928,a315))))))),f269(x103951,x103952,x103954,x103953))
% 28.73/28.52 [10457]~P1(f319(f319(f321(x104572),x104574),f319(f276(x104571,x104572),x104573)))+P1(f319(f242(x104571,x104572,f319(f319(f7(x104571,f932(f931(x104571,x104572),a923),f932(x104572,a923)),f319(f319(f8(f932(x104572,f932(f932(f931(x104571,x104572),a923),a923)),f932(f932(f931(x104571,x104572),a923),f932(x104572,a923)),x104571),f7(x104572,f932(f931(x104571,x104572),a923),a923)),f319(f319(f8(f932(x104572,f931(x104571,x104572)),f932(x104572,f932(f932(f931(x104571,x104572),a923),a923)),x104571),f319(f8(f931(x104571,x104572),f932(f932(f931(x104571,x104572),a923),a923),x104572),f321(f931(x104571,x104572)))),f244(x104571,x104572)))),x104573)),x104574))
% 28.73/28.52 [10458]~P1(f319(f319(f321(x104581),x104584),f319(f256(x104581,x104582),x104583)))+P1(f319(f241(x104581,x104582,f319(f319(f7(x104581,f932(f931(x104581,x104582),a923),f932(x104582,a923)),f319(f319(f8(f932(x104582,f932(f932(f931(x104581,x104582),a923),a923)),f932(f932(f931(x104581,x104582),a923),f932(x104582,a923)),x104581),f7(x104582,f932(f931(x104581,x104582),a923),a923)),f319(f319(f8(f932(x104582,f931(x104581,x104582)),f932(x104582,f932(f932(f931(x104581,x104582),a923),a923)),x104581),f319(f8(f931(x104581,x104582),f932(f932(f931(x104581,x104582),a923),a923),x104582),f321(f931(x104581,x104582)))),f244(x104581,x104582)))),x104583)),x104584))
% 28.73/28.52 [10470]P1(f319(f319(f321(x104701),x104702),f319(f276(x104703,x104701),x104704)))+~P1(f319(f242(x104703,x104701,f319(f319(f7(x104703,f932(f931(x104703,x104701),a923),f932(x104701,a923)),f319(f319(f8(f932(x104701,f932(f932(f931(x104703,x104701),a923),a923)),f932(f932(f931(x104703,x104701),a923),f932(x104701,a923)),x104703),f7(x104701,f932(f931(x104703,x104701),a923),a923)),f319(f319(f8(f932(x104701,f931(x104703,x104701)),f932(x104701,f932(f932(f931(x104703,x104701),a923),a923)),x104703),f319(f8(f931(x104703,x104701),f932(f932(f931(x104703,x104701),a923),a923),x104701),f321(f931(x104703,x104701)))),f244(x104703,x104701)))),x104704)),x104702))
% 28.73/28.52 [10471]P1(f319(f319(f321(x104711),x104712),f319(f256(x104711,x104713),x104714)))+~P1(f319(f241(x104711,x104713,f319(f319(f7(x104711,f932(f931(x104711,x104713),a923),f932(x104713,a923)),f319(f319(f8(f932(x104713,f932(f932(f931(x104711,x104713),a923),a923)),f932(f932(f931(x104711,x104713),a923),f932(x104713,a923)),x104711),f7(x104713,f932(f931(x104711,x104713),a923),a923)),f319(f319(f8(f932(x104713,f931(x104711,x104713)),f932(x104713,f932(f932(f931(x104711,x104713),a923),a923)),x104711),f319(f8(f931(x104711,x104713),f932(f932(f931(x104711,x104713),a923),a923),x104713),f321(f931(x104711,x104713)))),f244(x104711,x104713)))),x104714)),x104712))
% 28.73/28.52 [10124]P1(f319(f152(x101241,x101242),x101243))+~P1(f319(f152(x101241,f319(f319(f18(x101241,a923,a923),f319(f319(f8(a923,f932(a923,a923),x101241),a317),x101244)),x101242)),x101243))
% 28.73/28.52 [10125]P1(f319(f152(x101251,x101252),x101253))+~P1(f319(f152(x101251,f319(f319(f18(x101251,a923,a923),f319(f319(f8(a923,f932(a923,a923),x101251),a317),x101252)),x101254)),x101253))
% 28.73/28.52 [10212]~P121(x102121)+E(f319(f319(f75(x102121),f319(f319(f74(x102121),f72(x102121)),f72(x102121))),f319(f319(f6(a925,x102121),f319(f319(f8(x102121,x102121,a925),f319(f74(x102121),x102122)),f319(f319(f7(a925,x102121,x102121),f319(f319(f8(x102121,f932(x102121,x102121),a925),f75(x102121)),f92(x102121))),x102123))),f319(f274(a925),x102124))),f319(f319(f75(x102121),f319(f92(x102121),x102124)),f319(f319(f74(x102121),x102122),f319(f319(f74(x102121),x102122),f319(f319(f75(x102121),f319(f92(x102121),f319(f319(f23(a925),x102124),f72(a925)))),x102123)))))
% 28.73/28.52 [10357]P1(f319(x103571,f570(x103572,x103573,x103574,x103571)))+P38(x103572,f319(f254(f931(x103572,x103572)),f319(f249(x103572,x103572,a923),f319(f319(f8(f932(x103572,a923),f932(x103572,a923),x103572),f319(f18(x103572,a923,a923),f319(f319(f8(a923,f932(a923,a923),x103572),a317),x103571))),f319(f319(f7(x103572,f932(x103572,x103572),f932(x103572,a923)),f319(f319(f8(f932(x103572,a923),f932(f932(x103572,x103572),f932(x103572,a923)),x103572),f8(x103572,a923,x103572)),a316)),x103573)))))
% 28.73/28.52 [10372]~P1(f319(f319(f227(a925),f319(x103724,f319(x103723,f570(x103721,x103723,x103724,x103722)))),f319(x103724,f570(x103721,x103723,x103724,x103722))))+P38(x103721,f319(f254(f931(x103721,x103721)),f319(f249(x103721,x103721,a923),f319(f319(f8(f932(x103721,a923),f932(x103721,a923),x103721),f319(f18(x103721,a923,a923),f319(f319(f8(a923,f932(a923,a923),x103721),a317),x103722))),f319(f319(f7(x103721,f932(x103721,x103721),f932(x103721,a923)),f319(f319(f8(f932(x103721,a923),f932(f932(x103721,x103721),f932(x103721,a923)),x103721),f8(x103721,a923,x103721)),a316)),x103723)))))
% 28.73/28.52 [10443]~P6(x104431)+E(f32(x104431,f319(f254(x104431),f319(f319(f8(f932(f932(x104432,x104431),a923),a923,x104431),f81(f932(x104432,x104431))),f319(f319(f8(f932(f932(x104432,x104431),a923),f932(f932(x104432,x104431),a923),x104431),f319(f18(f932(x104432,x104431),a923,a923),f319(f319(f8(a923,f932(a923,a923),f932(x104432,x104431)),a317),f319(f319(f7(f932(x104432,x104431),f932(f932(x104432,x104431),a923),a923),f321(f932(x104432,x104431))),x104433)))),f319(f319(f7(x104431,f932(f932(x104432,x104431),x104431),f932(f932(x104432,x104431),a923)),f319(f319(f8(f932(x104431,a923),f932(f932(f932(x104432,x104431),x104431),f932(f932(x104432,x104431),a923)),x104431),f8(x104431,a923,f932(x104432,x104431))),a316)),f319(f319(f7(f932(x104432,x104431),x104432,x104431),f5(f932(x104432,x104431))),x104434)))))),f319(f32(f932(x104432,x104431),x104433),x104434))
% 28.73/28.52 [10444]~P6(x104441)+E(f32(x104441,f319(f254(x104441),f319(f319(f8(f932(f932(x104442,x104441),a923),a923,x104441),f81(f932(x104442,x104441))),f319(f319(f8(f932(f932(x104442,x104441),a923),f932(f932(x104442,x104441),a923),x104441),f319(f18(f932(x104442,x104441),a923,a923),f319(f319(f8(a923,f932(a923,a923),f932(x104442,x104441)),a317),f319(f319(f7(f932(x104442,x104441),f932(f932(x104442,x104441),a923),a923),f321(f932(x104442,x104441))),x104443)))),f319(f319(f7(x104441,f932(f932(x104442,x104441),x104441),f932(f932(x104442,x104441),a923)),f319(f319(f8(f932(x104441,a923),f932(f932(f932(x104442,x104441),x104441),f932(f932(x104442,x104441),a923)),x104441),f8(x104441,a923,f932(x104442,x104441))),a316)),f319(f319(f7(f932(x104442,x104441),x104442,x104441),f5(f932(x104442,x104441))),x104444)))))),f319(f32(f932(x104442,x104441),x104443),x104444))
% 28.73/28.52 [10445]~P6(x104451)+E(f31(x104451,f319(f254(x104451),f319(f319(f8(f932(f932(x104452,x104451),a923),a923,x104451),f81(f932(x104452,x104451))),f319(f319(f8(f932(f932(x104452,x104451),a923),f932(f932(x104452,x104451),a923),x104451),f319(f18(f932(x104452,x104451),a923,a923),f319(f319(f8(a923,f932(a923,a923),f932(x104452,x104451)),a317),f319(f319(f7(f932(x104452,x104451),f932(f932(x104452,x104451),a923),a923),f321(f932(x104452,x104451))),x104453)))),f319(f319(f7(x104451,f932(f932(x104452,x104451),x104451),f932(f932(x104452,x104451),a923)),f319(f319(f8(f932(x104451,a923),f932(f932(f932(x104452,x104451),x104451),f932(f932(x104452,x104451),a923)),x104451),f8(x104451,a923,f932(x104452,x104451))),a316)),f319(f319(f7(f932(x104452,x104451),x104452,x104451),f5(f932(x104452,x104451))),x104454)))))),f319(f31(f932(x104452,x104451),x104453),x104454))
% 28.73/28.52 [10446]~P6(x104461)+E(f31(x104461,f319(f254(x104461),f319(f319(f8(f932(f932(x104462,x104461),a923),a923,x104461),f81(f932(x104462,x104461))),f319(f319(f8(f932(f932(x104462,x104461),a923),f932(f932(x104462,x104461),a923),x104461),f319(f18(f932(x104462,x104461),a923,a923),f319(f319(f8(a923,f932(a923,a923),f932(x104462,x104461)),a317),f319(f319(f7(f932(x104462,x104461),f932(f932(x104462,x104461),a923),a923),f321(f932(x104462,x104461))),x104463)))),f319(f319(f7(x104461,f932(f932(x104462,x104461),x104461),f932(f932(x104462,x104461),a923)),f319(f319(f8(f932(x104461,a923),f932(f932(f932(x104462,x104461),x104461),f932(f932(x104462,x104461),a923)),x104461),f8(x104461,a923,f932(x104462,x104461))),a316)),f319(f319(f7(f932(x104462,x104461),x104462,x104461),f5(f932(x104462,x104461))),x104464)))))),f319(f31(f932(x104462,x104461),x104463),x104464))
% 28.73/28.52 [10498]~P1(f319(f319(f321(f931(x104981,x104981)),f319(f319(f244(x104981,x104981),x104983),x104984)),f319(f319(f102(f932(f931(x104981,x104981),a923)),x104982),f299(x104981,f180(f932(f931(x104981,x104981),a923))))))+P1(f319(f319(f319(f319(f102(f932(x104981,f932(x104981,a923))),f319(f319(f7(x104981,f932(f931(x104981,x104981),a923),f932(x104981,a923)),f319(f319(f8(f932(x104981,f932(f932(f931(x104981,x104981),a923),a923)),f932(f932(f931(x104981,x104981),a923),f932(x104981,a923)),x104981),f7(x104981,f932(f931(x104981,x104981),a923),a923)),f319(f319(f8(f932(x104981,f931(x104981,x104981)),f932(x104981,f932(f932(f931(x104981,x104981),a923),a923)),x104981),f319(f8(f931(x104981,x104981),f932(f932(f931(x104981,x104981),a923),a923),x104981),f321(f931(x104981,x104981)))),f244(x104981,x104981)))),x104982)),a316),x104983),x104984))
% 28.73/28.52 [10509]P1(f319(f319(f321(f931(x105091,x105091)),f319(f319(f244(x105091,x105091),x105092),x105093)),f319(f319(f102(f932(f931(x105091,x105091),a923)),x105094),f299(x105091,f180(f932(f931(x105091,x105091),a923))))))+~P1(f319(f319(f319(f319(f102(f932(x105091,f932(x105091,a923))),f319(f319(f7(x105091,f932(f931(x105091,x105091),a923),f932(x105091,a923)),f319(f319(f8(f932(x105091,f932(f932(f931(x105091,x105091),a923),a923)),f932(f932(f931(x105091,x105091),a923),f932(x105091,a923)),x105091),f7(x105091,f932(f931(x105091,x105091),a923),a923)),f319(f319(f8(f932(x105091,f931(x105091,x105091)),f932(x105091,f932(f932(f931(x105091,x105091),a923),a923)),x105091),f319(f8(f931(x105091,x105091),f932(f932(f931(x105091,x105091),a923),a923),x105091),f321(f931(x105091,x105091)))),f244(x105091,x105091)))),x105094)),a316),x105092),x105093))
% 28.73/28.52 [10454]E(f319(f319(f143(f926(x104541)),f319(f319(f143(x104541),x104542),f319(f134(f926(x104541),f926(x104541),f126(x104541),f105(x104541)),f319(f319(f146(f926(x104541),f926(x104541)),f148(f926(x104541),x104541,f105(x104541),f319(f319(f8(f926(x104541),f932(f926(x104541),f926(x104541)),x104541),f16(f926(x104541),f926(x104541))),f319(f319(f7(x104541,f926(x104541),f926(x104541)),f143(x104541)),f105(x104541))))),x104543)))),f171(x104541,f319(f319(f143(f926(x104541)),x104544),f319(f134(f926(f926(x104541)),f926(f926(x104541)),f126(f926(x104541)),f105(f926(x104541))),f319(f319(f146(f926(x104541),f926(f926(x104541))),f148(f926(f926(x104541)),x104541,f105(f926(x104541)),f319(f16(f932(f926(x104541),f926(f926(x104541))),x104541),f319(f319(f7(f926(x104541),f926(f926(x104541)),f926(f926(x104541))),f143(f926(x104541))),f105(f926(x104541)))))),x104543))))),f171(x104541,f319(f319(f143(f926(x104541)),f319(f319(f143(x104541),x104542),x104544)),x104543)))+~P1(f319(f307(f926(f926(x104541)),f172(x104541)),f319(f319(f143(f926(x104541)),f319(f319(f143(x104541),x104542),x104544)),x104543)))
% 28.73/28.52 [10497]~P1(f319(f55(x104972),f319(f254(x104972),x104974)))+P1(f319(f55(x104971),f319(f254(x104971),f319(f319(f8(f932(x104972,a923),a923,x104971),f81(x104972)),f319(f319(f7(x104971,f932(x104972,a923),f932(x104972,a923)),f319(f319(f8(f932(x104972,f932(a923,a923)),f932(f932(x104972,a923),f932(x104972,a923)),x104971),f18(x104972,a923,a923)),f319(f319(f8(f932(x104972,a923),f932(x104972,f932(a923,a923)),x104971),f319(f8(a923,f932(a923,a923),x104972),a317)),f319(f319(f7(x104971,f932(x104972,x104971),f932(x104972,a923)),f319(f319(f8(f932(x104971,a923),f932(f932(x104972,x104971),f932(x104972,a923)),x104971),f8(x104971,a923,x104972)),a316)),x104973)))),x104974)))))
% 28.73/28.52 [8982]P26(x89821,x89822,x89823,x89824)+~P27(x89821,x89822,x89823,x89824,x89825)
% 28.73/28.52 [8983]P26(x89831,x89832,x89833,x89834)+~P27(x89831,x89832,x89833,x89834,x89835)
% 28.73/28.52 [5475]E(x54751,x54752)+~E(f161(x54753,x54751,x54754),f161(x54753,x54752,x54755))
% 28.73/28.52 [5476]E(x54761,x54762)+~E(f118(x54763,x54764,x54761),f118(x54763,x54765,x54762))
% 28.73/28.52 [5477]E(x54771,x54772)+~E(f118(x54773,x54771,x54774),f118(x54773,x54772,x54775))
% 28.73/28.52 [8304]~E(f319(x83043,x83044),x83045)+E(f68(x83041,x83042,x83043,x83044,x83045),x83043)
% 28.73/28.52 [8305]~E(f319(x83053,x83054),x83055)+E(f68(x83051,x83052,x83053,x83054,x83055),x83053)
% 28.73/28.52 [8841]~E(f68(x88414,x88415,x88411,x88412,x88413),x88411)+E(f319(x88411,x88412),x88413)
% 28.73/28.52 [9466]~P27(x94662,x94661,x94664,x94663,x94665)+P27(x94661,x94662,f71(x94662,x94661,x94663,x94664),x94665,x94663)
% 28.73/28.52 [9467]~P27(x94672,x94671,x94674,x94673,x94675)+P27(x94671,x94672,f85(x94672,x94671,x94673,x94674),x94675,x94673)
% 28.73/28.52 [6280]P1(f319(f242(x62801,x62802,x62803),x62804))+~P1(f319(f319(x62803,x62805),x62804))
% 28.73/28.52 [6281]P1(f319(f242(x62811,x62812,x62813),x62814))+~P1(f319(f319(x62813,x62815),x62814))
% 28.73/28.52 [6282]P1(f319(f241(x62821,x62822,x62823),x62824))+~P1(f319(f319(x62823,x62824),x62825))
% 28.73/28.52 [6283]P1(f319(f241(x62831,x62832,x62833),x62834))+~P1(f319(f319(x62833,x62834),x62835))
% 28.73/28.52 [6757]~E(x67575,f2(a91))+E(f319(f188(x67571,x67572,x67573,x67574),x67575),f116(x67572))
% 28.73/28.52 [6758]~E(x67585,f2(a91))+E(f319(f190(x67581,x67582,x67583,x67584),x67585),f107(x67582))
% 28.73/28.52 [6899]~E(x68993,f2(a91))+E(f319(f265(x68991,x68992,x68993,x68994),x68995),f319(f244(x68991,x68992),x68995))
% 28.73/28.52 [7950]~P22(x79504,x79501,x79502,x79505)+E(f319(f66(x79501,x79501,x79501,f319(x79502,x79503)),f319(x79502,x79503)),f319(x79502,x79503))
% 28.73/28.52 [8345]~P18(x83455,x83451,x83452)+E(f319(f66(x83451,x83451,x83451,f319(x83452,x83453)),f319(x83452,x83454)),f319(f66(x83451,x83451,x83451,f319(x83452,x83454)),f319(x83452,x83453)))
% 28.73/28.52 [8673]P1(f319(f319(f321(f931(x86731,x86731)),f319(f319(f244(x86731,x86731),x86732),x86733)),f313(x86731,x86734,x86735)))+~P1(f319(f319(f227(a925),f319(x86734,x86732)),f319(x86734,x86733)))
% 28.73/28.52 [8768]~P1(f319(f319(f321(x87684),x87683),f291(x87684,x87681,x87682,x87685)))+P1(f319(f319(x87681,x87682),x87683))
% 28.73/28.52 [8769]~P1(f319(f319(f321(x87694),x87693),f282(x87694,x87691,x87692,x87695)))+P1(f319(f319(x87691,x87692),x87693))
% 28.73/28.52 [8770]~P1(f319(f319(f321(x87704),x87702),f291(x87704,x87701,x87705,x87703)))+P1(f319(f319(x87701,x87702),x87703))
% 28.73/28.52 [8771]~P1(f319(f319(f321(x87714),x87712),f282(x87714,x87711,x87715,x87713)))+P1(f319(f319(x87711,x87712),x87713))
% 28.73/28.52 [8853]~P27(x88531,x88533,x88535,x88532,x88534)+E(f319(f29(x88531),x88532),f319(f29(x88533),x88534))
% 28.73/28.52 [8901]~P27(x89011,x89012,x89013,x89014,x89015)+E(f319(f302(x89011,x89012,x89013),x89014),x89015)
% 28.73/28.52 [8921]~P61(x89212,x89211,x89215,x89213,x89214)+E(f319(f302(x89211,x89212,x89213),x89214),f234(f932(x89212,a923)))
% 28.73/28.52 [9374]~P35(x93741,x93742,x93743,x93744,x93745)+P35(x93741,x93742,x93743,f319(f160(x93741),x93744),f319(f160(x93742),x93745))
% 28.73/28.52 [9376]~P35(x93761,x93762,x93763,f319(f160(x93761),x93764),x93765)+P35(x93761,x93762,x93763,x93764,f319(f160(x93762),x93765))
% 28.73/28.52 [9377]~P35(x93771,x93772,x93773,x93774,f319(f160(x93772),x93775))+P35(x93771,x93772,x93773,f319(f160(x93771),x93774),x93775)
% 28.73/28.52 [9383]P35(x93831,x93832,x93833,x93834,x93835)+~P35(x93831,x93832,x93833,f319(f160(x93831),x93834),f319(f160(x93832),x93835))
% 28.73/28.52 [9791]P1(f319(f319(f321(f931(f926(x97911),f926(x97911))),f319(f319(f244(f926(x97911),f926(x97911)),f319(f319(f143(x97911),x97912),x97913)),f319(f319(f143(x97911),x97912),x97914))),f149(x97911,x97915)))+~P1(f319(f319(f321(f931(f926(x97911),f926(x97911))),f319(f319(f244(f926(x97911),f926(x97911)),x97913),x97914)),f149(x97911,x97915)))
% 28.73/28.52 [9792]P1(f319(f319(f321(f931(f926(x97921),f926(x97921))),f319(f319(f244(f926(x97921),f926(x97921)),f319(f319(f126(x97921),x97922),x97923)),f319(f319(f126(x97921),x97922),x97924))),f139(x97921,x97925)))+~P1(f319(f319(f321(f931(f926(x97921),f926(x97921))),f319(f319(f244(f926(x97921),f926(x97921)),x97923),x97924)),f139(x97921,x97925)))
% 28.73/28.52 [10001]E(f319(f319(f143(x100011),f672(x100012,x100013,x100014,x100015,x100011)),f674(x100012,x100013,x100014,x100015,x100011)),x100015)+~P1(f319(f319(f321(f931(f926(x100011),f926(x100011))),f319(f319(f244(f926(x100011),f926(x100011)),x100015),f319(f319(f143(x100011),x100014),x100013))),f150(x100011,x100012)))
% 28.73/28.52 [10024]E(f319(f319(f143(x100241),f675(x100242,x100243,x100244,x100245,x100241)),f676(x100242,x100243,x100244,x100245,x100241)),x100243)+~P1(f319(f319(f321(f931(f926(x100241),f926(x100241))),f319(f319(f244(f926(x100241),f926(x100241)),f319(f319(f143(x100241),x100245),x100244)),x100243)),f150(x100241,x100242)))
% 28.73/28.52 [10174]~P1(f319(f319(f321(f931(f926(x101741),f926(x101741))),f319(f319(f244(f926(x101741),f926(x101741)),f319(f319(f143(x101741),x101745),x101742)),x101744)),f150(x101741,x101743)))+P1(f319(f319(f321(f931(f926(x101741),f926(x101741))),f319(f319(f244(f926(x101741),f926(x101741)),x101742),f676(x101743,x101744,x101742,x101745,x101741))),f150(x101741,x101743)))
% 28.73/28.52 [10257]~P1(f319(f319(f321(f931(f926(x102571),f926(x102571))),f319(f319(f244(f926(x102571),f926(x102571)),x102575),f319(f319(f143(x102571),x102574),x102573))),f150(x102571,x102572)))+P1(f319(f319(f321(f931(f926(x102571),f926(x102571))),f319(f319(f244(f926(x102571),f926(x102571)),f674(x102572,x102573,x102574,x102575,x102571)),x102573)),f150(x102571,x102572)))
% 28.73/28.52 [10448]P1(f319(f319(f321(f931(x104481,x104481)),f319(f319(f244(x104481,x104481),f319(x104482,f319(f319(f74(a925),x104483),x104484))),f319(x104482,x104483))),f299(x104481,x104485)))+~P1(f319(f319(f321(f931(x104481,x104481)),f319(f319(f244(x104481,x104481),f319(x104482,f319(a104,f624(x104484,x104483,x104485,x104482,x104481)))),f319(x104482,f624(x104484,x104483,x104485,x104482,x104481)))),f299(x104481,x104485)))
% 28.73/28.52 [5449]E(x54491,x54492)+~E(f319(f319(f143(x54493),x54494),x54491),f319(f319(f143(x54493),x54495),x54492))
% 28.73/28.52 [5450]E(x54501,x54502)+~E(f319(f319(f143(x54503),x54501),x54504),f319(f319(f143(x54503),x54502),x54505))
% 28.73/28.52 [5492]P1(f319(x54921,x54922))+~E(f319(f128(x54923,x54921),x54924),f319(f319(f143(x54923),x54922),x54925))
% 28.73/28.52 [5493]P1(f319(x54931,x54932))+~E(f319(f319(f143(x54933),x54932),x54934),f319(f128(x54933,x54931),x54935))
% 28.73/28.52 [5650]~E(f319(f319(f130(x56501),x56503),x56502),f319(f319(f143(x56501),x56504),x56505))+E(f319(f319(f156(x56501),x56502),x56503),x56504)
% 28.73/28.52 [5788]~P16(x57884,x57885,x57881)+E(f319(f319(x57881,x57882),f319(f319(x57881,x57882),x57883)),f319(f319(x57881,x57882),x57883))
% 28.73/28.52 [6339]~E(x63394,f2(a91))+E(f319(f319(f109(x63391,x63392,x63393),x63394),x63395),f319(f319(f244(f926(x63392),x63391),f105(x63392)),x63395))
% 28.73/28.52 [6408]~P4(x64082)+~E(f319(f319(f140(x64081,x64082,x64083),x64084),x64085),f105(x64081))
% 28.73/28.52 [6796]E(x67961,x67962)+~E(f319(f319(f126(x67963),x67964),f319(f319(f143(x67963),x67961),f105(x67963))),f319(f319(f126(x67963),x67965),f319(f319(f143(x67963),x67962),f105(x67963))))
% 28.73/28.52 [6797]E(x67971,x67972)+~E(f319(f319(f126(x67973),x67971),f319(f319(f143(x67973),x67974),f105(x67973))),f319(f319(f126(x67973),x67972),f319(f319(f143(x67973),x67975),f105(x67973))))
% 28.73/28.52 [7120]E(f319(f319(f301(x71201),f319(x71202,x71203)),f319(f302(x71204,x71201,x71202),x71205)),f319(f302(x71204,x71201,x71202),x71205))+~P1(f319(f319(f321(x71204),x71203),x71205))
% 28.73/28.52 [7126]~P1(f319(x71264,f319(x71263,x71265)))+P1(f319(f319(f303(x71261,x71262,x71263),x71264),x71265))
% 28.73/28.52 [7127]~P1(f319(f319(x71273,x71275),x71274))+P1(f319(f319(f235(x71271,x71272,x71273),x71274),x71275))
% 28.73/28.52 [7128]~P1(f319(f319(x71283,x71285),x71284))+P1(f319(f319(f235(x71281,x71282,x71283),x71284),x71285))
% 28.73/28.52 [7129]~P1(f319(f319(x71293,x71295),x71294))+P1(f319(f319(f235(x71291,x71292,x71293),x71294),x71295))
% 28.73/28.52 [7224]~E(f319(f302(x72241,x72242,x72243),x72244),x72245)+E(f319(f302(f932(x72241,a923),f932(x72242,a923),f302(x72241,x72242,x72243)),f319(f300(x72241),x72244)),f319(f300(x72242),x72245))
% 28.73/28.52 [7251]E(f319(f263(x72511,x72512,x72513,x72514),x72515),f319(x72514,x72515))+~P1(f319(f319(f321(x72511),x72515),x72513))
% 28.73/28.52 [7565]P26(x75651,x75652,x75653,x75654)+~P26(x75651,x75652,x75653,f319(f319(f301(x75651),x75655),x75654))
% 28.73/28.52 [7669]~P1(f319(f319(f321(x76694),x76693),x76695))+P1(f319(f319(f321(x76691),f319(x76692,x76693)),f319(f302(x76694,x76691,x76692),x76695)))
% 28.73/28.52 [7690]~P4(x76902)+E(f142(x76901,x76902,x76903,f319(f128(x76901,x76904),x76905)),f319(f128(x76901,x76904),f142(x76901,x76902,x76903,x76905)))
% 28.73/28.52 [7720]P1(f319(x77201,f319(x77202,x77203)))+~P1(f319(f319(f303(x77204,x77205,x77202),x77201),x77203))
% 28.73/28.52 [7721]P1(f319(f319(x77211,x77212),x77213))+~P1(f319(f319(f235(x77214,x77215,x77211),x77213),x77212))
% 28.73/28.52 [7722]P1(f319(f319(x77221,x77222),x77223))+~P1(f319(f319(f235(x77224,x77225,x77221),x77223),x77222))
% 28.73/28.52 [7723]P1(f319(f319(x77231,x77232),x77233))+~P1(f319(f319(f235(x77234,x77235,x77231),x77233),x77232))
% 28.73/28.52 [7785]~P1(f319(f319(f321(x77853),f319(x77854,x77852)),x77855))+P1(f319(f319(f321(x77851),x77852),f319(f303(x77851,x77853,x77854),x77855)))
% 28.73/28.52 [7786]~P1(f319(f319(f321(x77863),f319(x77864,x77862)),x77865))+P1(f319(f319(f321(x77861),x77862),f319(f303(x77861,x77863,x77864),x77865)))
% 28.73/28.52 [8184]~P1(f319(f319(f321(x81845),x81843),f319(f303(x81845,x81841,x81842),x81844)))+P1(f319(f319(f321(x81841),f319(x81842,x81843)),x81844))
% 28.73/28.52 [8185]~P1(f319(f319(f321(x81855),x81853),f319(f303(x81855,x81851,x81852),x81854)))+P1(f319(f319(f321(x81851),f319(x81852,x81853)),x81854))
% 28.73/28.52 [8485]~P18(x84852,x84851,x84853)+E(f319(f134(x84851,x84852,f319(f7(x84852,x84851,x84851),x84853),x84854),f144(x84852,x84855)),f319(f319(f58(x84852,x84851,x84853),x84854),f319(f164(x84852),x84855)))
% 28.73/28.52 [8507]E(f319(x85071,f760(x85072,x85071,x85073,x85074)),x85074)+~P1(f319(f319(f321(x85075),x85074),f319(f302(x85073,x85075,x85071),x85072)))
% 28.73/28.52 [8508]E(f319(x85081,f813(x85082,x85081,x85083,x85084)),x85084)+~P1(f319(f319(f321(x85085),x85084),f319(f302(x85083,x85085,x85081),x85082)))
% 28.73/28.52 [8816]~E(x88162,f319(f319(f143(x88161),x88164),x88165))+P1(f319(f319(f321(f931(f926(x88161),f926(x88161))),f319(f319(f244(f926(x88161),f926(x88161)),f105(x88161)),x88162)),f139(x88161,x88163)))
% 28.73/28.52 [8862]E(f319(x88621,f319(f85(x88622,x88623,x88624,x88621),x88625)),x88625)+~P1(f319(f319(f321(x88623),x88625),f319(f302(x88622,x88623,x88621),x88624)))
% 28.73/28.52 [8865]P26(x88651,x88652,f85(x88652,x88651,x88653,x88654),x88655)+~P1(f319(f319(f226(f932(x88651,a923)),x88655),f319(f302(x88652,x88651,x88654),x88653)))
% 28.73/28.52 [8870]~P35(x88701,x88703,x88705,x88702,x88704)+E(f319(f181(f926(x88701)),x88702),f319(f181(f926(x88703)),x88704))
% 28.73/28.52 [8871]~P35(x88711,x88713,x88715,x88712,x88714)+E(f319(f181(f926(x88711)),x88712),f319(f181(f926(x88713)),x88714))
% 28.73/28.52 [8872]~P35(x88721,x88723,x88725,x88722,x88724)+E(f319(f181(f926(x88721)),x88722),f319(f181(f926(x88723)),x88724))
% 28.73/28.52 [8883]P1(f319(f319(f226(f932(x88831,a923)),f319(f319(f34(x88832,f932(x88831,a923)),x88833),x88834)),f319(x88834,x88835)))+~P1(f319(f319(f321(x88832),x88835),x88833))
% 28.73/28.52 [8937]~P61(x89371,x89372,x89373,x89375,x89374)+E(f319(f302(x89371,x89372,x89373),f234(f932(x89371,a923))),x89374)
% 28.73/28.52 [9166]E(f319(f128(x91661,x91662),f763(x91663,x91664,x91665,x91662,x91661)),x91663)+~E(f319(f128(x91661,x91662),x91665),f319(f319(f143(x91661),x91664),x91663))
% 28.73/28.52 [9167]E(f319(f128(x91671,x91672),f764(x91673,x91672,x91674,x91675,x91671)),x91674)+~E(f319(f319(f143(x91671),x91675),x91674),f319(f128(x91671,x91672),x91673))
% 28.73/28.52 [9262]E(f319(f181(f926(x92621)),x92622),x92623)+~P1(f319(f319(f321(f931(f926(x92621),f926(x92621))),f319(f319(f244(f926(x92621),f926(x92621)),x92624),x92622)),f319(f135(x92621,x92625),x92623)))
% 28.73/28.52 [9263]E(f319(f181(f926(x92631)),x92632),x92633)+~P1(f319(f319(f321(f931(f926(x92631),f926(x92631))),f319(f319(f244(f926(x92631),f926(x92631)),x92632),x92634)),f319(f135(x92631,x92635),x92633)))
% 28.73/28.52 [9332]P1(f319(f319(f321(x93321),f760(x93322,x93323,x93321,x93324)),x93322))+~P1(f319(f319(f321(x93325),x93324),f319(f302(x93321,x93325,x93323),x93322)))
% 28.73/28.52 [9333]P1(f319(f319(f321(x93331),f813(x93332,x93333,x93331,x93334)),x93332))+~P1(f319(f319(f321(x93335),x93334),f319(f302(x93331,x93335,x93333),x93332)))
% 28.73/28.52 [9492]~P41(f932(x94923,a923),f932(x94921,a923),x94922)+P1(f319(f319(f226(f932(x94921,a923)),f319(x94922,f319(f319(f93(f932(x94923,a923)),x94924),x94925))),f319(f319(f93(f932(x94921,a923)),f319(x94922,x94924)),f319(x94922,x94925))))
% 28.73/28.52 [9494]E(f319(f302(x94941,x94942,x94943),f770(x94944,x94943,x94941,x94945,x94942)),x94945)+~P1(f319(f319(f226(f932(x94942,a923)),x94945),f319(f302(x94941,x94942,x94943),x94944)))
% 28.73/28.52 [9809]P1(f319(f319(f321(f931(f926(x98091),f926(x98091))),f319(f319(f244(f926(x98091),f926(x98091)),f319(f319(f143(x98091),x98092),x98093)),f319(f319(f143(x98091),x98092),x98094))),f299(f926(x98091),f149(x98091,x98095))))+~P1(f319(f319(f321(f931(f926(x98091),f926(x98091))),f319(f319(f244(f926(x98091),f926(x98091)),x98093),x98094)),f299(f926(x98091),f149(x98091,x98095))))
% 28.73/28.52 [9840]~E(f319(x98403,f715(x98405,x98404,x98403,x98402,x98401)),f319(x98405,f715(x98405,x98404,x98403,x98402,x98401)))+E(f319(f319(f146(x98401,x98402),x98403),x98404),f319(f319(f146(x98401,x98402),x98405),x98404))
% 28.73/28.52 [9918]~E(f319(f128(x99181,x99185),x99184),f319(f319(f143(x99181),x99183),x99182))+E(f319(f319(f126(x99181),f767(x99182,x99183,x99184,x99185,x99181)),f319(f319(f143(x99181),x99183),f763(x99182,x99183,x99184,x99185,x99181))),x99184)
% 28.73/28.52 [9919]~E(f319(f319(f143(x99191),x99195),x99194),f319(f128(x99191,x99193),x99192))+E(f319(f319(f126(x99191),f765(x99192,x99193,x99194,x99195,x99191)),f319(f319(f143(x99191),x99195),f764(x99192,x99193,x99194,x99195,x99191))),x99192)
% 28.73/28.52 [9923]E(f319(f319(f146(x99231,x99232),x99233),x99234),f319(f319(f146(x99231,x99232),x99235),x99234))+P1(f319(f319(f321(x99231),f715(x99233,x99234,x99235,x99232,x99231)),f319(f164(x99231),x99234)))
% 28.73/28.52 [9959]~P1(f319(f319(f321(x99595),x99594),f319(f277(x99591,x99595,x99593),x99592)))+P1(f319(f319(f321(x99591),f530(x99592,x99593,x99591,x99594,x99595)),x99592))
% 28.73/28.52 [9960]~P1(f319(f319(f321(x99605),x99604),f319(f277(x99601,x99605,x99603),x99602)))+P1(f319(f319(f321(x99601),f556(x99602,x99603,x99601,x99604,x99605)),x99602))
% 28.73/28.52 [9995]~P1(f319(f319(f226(f932(x99955,a923)),x99954),f319(f302(x99951,x99955,x99953),x99952)))+P1(f319(f319(f226(f932(x99951,a923)),f770(x99952,x99953,x99951,x99954,x99955)),x99952))
% 28.73/28.52 [10449]E(x104491,f2(a91))+E(f215(f931(f926(x104492),x104493),f931(x104492,x104493),f319(f319(f244(f926(x104492),x104493),f105(x104492)),x104494),f319(f249(x104492,x104493,f931(f926(x104492),x104493)),f319(f319(f7(x104492,f932(x104493,f931(f926(x104492),x104493)),f932(x104493,f931(f926(x104492),x104493))),f319(f319(f8(f932(f931(f926(x104492),x104493),f931(f926(x104492),x104493)),f932(f932(x104493,f931(f926(x104492),x104493)),f932(x104493,f931(f926(x104492),x104493))),x104492),f8(f931(f926(x104492),x104493),f931(f926(x104492),x104493),x104493)),f319(f319(f8(f932(f926(x104492),f932(x104493,f931(f926(x104492),x104493))),f932(f931(f926(x104492),x104493),f931(f926(x104492),x104493)),x104492),f249(f926(x104492),x104493,f931(f926(x104492),x104493))),f319(f319(f8(f932(f926(x104492),f926(x104492)),f932(f926(x104492),f932(x104493,f931(f926(x104492),x104493))),x104492),f319(f8(f926(x104492),f932(x104493,f931(f926(x104492),x104493)),f926(x104492)),f244(f926(x104492),x104493))),f143(x104492))))),f319(f109(x104493,x104492,x104495),f319(f319(f23(a91),x104491),f72(a91))))),f319(x104495,x104494)),f319(f319(f109(x104493,x104492,x104495),x104491),x104494))
% 28.73/28.52 [6222]E(x62221,x62222)+~E(f319(f248(x62223,x62224),f319(f319(f244(x62223,x62224),x62225),x62221)),x62222)
% 28.73/28.52 [6223]E(x62231,x62232)+~E(f319(f243(x62233,x62234),f319(f319(f244(x62233,x62234),x62231),x62235)),x62232)
% 28.73/28.52 [6482]~E(x64823,f319(f319(f126(x64821),x64824),f319(f319(f143(x64821),x64822),x64825)))+P1(f319(f319(f321(x64821),x64822),f319(f164(x64821),x64823)))
% 28.73/28.52 [6885]E(f319(f302(x68851,x68852,f319(f16(x68852,x68851),x68853)),x68854),f319(f319(f301(x68852),x68853),f180(f932(x68852,a923))))+~P1(f319(f319(f321(x68851),x68855),x68854))
% 28.73/28.52 [6959]E(f319(f319(f102(f932(x69591,a923)),f319(f164(x69591),x69592)),f319(f164(x69591),x69593)),f319(f164(x69591),x69594))+~E(f158(x69591,x69595,x69594),f319(f319(f244(f926(x69591),f926(x69591)),x69592),x69593))
% 28.73/28.52 [7058]~P4(x70582)+E(f319(f181(f926(x70581)),f319(f319(f140(x70581,x70582,x70583),x70584),x70585)),f319(a104,f319(f181(f926(x70581)),x70585)))
% 28.73/28.52 [7074]~P4(x70742)+E(f319(f164(x70741),f319(f319(f140(x70741,x70742,x70743),x70744),x70745)),f319(f319(f301(x70741),x70744),f319(f164(x70741),x70745)))
% 28.73/28.52 [7346]~P121(x73461)+E(f319(f319(f75(x73461),f319(f319(f75(x73461),x73462),x73463)),f319(f319(f75(x73461),x73464),x73465)),f319(f319(f75(x73461),f319(f319(f75(x73461),x73462),x73464)),f319(f319(f75(x73461),x73463),x73465)))
% 28.73/28.52 [7347]~P121(x73471)+E(f319(f319(f74(x73471),f319(f319(f74(x73471),x73472),x73473)),f319(f319(f74(x73471),x73474),x73475)),f319(f319(f74(x73471),f319(f319(f74(x73471),x73472),x73474)),f319(f319(f74(x73471),x73473),x73475)))
% 28.73/28.52 [7348]~P72(x73481)+E(f319(f319(f283(x73481),f319(f319(f75(x73481),x73482),x73483)),f319(f319(f75(x73481),x73484),x73485)),f319(f319(f75(x73481),f319(f319(f283(x73481),x73482),x73484)),f319(f319(f283(x73481),x73483),x73485)))
% 28.73/28.52 [7362]~P4(x73621)+E(f295(x73621,f319(f319(f225(x73621),x73622),x73623),f319(f319(f224(x73621),x73624),x73625)),f319(f319(f93(f932(x73621,a923)),f295(x73621,x73622,x73624)),f295(x73621,x73623,x73625)))
% 28.73/28.52 [7363]~P4(x73631)+E(f297(x73631,f319(f319(f225(x73631),x73632),x73633),f319(f319(f224(x73631),x73634),x73635)),f319(f319(f93(f932(x73631,a923)),f297(x73631,x73632,x73634)),f297(x73631,x73633,x73635)))
% 28.73/28.52 [7364]~P4(x73641)+E(f298(x73641,f319(f319(f225(x73641),x73642),x73643),f319(f319(f224(x73641),x73644),x73645)),f319(f319(f93(f932(x73641,a923)),f298(x73641,x73642,x73644)),f298(x73641,x73643,x73645)))
% 28.73/28.52 [7365]~P4(x73651)+E(f319(f319(f93(f932(x73651,a923)),f319(f294(x73651,x73652),x73653)),f319(f294(x73651,x73654),x73655)),f319(f294(x73651,f319(f319(f225(x73651),x73652),x73654)),f319(f319(f224(x73651),x73653),x73655)))
% 28.73/28.52 [7487]~P1(f319(x74871,f529(x74873,x74872,x74871)))+P1(f319(x74871,f319(f319(f244(x74872,x74873),x74874),x74875)))
% 28.73/28.52 [7595]~E(x75952,f319(x75954,x75955))+P1(f319(f319(f321(x75951),x75952),f319(f302(x75953,x75951,x75954),f234(f932(x75953,a923)))))
% 28.73/28.52 [7666]~P16(x76663,x76662,x76664)+P16(x76661,x76662,f319(f319(f8(x76663,f932(x76662,x76662),x76661),x76664),x76665))
% 28.73/28.52 [7667]~P18(x76673,x76672,x76674)+P18(x76671,x76672,f319(f319(f8(x76673,f932(x76672,x76672),x76671),x76674),x76675))
% 28.73/28.52 [7803]~P26(x78031,x78032,x78033,x78034)+P26(x78031,x78032,x78033,f319(f319(f23(f932(x78031,a923)),x78034),x78035))
% 28.73/28.52 [7958]~P1(f319(f319(x79583,x79584),x79585))+P1(f319(f319(f249(x79581,x79582,a923),x79583),f319(f319(f244(x79581,x79582),x79584),x79585)))
% 28.73/28.52 [7959]~P1(f319(f319(x79593,x79594),x79595))+P1(f319(f319(f249(x79591,x79592,a923),x79593),f319(f319(f244(x79591,x79592),x79594),x79595)))
% 28.73/28.52 [8073]~P1(f319(x80732,x80734))+~E(f319(f319(f130(x80731),f319(f181(f926(x80731)),f169(x80731,x80732,x80733))),x80733),f319(f319(f143(x80731),x80734),x80735))
% 28.73/28.52 [8093]P26(x80931,x80932,x80933,x80934)+~P26(x80931,x80932,x80933,f319(f319(f102(f932(x80931,a923)),x80935),x80934))
% 28.73/28.52 [8094]P26(x80941,x80942,x80943,x80944)+~P26(x80941,x80942,x80943,f319(f319(f102(f932(x80941,a923)),x80944),x80945))
% 28.73/28.52 [8141]~P4(x81412)+E(f319(f319(f140(x81411,x81412,x81413),x81414),f142(x81411,x81412,x81413,x81415)),f142(x81411,x81412,x81413,f319(f319(f143(x81411),x81414),x81415)))
% 28.73/28.52 [8461]~P16(x84612,x84611,x84613)+E(f319(f134(x84611,x84612,f319(f7(x84612,x84611,x84611),x84613),x84614),x84615),f319(f319(f58(x84612,x84611,x84613),x84614),f319(f164(x84612),x84615)))
% 28.73/28.52 [8490]~E(f319(f319(f130(x84901),f319(f181(f926(x84901)),f169(x84901,x84902,x84903))),x84903),f319(f319(f143(x84901),x84904),x84905))+E(f319(f319(f126(x84901),f169(x84901,x84902,x84903)),f319(f319(f143(x84901),x84904),x84905)),x84903)
% 28.73/28.52 [8518]P1(f319(f319(x85181,x85182),x85183))+~P1(f319(f319(f249(x85184,x85185,a923),x85181),f319(f319(f244(x85184,x85185),x85182),x85183)))
% 28.73/28.52 [9001]P1(f319(f319(f226(f932(x90011,a923)),f319(f302(x90012,x90011,x90013),x90014)),f319(f302(x90012,x90011,x90013),x90015)))+~P1(f319(f319(f226(f932(x90012,a923)),x90014),x90015))
% 28.73/28.52 [9002]P1(f319(f319(f226(f932(x90021,a923)),f319(f303(x90021,x90022,x90023),x90024)),f319(f303(x90021,x90022,x90023),x90025)))+~P1(f319(f319(f226(f932(x90022,a923)),x90024),x90025))
% 28.73/28.52 [9081]E(x90811,f2(a91))+E(f319(f319(f251(x90812,x90813,x90812,f931(x90813,x90812)),f319(x90814,x90815)),f265(x90813,x90812,f319(f319(f23(a91),x90811),f72(a91)),x90814)),f319(f265(x90813,x90812,x90811,x90814),x90815))
% 28.73/28.52 [9193]P1(f319(f319(f247(x91931,x91932,a923,x91933),x91934),x91935))+~P1(f319(x91933,f319(f319(f244(x91931,x91932),x91934),x91935)))
% 28.73/28.52 [9471]~P1(f319(f319(f247(x94712,x94713,a923,x94711),x94714),x94715))+P1(f319(x94711,f319(f319(f244(x94712,x94713),x94714),x94715)))
% 28.73/28.52 [9472]~P1(f319(f319(f247(x94722,x94723,a923,x94721),x94724),x94725))+P1(f319(x94721,f319(f319(f244(x94722,x94723),x94724),x94725)))
% 28.73/28.52 [9658]~P1(f319(f319(f321(x96582),x96585),f319(f302(x96581,x96582,x96584),x96583)))+P1(f319(f319(f321(x96581),f319(f85(x96581,x96582,x96583,x96584),x96585)),x96583))
% 28.73/28.52 [9749]~P1(f319(f55(x97493),f319(f302(x97492,x97493,x97495),f234(f932(x97492,a923)))))+P1(f319(f55(x97491),f319(f302(x97492,x97491,f319(f319(f8(x97493,x97491,x97492),x97494),x97495)),f234(f932(x97492,a923)))))
% 28.73/28.52 [9776]P1(f319(f319(f226(f932(f932(x97761,a923),a923)),f319(f302(f932(x97762,a923),f932(x97761,a923),f302(x97762,x97761,x97763)),f319(f300(x97762),x97764))),f319(f300(x97761),x97765)))+~P1(f319(f319(f226(f932(x97761,a923)),f319(f302(x97762,x97761,x97763),x97764)),x97765))
% 28.73/28.52 [9848]E(x98481,x98482)+~P1(f319(f60(x98483,x98484,x98485,x98481,f180(f932(x98483,a923))),x98482))
% 28.73/28.52 [9865]E(f319(f319(f244(x98651,x98652),f584(x98653,x98654,x98655,x98652,x98651)),f585(x98653,x98654,x98655,x98652,x98651)),x98655)+~P1(f319(f319(f321(f931(x98651,x98652)),x98655),f319(f319(f246(x98651,x98652),x98654),x98653)))
% 28.73/28.52 [9965]P1(f319(f319(f321(x99651),f584(x99652,x99653,x99654,x99655,x99651)),x99653))+~P1(f319(f319(f321(f931(x99651,x99655)),x99654),f319(f319(f246(x99651,x99655),x99653),x99652)))
% 28.73/28.52 [9977]P1(f319(f319(f321(x99771),f824(x99772,x99773,x99774,x99775,x99771)),x99775))+P1(f319(f319(f226(f932(x99774,a923)),f319(f302(x99771,x99774,x99773),x99775)),x99772))
% 28.73/28.52 [10133]P1(f319(f319(f321(x101331),f585(x101332,x101333,x101334,x101331,x101335)),f319(x101332,f584(x101332,x101333,x101334,x101331,x101335))))+~P1(f319(f319(f321(f931(x101335,x101331)),x101334),f319(f319(f246(x101335,x101331),x101333),x101332)))
% 28.73/28.52 [10153]P1(f319(f319(f321(f931(x101531,x101531)),f319(f319(f244(x101531,x101531),x101532),f645(x101533,x101534,x101535,x101532,x101531))),x101533))+~P1(f319(f319(f321(f931(x101531,x101531)),f319(f319(f244(x101531,x101531),x101532),x101535)),f319(f319(f175(f931(x101531,x101531),a923),f319(a104,x101534)),x101533)))
% 28.73/28.52 [10154]P1(f319(f319(f321(f931(x101541,x101541)),f319(f319(f244(x101541,x101541),x101542),f647(x101543,x101544,x101545,x101542,x101541))),x101543))+~P1(f319(f319(f321(f931(x101541,x101541)),f319(f319(f244(x101541,x101541),x101542),x101545)),f319(f319(f175(f931(x101541,x101541),a923),f319(a104,x101544)),x101543)))
% 28.73/28.52 [10171]~P1(f319(f319(f321(f931(f926(x101711),f926(x101711))),f319(f319(f244(f926(x101711),f926(x101711)),f319(f319(f143(x101711),x101712),x101715)),x101714)),f150(x101711,x101713)))+P1(f319(f319(f321(f931(x101711,x101711)),f319(f319(f244(x101711,x101711),x101712),f675(x101713,x101714,x101715,x101712,x101711))),x101713))
% 28.73/28.52 [10194]~P1(f319(f319(f321(x101941),f319(x101943,f824(x101945,x101943,x101941,x101944,x101942))),x101945))+P1(f319(f319(f226(f932(x101941,a923)),f319(f302(x101942,x101941,x101943),x101944)),x101945))
% 28.73/28.52 [6560]P1(f319(x65602,x65604))+E(f169(x65601,x65602,f319(f319(f126(x65601),x65603),f319(f319(f143(x65601),x65604),x65605))),f169(x65601,x65602,x65603))
% 28.73/28.52 [6610]~P102(x66102)+E(f319(f319(f319(f102(f932(x66101,x66102)),x66103),x66104),x66105),f319(f319(f102(x66102),f319(x66103,x66105)),f319(x66104,x66105)))
% 28.73/28.52 [6611]~P102(x66112)+E(f319(f319(f319(f102(f932(x66111,x66112)),x66113),x66114),x66115),f319(f319(f102(x66112),f319(x66113,x66115)),f319(x66114,x66115)))
% 28.73/28.52 [6612]~P102(x66122)+E(f319(f319(f319(f93(f932(x66121,x66122)),x66123),x66124),x66125),f319(f319(f93(x66122),f319(x66123,x66125)),f319(x66124,x66125)))
% 28.73/28.52 [6613]~P102(x66132)+E(f319(f319(f319(f93(f932(x66131,x66132)),x66133),x66134),x66135),f319(f319(f93(x66132),f319(x66133,x66135)),f319(x66134,x66135)))
% 28.73/28.52 [6614]~P83(x66142)+E(f319(f319(f319(f23(f932(x66141,x66142)),x66143),x66144),x66145),f319(f319(f23(x66142),f319(x66143,x66145)),f319(x66144,x66145)))
% 28.73/28.52 [6615]~P83(x66152)+E(f319(f319(f319(f23(f932(x66151,x66152)),x66153),x66154),x66155),f319(f319(f23(x66152),f319(x66153,x66155)),f319(x66154,x66155)))
% 28.73/28.52 [6632]E(x66321,x66322)+E(f319(f319(f156(x66323),f319(f319(f151(x66323,x66324),x66321),x66325)),x66322),f319(f319(f156(x66323),x66324),x66322))
% 28.73/28.52 [6905]~E(x69054,f180(f932(x69053,a923)))+E(f319(f319(f102(f932(x69051,a923)),x69052),f319(f319(f33(x69053,f932(x69051,a923)),x69054),x69055)),x69052)
% 28.73/28.52 [6906]~E(x69064,f180(f932(x69063,a923)))+E(f319(f319(f93(f932(x69061,a923)),x69062),f319(f319(f34(x69063,f932(x69061,a923)),x69064),x69065)),x69062)
% 28.73/28.52 [6907]~E(x69074,f180(f932(x69073,a923)))+E(f319(f319(f23(f932(x69071,a923)),x69072),f319(f319(f33(x69073,f932(x69071,a923)),x69074),x69075)),x69072)
% 28.73/28.52 [6924]~E(x69244,f180(f932(x69243,a923)))+E(f319(f319(f301(x69241),x69242),f319(f319(f33(x69243,f932(x69241,a923)),x69244),x69245)),f319(f319(f301(x69241),x69242),f180(f932(x69241,a923))))
% 28.73/28.52 [7345]~P121(x73451)+E(f319(f319(f75(x73451),f319(f319(f75(x73451),x73452),x73453)),f319(f319(f75(x73451),x73454),x73455)),f319(f319(f75(x73451),x73452),f319(f319(f75(x73451),x73453),f319(f319(f75(x73451),x73454),x73455))))
% 28.73/28.52 [7712]E(f319(f319(f156(x77121),f319(f319(f146(x77122,x77121),x77123),x77124)),x77125),f319(x77123,f319(f319(f156(x77122),x77124),x77125)))+~P1(f319(f319(f227(a925),x77125),f319(f181(f926(x77122)),x77124)))
% 28.73/28.52 [7774]E(f319(f319(f102(f932(x77741,a923)),f319(x77742,x77743)),f319(f319(f33(x77744,f932(x77741,a923)),x77745),x77742)),f319(f319(f33(x77744,f932(x77741,a923)),x77745),x77742))+~P1(f319(f319(f321(x77744),x77743),x77745))
% 28.73/28.52 [7775]E(f319(f319(f93(f932(x77751,a923)),f319(x77752,x77753)),f319(f319(f34(x77754,f932(x77751,a923)),x77755),x77752)),f319(f319(f34(x77754,f932(x77751,a923)),x77755),x77752))+~P1(f319(f319(f321(x77754),x77753),x77755))
% 28.73/28.52 [8383]~E(x83833,f180(f932(x83831,a923)))+E(f319(f319(f33(x83831,f932(x83832,a923)),x83833),f319(f319(f8(f932(x83832,a923),f932(x83832,a923),x83831),f319(f301(x83832),x83834)),x83835)),f180(f932(x83832,a923)))
% 28.73/28.52 [8388]~P1(f319(f319(f321(x83884),x83883),x83885))+P1(f319(f319(f226(f932(x83881,a923)),f319(x83882,x83883)),f319(f319(f33(x83884,f932(x83881,a923)),x83885),x83882)))
% 28.73/28.52 [8517]~E(f319(x85174,x85172),x85175)+P1(f319(f319(f321(x85171),x85172),f319(f303(x85171,x85173,x85174),f319(f319(f301(x85173),x85175),f180(f932(x85173,a923))))))
% 28.73/28.52 [8565]~P59(x85651,x85652,f319(f278(x85652,x85651),x85653))+E(f319(f319(f93(f932(x85651,a923)),f319(f277(x85652,x85651,x85653),x85654)),f319(f277(x85652,x85651,x85653),x85655)),f319(f277(x85652,x85651,x85653),f319(f319(f93(f932(x85652,a923)),x85654),x85655)))
% 28.73/28.52 [8640]E(x86401,f2(a91))+E(f319(f110(x86402,x86403,f319(x86404,f319(f319(f23(a91),x86401),f72(a91)))),f319(f319(f7(x86402,a91,f927(x86403)),x86405),x86401)),f319(f190(x86402,x86403,x86404,x86405),x86401))
% 28.73/28.52 [8679]E(x86791,f180(f932(x86792,a923)))+E(f319(f319(f33(x86792,f932(x86793,a923)),x86791),f319(f319(f8(f932(x86793,a923),f932(x86793,a923),x86792),f319(f301(x86793),x86794)),x86795)),f319(f319(f301(x86793),x86794),f319(f319(f33(x86792,f932(x86793,a923)),x86791),x86795)))
% 28.73/28.52 [8680]E(x86801,f180(f932(x86802,a923)))+E(f319(f319(f33(x86802,f932(x86803,a923)),x86801),f319(f319(f8(f932(x86803,a923),f932(x86803,a923),x86802),f319(f301(x86803),x86804)),x86805)),f319(f319(f301(x86803),x86804),f319(f319(f33(x86802,f932(x86803,a923)),x86801),x86805)))
% 28.73/28.52 [8733]~P26(x87332,x87331,x87333,f234(f932(x87332,a923)))+E(f319(f319(f93(f932(x87331,a923)),f319(f302(x87332,x87331,x87333),x87334)),f319(f302(x87332,x87331,x87333),x87335)),f319(f302(x87332,x87331,x87333),f319(f319(f93(f932(x87332,a923)),x87334),x87335)))
% 28.73/28.52 [8734]~P26(x87342,x87341,x87343,f234(f932(x87342,a923)))+E(f319(f319(f23(f932(x87341,a923)),f319(f302(x87342,x87341,x87343),x87344)),f319(f302(x87342,x87341,x87343),x87345)),f319(f302(x87342,x87341,x87343),f319(f319(f23(f932(x87342,a923)),x87344),x87345)))
% 28.73/28.52 [8803]~P1(f319(f319(f61(x88031,x88032,x88035),x88033),x88034))+P1(f319(f319(f321(f931(x88031,x88032)),f319(f319(f244(x88031,x88032),x88033),x88034)),x88035))
% 28.73/28.52 [8834]P1(f319(f319(f321(x88341),x88342),f319(f276(x88343,x88341),x88344)))+~P1(f319(f319(f321(f931(x88343,x88341)),f319(f319(f244(x88343,x88341),x88345),x88342)),x88344))
% 28.73/28.52 [8835]P1(f319(f319(f321(x88351),x88352),f319(f276(x88353,x88351),x88354)))+~P1(f319(f319(f321(f931(x88353,x88351)),f319(f319(f244(x88353,x88351),x88355),x88352)),x88354))
% 28.73/28.52 [8836]P1(f319(f319(f321(x88361),x88362),f319(f256(x88361,x88363),x88364)))+~P1(f319(f319(f321(f931(x88361,x88363)),f319(f319(f244(x88361,x88363),x88362),x88365)),x88364))
% 28.73/28.52 [8837]P1(f319(f319(f321(x88371),x88372),f319(f256(x88371,x88373),x88374)))+~P1(f319(f319(f321(f931(x88371,x88373)),f319(f319(f244(x88371,x88373),x88372),x88375)),x88374))
% 28.73/28.52 [8984]P1(f319(f319(f61(x89841,x89842,x89843),x89844),x89845))+~P1(f319(f319(f321(f931(x89841,x89842)),f319(f319(f244(x89841,x89842),x89844),x89845)),x89843))
% 28.73/28.52 [9024]E(f319(x90241,x90242),x90243)+~P1(f319(f319(f321(x90244),x90242),f319(f303(x90244,x90245,x90241),f319(f319(f301(x90245),x90243),f180(f932(x90245,a923))))))
% 28.73/28.52 [9258]P1(f319(f319(f321(f931(x92581,x92582)),f319(f319(f244(x92581,x92582),x92583),x92584)),f319(f278(x92582,x92581),x92585)))+~P1(f319(f319(f321(f931(x92582,x92581)),f319(f319(f244(x92582,x92581),x92584),x92583)),x92585))
% 28.73/28.52 [9259]P1(f319(f319(f321(f931(x92591,x92592)),f319(f319(f244(x92591,x92592),x92593),x92594)),f319(f278(x92592,x92591),x92595)))+~P1(f319(f319(f321(f931(x92592,x92591)),f319(f319(f244(x92592,x92591),x92594),x92593)),x92595))
% 28.73/28.52 [9277]~P1(f319(f319(x92771,x92775),x92774))+P1(f319(f319(x92771,f319(f248(x92772,x92773),f319(f319(f244(x92772,x92773),x92774),x92775))),f319(f243(x92772,x92773),f319(f319(f244(x92772,x92773),x92774),x92775))))
% 28.73/28.52 [9306]~P1(f319(f319(f321(f931(x93062,x93061)),f319(f319(f244(x93062,x93061),x93064),x93063)),f319(f278(x93061,x93062),x93065)))+P1(f319(f319(f321(f931(x93061,x93062)),f319(f319(f244(x93061,x93062),x93063),x93064)),x93065))
% 28.73/28.52 [9307]~P1(f319(f319(f321(f931(x93072,x93071)),f319(f319(f244(x93072,x93071),x93074),x93073)),f319(f278(x93071,x93072),x93075)))+P1(f319(f319(f321(f931(x93071,x93072)),f319(f319(f244(x93071,x93072),x93073),x93074)),x93075))
% 28.73/28.52 [9340]~P1(f319(f319(f321(f931(x93403,x93401)),f319(f319(f244(x93403,x93401),x93405),x93402)),x93404))+P1(f319(f319(f321(x93401),x93402),f319(f277(x93403,x93401,x93404),f319(f319(f301(x93403),x93405),f180(f932(x93403,a923))))))
% 28.73/28.52 [9389]P1(f319(f319(f321(f931(x93891,x93892)),f319(f319(f244(x93891,x93892),x93893),x93894)),x93895))+~P1(f319(f319(f321(x93892),x93894),f319(f277(x93891,x93892,x93895),f319(f319(f301(x93891),x93893),f180(f932(x93891,a923))))))
% 28.73/28.52 [9479]~P79(x94791)+E(f319(f319(f6(a925,x94791),x94792),f295(a925,f319(f319(f74(a925),x94793),x94794),f319(f319(f74(a925),x94795),x94794))),f319(f319(f6(a925,x94791),f319(f319(f8(a925,x94791,a925),x94792),f319(f319(f7(a925,a925,a925),f74(a925)),x94794))),f295(a925,x94793,x94795)))
% 28.73/28.52 [9499]~P79(x94991)+E(f319(f319(f6(a925,x94991),x94992),f319(f294(a925,f319(f319(f74(a925),x94993),x94994)),f319(f319(f74(a925),x94995),x94994))),f319(f319(f6(a925,x94991),f319(f319(f8(a925,x94991,a925),x94992),f319(f319(f7(a925,a925,a925),f74(a925)),x94994))),f319(f294(a925,x94993),x94995)))
% 28.73/28.52 [9557]~P26(x95571,x95572,x95573,f234(f932(x95571,a923)))+E(f319(f319(f146(x95571,x95572),x95573),f319(f128(x95571,f319(f319(f8(a923,a923,x95571),a314),f319(a316,x95574))),x95575)),f319(f128(x95572,f319(f319(f8(a923,a923,x95572),a314),f319(a316,f319(x95573,x95574)))),f319(f319(f146(x95571,x95572),x95573),x95575)))
% 28.73/28.52 [9575]~P26(x95751,x95752,x95753,f319(f319(f301(x95751),x95754),f319(f164(x95751),x95755)))+E(f319(f319(f146(x95751,x95752),x95753),f319(f128(x95751,f319(f319(f8(a923,a923,x95751),a314),f319(a316,x95754))),x95755)),f319(f128(x95752,f319(f319(f8(a923,a923,x95752),a314),f319(a316,f319(x95753,x95754)))),f319(f319(f146(x95751,x95752),x95753),x95755)))
% 28.73/28.52 [9737]P1(f319(f319(f321(f931(f926(x97371),f926(x97371))),f319(f319(f244(f926(x97371),f926(x97371)),f319(f319(f143(x97371),x97372),x97373)),f319(f319(f143(x97371),x97374),x97373))),f149(x97371,x97375)))+~P1(f319(f319(f321(f931(x97371,x97371)),f319(f319(f244(x97371,x97371),x97372),x97374)),x97375))
% 28.73/28.52 [9860]E(f319(f319(f301(x98601),f906(x98602,x98603,x98604,x98605,x98601)),f908(x98602,x98603,x98604,x98605,x98601)),f319(f319(f301(x98601),x98604),x98603))+~P1(f319(f56(x98601,x98605,f319(f319(f301(x98601),x98604),x98603)),x98602))
% 28.73/28.52 [9861]E(f319(f319(f301(x98611),f909(x98612,x98613,x98614,x98615,x98611)),f910(x98612,x98613,x98614,x98615,x98611)),f319(f319(f301(x98611),x98614),x98613))+~P1(f319(f56(x98611,x98615,f319(f319(f301(x98611),x98614),x98613)),x98612))
% 28.73/28.52 [9946]P1(f319(f319(f321(x99461),f392(x99462,x99463,x99464,x99465,x99461)),x99464))+P1(f319(f319(f319(f34(x99461,f932(x99465,a923)),x99464),x99463),x99462))
% 28.73/28.52 [9947]P1(f319(f319(f321(x99471),f670(x99472,x99473,x99474,x99475,x99471)),x99475))+P1(f319(f319(f319(f34(x99471,f932(x99472,a923)),x99475),x99474),x99473))
% 28.73/28.52 [9952]P1(f319(f319(f321(x99521),f409(x99522,x99523,x99521,x99524,x99525)),x99523))+P1(f319(f319(f321(x99525),x99524),f319(f319(f34(x99521,f932(x99525,a923)),x99523),x99522)))
% 28.73/28.52 [9953]P1(f319(f319(f321(x99531),f682(x99532,x99533,x99534,x99535,x99531)),x99535))+P1(f319(f319(f321(x99534),x99533),f319(f319(f34(x99531,f932(x99534,a923)),x99535),x99532)))
% 28.73/28.52 [9963]P1(f319(f319(f321(x99631),f891(x99632,x99633,x99631,x99634,x99635)),x99633))+P1(f319(f319(f226(f932(x99635,a923)),x99634),f319(f319(f34(x99631,f932(x99635,a923)),x99633),x99632)))
% 28.73/28.52 [9964]P1(f319(f319(f321(x99641),f514(x99642,x99643,x99644,x99645,x99641)),x99645))+P1(f319(f319(f226(f932(x99644,a923)),x99643),f319(f319(f34(x99641,f932(x99644,a923)),x99645),x99642)))
% 28.73/28.52 [9966]P1(f319(f319(x99661,f402(x99662,x99661,x99663,x99664,x99665)),x99662))+~P1(f319(f319(f319(f33(x99665,f932(x99664,a923)),x99663),x99661),x99662))
% 28.73/28.52 [9967]P1(f319(f319(x99671,f691(x99672,x99671,x99673,x99674,x99675)),x99672))+~P1(f319(f319(f319(f33(x99675,f932(x99674,a923)),x99673),x99671),x99672))
% 28.73/28.52 [9971]P1(f319(f319(f321(x99711),f402(x99712,x99713,x99714,x99715,x99711)),x99714))+~P1(f319(f319(f319(f33(x99711,f932(x99715,a923)),x99714),x99713),x99712))
% 28.73/28.52 [9972]P1(f319(f319(f321(x99721),f691(x99722,x99723,x99724,x99725,x99721)),x99724))+~P1(f319(f319(f319(f33(x99721,f932(x99725,a923)),x99724),x99723),x99722))
% 28.73/28.52 [9973]P57(x99734,f319(f319(f34(x99731,f932(x99734,a923)),x99735),x99733),f319(f319(f34(x99731,f932(f931(x99734,x99734),a923)),x99735),x99732))+P1(f319(f319(f321(x99731),f797(x99732,x99733,x99734,x99735,x99731)),x99735))
% 28.73/28.52 [9974]P57(x99744,f319(f319(f33(x99741,f932(x99744,a923)),x99745),x99743),f319(f319(f33(x99741,f932(f931(x99744,x99744),a923)),x99745),x99742))+P1(f319(f319(f321(x99741),f842(x99742,x99743,x99744,x99745,x99741)),x99745))
% 28.73/28.52 [9985]P1(f319(f319(f321(x99851),f417(x99852,x99853,x99851,x99854,x99855)),x99853))+~P1(f319(f319(f321(x99855),x99854),f319(f319(f33(x99851,f932(x99855,a923)),x99853),x99852)))
% 28.73/28.52 [9986]P1(f319(f319(f321(x99861),f704(x99862,x99863,x99861,x99864,x99865)),x99863))+~P1(f319(f319(f321(x99865),x99864),f319(f319(f33(x99861,f932(x99865,a923)),x99863),x99862)))
% 28.73/28.52 [9992]P1(f319(f319(f321(x99921),x99922),f319(x99923,f417(x99923,x99924,x99925,x99922,x99921))))+~P1(f319(f319(f321(x99921),x99922),f319(f319(f33(x99925,f932(x99921,a923)),x99924),x99923)))
% 28.73/28.52 [9993]P1(f319(f319(f321(x99931),x99932),f319(x99933,f704(x99933,x99934,x99935,x99932,x99931))))+~P1(f319(f319(f321(x99931),x99932),f319(f319(f33(x99935,f932(x99931,a923)),x99934),x99933)))
% 28.73/28.52 [10080]~P1(f319(f319(x100804,f392(x100805,x100804,x100803,x100802,x100801)),x100805))+P1(f319(f319(f319(f34(x100801,f932(x100802,a923)),x100803),x100804),x100805))
% 28.73/28.52 [10081]~P1(f319(f319(x100814,f670(x100812,x100815,x100814,x100813,x100811)),x100815))+P1(f319(f319(f319(f34(x100811,f932(x100812,a923)),x100813),x100814),x100815))
% 28.73/28.52 [10084]~P1(f319(f319(f321(x100841),x100842),f319(x100845,f409(x100845,x100844,x100843,x100842,x100841))))+P1(f319(f319(f321(x100841),x100842),f319(f319(f34(x100843,f932(x100841,a923)),x100844),x100845)))
% 28.73/28.52 [10085]~P1(f319(f319(f321(x100851),x100852),f319(x100855,f682(x100855,x100852,x100851,x100854,x100853))))+P1(f319(f319(f321(x100851),x100852),f319(f319(f34(x100853,f932(x100851,a923)),x100854),x100855)))
% 28.73/28.52 [10089]~P57(x100891,f319(x100894,f842(x100895,x100894,x100891,x100893,x100892)),f319(x100895,f842(x100895,x100894,x100891,x100893,x100892)))+P57(x100891,f319(f319(f33(x100892,f932(x100891,a923)),x100893),x100894),f319(f319(f33(x100892,f932(f931(x100891,x100891),a923)),x100893),x100895))
% 28.73/28.52 [10090]~P57(x100901,f319(x100904,f797(x100905,x100904,x100901,x100903,x100902)),f319(x100905,f797(x100905,x100904,x100901,x100903,x100902)))+P57(x100901,f319(f319(f34(x100902,f932(x100901,a923)),x100903),x100904),f319(f319(f34(x100902,f932(f931(x100901,x100901),a923)),x100903),x100905))
% 28.73/28.52 [10091]~P1(f319(f319(f226(f932(x100911,a923)),x100912),f319(x100915,f891(x100915,x100914,x100913,x100912,x100911))))+P1(f319(f319(f226(f932(x100911,a923)),x100912),f319(f319(f34(x100913,f932(x100911,a923)),x100914),x100915)))
% 28.73/28.52 [10092]~P1(f319(f319(f226(f932(x100921,a923)),x100922),f319(x100925,f514(x100925,x100922,x100921,x100924,x100923))))+P1(f319(f319(f226(f932(x100921,a923)),x100922),f319(f319(f34(x100923,f932(x100921,a923)),x100924),x100925)))
% 28.73/28.52 [10157]~P1(f319(f319(f321(x101571),f906(x101575,x101574,x101573,x101572,x101571)),f908(x101575,x101574,x101573,x101572,x101571)))+~P1(f319(f56(x101571,x101572,f319(f319(f301(x101571),x101573),x101574)),x101575))
% 28.73/28.52 [10158]~P1(f319(f319(f321(x101581),f909(x101585,x101584,x101583,x101582,x101581)),f910(x101585,x101584,x101583,x101582,x101581)))+~P1(f319(f56(x101581,x101582,f319(f319(f301(x101581),x101583),x101584)),x101585))
% 28.73/28.52 [10159]~P1(f319(f319(f321(f931(x101591,x101591)),f319(f319(f244(x101591,x101591),x101592),x101595)),f319(f319(f175(f931(x101591,x101591),a923),f319(a104,x101594)),x101593)))+P1(f319(f319(f321(f931(x101591,x101591)),f319(f319(f244(x101591,x101591),x101592),f646(x101593,x101594,x101595,x101592,x101591))),f319(f319(f175(f931(x101591,x101591),a923),x101594),x101593)))
% 28.73/28.52 [10165]P1(f319(f60(x101651,x101651,x101652,f906(x101653,x101654,x101655,x101652,x101651),f908(x101653,x101654,x101655,x101652,x101651)),x101653))+~P1(f319(f56(x101651,x101652,f319(f319(f301(x101651),x101655),x101654)),x101653))
% 28.73/28.52 [10166]P1(f319(f60(x101661,x101661,x101662,f909(x101663,x101664,x101665,x101662,x101661),f910(x101663,x101664,x101665,x101662,x101661)),x101663))+~P1(f319(f56(x101661,x101662,f319(f319(f301(x101661),x101665),x101664)),x101663))
% 28.73/28.52 [10176]~P4(x101761)+P14(x101761,f319(f319(f146(x101762,x101761),x101763),f319(f128(x101762,f319(f319(f7(x101762,x101761,a923),f319(f319(f8(x101761,f932(x101761,a923),x101762),a316),x101763)),f319(x101764,x101765))),x101765)))
% 28.73/28.52 [10229]~P1(f319(f319(f321(x102292),x102295),f319(f277(x102291,x102292,x102294),x102293)))+P1(f319(f319(f321(f931(x102291,x102292)),f319(f319(f244(x102291,x102292),f530(x102293,x102294,x102291,x102295,x102292)),x102295)),x102294))
% 28.73/28.52 [10230]~P1(f319(f319(f321(x102302),x102305),f319(f277(x102301,x102302,x102304),x102303)))+P1(f319(f319(f321(f931(x102301,x102302)),f319(f319(f244(x102301,x102302),f556(x102303,x102304,x102301,x102305,x102302)),x102305)),x102304))
% 28.73/28.52 [10250]~P1(f319(f319(f321(f931(x102501,x102501)),f319(f319(f244(x102501,x102501),x102505),x102504)),f319(f319(f175(f931(x102501,x102501),a923),f319(a104,x102503)),x102502)))+P1(f319(f319(f321(f931(x102501,x102501)),f319(f319(f244(x102501,x102501),f646(x102502,x102503,x102504,x102505,x102501)),x102504)),x102502))
% 28.73/28.52 [10253]~P1(f319(f319(f321(f931(x102531,x102531)),f319(f319(f244(x102531,x102531),x102535),x102534)),f319(f319(f175(f931(x102531,x102531),a923),f319(a104,x102533)),x102532)))+P1(f319(f319(f321(f931(x102531,x102531)),f319(f319(f244(x102531,x102531),f645(x102532,x102533,x102534,x102535,x102531)),x102534)),f319(f319(f175(f931(x102531,x102531),a923),x102533),x102532)))
% 28.73/28.52 [10254]~P1(f319(f319(f321(f931(x102541,x102541)),f319(f319(f244(x102541,x102541),x102545),x102544)),f319(f319(f175(f931(x102541,x102541),a923),f319(a104,x102543)),x102542)))+P1(f319(f319(f321(f931(x102541,x102541)),f319(f319(f244(x102541,x102541),f647(x102542,x102543,x102544,x102545,x102541)),x102544)),f319(f319(f175(f931(x102541,x102541),a923),x102543),x102542)))
% 28.73/28.52 [10255]~P1(f319(f319(f321(f931(f926(x102551),f926(x102551))),f319(f319(f244(f926(x102551),f926(x102551)),x102555),f319(f319(f143(x102551),x102554),x102553))),f150(x102551,x102552)))+P1(f319(f319(f321(f931(x102551,x102551)),f319(f319(f244(x102551,x102551),f672(x102552,x102553,x102554,x102555,x102551)),x102554)),x102552))
% 28.73/28.52 [7795]~E(x77953,f180(f932(x77952,a923)))+E(f319(f319(f102(f932(x77951,a923)),f319(f319(f33(x77952,f932(x77951,a923)),x77953),x77954)),x77955),x77955)
% 28.73/28.52 [7796]~E(x77963,f180(f932(x77962,a923)))+E(f319(f319(f93(f932(x77961,a923)),f319(f319(f34(x77962,f932(x77961,a923)),x77963),x77964)),x77965),x77965)
% 28.73/28.52 [7849]~P121(x78491)+E(f319(f319(f75(x78491),f319(f319(f75(x78491),x78492),x78493)),f319(f319(f75(x78491),x78494),x78495)),f319(f319(f75(x78491),x78494),f319(f319(f75(x78491),f319(f319(f75(x78491),x78492),x78493)),x78495)))
% 28.73/28.52 [8225]~E(x82253,f180(f932(x82252,a923)))+E(f319(f319(f23(f932(x82251,a923)),f319(f319(f34(x82252,f932(x82251,a923)),x82253),x82254)),x82255),f319(f319(f23(f932(x82251,a923)),f234(f932(x82251,a923))),x82255))
% 28.73/28.52 [8355]E(f319(f319(f151(x83551,f319(f319(f126(x83551),x83552),x83553)),x83554),x83555),f319(f319(f126(x83551),f319(f319(f151(x83551,x83552),x83554),x83555)),x83553))+~P1(f319(f319(f227(a925),x83554),f319(f181(f926(x83551)),x83552)))
% 28.73/28.52 [8356]E(f319(f319(f151(x83561,f319(f319(f126(x83561),x83562),x83563)),x83564),x83565),f319(f319(f126(x83561),f319(f319(f151(x83561,x83562),x83564),x83565)),x83563))+~P1(f319(f319(f227(a925),x83564),f319(f181(f926(x83561)),x83562)))
% 28.73/28.52 [8630]E(f319(f319(f156(x86301),f319(f319(f146(a925,x86301),x86302),f131(a925,f319(f294(a925,x86303),x86304)))),x86305),f319(x86302,f319(f319(f74(a925),x86303),x86305)))+~P1(f319(f319(f227(a925),x86305),f319(f319(f23(a925),x86304),x86303)))
% 28.73/28.52 [8644]E(x86441,f2(a91))+E(f114(x86442,x86443,f319(x86444,f319(f319(f23(a91),x86441),f72(a91))),f319(f319(f7(x86442,a91,f927(f929(x86443))),x86445),x86441)),f319(f188(x86442,x86443,x86444,x86445),x86441))
% 28.73/28.52 [8670]~E(x86703,f180(f932(x86701,a923)))+E(f319(f319(f33(x86701,f932(x86702,a923)),x86703),f319(f319(f8(f932(x86702,a923),f932(x86702,a923),x86701),f319(f102(f932(x86702,a923)),x86704)),x86705)),f180(f932(x86702,a923)))
% 28.73/28.52 [8671]~E(x86713,f180(f932(x86711,a923)))+E(f319(f319(f34(x86711,f932(x86712,a923)),x86713),f319(f319(f8(f932(x86712,a923),f932(x86712,a923),x86711),f319(f93(f932(x86712,a923)),x86714)),x86715)),f234(f932(x86712,a923)))
% 28.73/28.52 [8672]~E(x86723,f180(f932(x86721,a923)))+E(f319(f319(f34(x86721,f932(x86722,a923)),x86723),f319(f319(f8(f932(x86722,a923),f932(x86722,a923),x86721),f319(f23(f932(x86722,a923)),x86724)),x86725)),f234(f932(x86722,a923)))
% 28.73/28.52 [8674]~P143(x86742)+E(f319(f319(f6(x86741,x86742),f319(f319(f8(x86742,x86742,x86741),f319(f75(x86742),x86743)),x86744)),x86745),f319(f319(f75(x86742),x86743),f319(f319(f6(x86741,x86742),x86744),x86745)))
% 28.73/28.52 [8965]E(x89651,f180(f932(x89652,a923)))+E(f319(f319(f33(x89652,f932(x89653,a923)),x89651),f319(f319(f8(f932(x89653,a923),f932(x89653,a923),x89652),f319(f102(f932(x89653,a923)),x89654)),x89655)),f319(f319(f102(f932(x89653,a923)),x89654),f319(f319(f33(x89652,f932(x89653,a923)),x89651),x89655)))
% 28.73/28.52 [8966]E(x89661,f180(f932(x89662,a923)))+E(f319(f319(f34(x89662,f932(x89663,a923)),x89661),f319(f319(f8(f932(x89663,a923),f932(x89663,a923),x89662),f319(f93(f932(x89663,a923)),x89664)),x89665)),f319(f319(f93(f932(x89663,a923)),x89664),f319(f319(f34(x89662,f932(x89663,a923)),x89661),x89665)))
% 28.73/28.52 [8967]E(x89671,f180(f932(x89672,a923)))+E(f319(f319(f34(x89672,f932(x89673,a923)),x89671),f319(f319(f8(f932(x89673,a923),f932(x89673,a923),x89672),f319(f23(f932(x89673,a923)),x89674)),x89675)),f319(f319(f23(f932(x89673,a923)),x89674),f319(f319(f33(x89672,f932(x89673,a923)),x89671),x89675)))
% 28.73/28.52 [8968]E(x89681,f180(f932(x89682,a923)))+E(f319(f319(f33(x89682,f932(x89683,a923)),x89681),f319(f319(f8(f932(x89683,a923),f932(x89683,a923),x89682),f319(f102(f932(x89683,a923)),x89684)),x89685)),f319(f319(f102(f932(x89683,a923)),x89684),f319(f319(f33(x89682,f932(x89683,a923)),x89681),x89685)))
% 28.73/28.52 [8969]E(x89691,f180(f932(x89692,a923)))+E(f319(f319(f34(x89692,f932(x89693,a923)),x89691),f319(f319(f8(f932(x89693,a923),f932(x89693,a923),x89692),f319(f93(f932(x89693,a923)),x89694)),x89695)),f319(f319(f93(f932(x89693,a923)),x89694),f319(f319(f34(x89692,f932(x89693,a923)),x89691),x89695)))
% 28.73/28.52 [8970]E(x89701,f180(f932(x89702,a923)))+E(f319(f319(f34(x89702,f932(x89703,a923)),x89701),f319(f319(f8(f932(x89703,a923),f932(x89703,a923),x89702),f319(f23(f932(x89703,a923)),x89704)),x89705)),f319(f319(f23(f932(x89703,a923)),x89704),f319(f319(f33(x89702,f932(x89703,a923)),x89701),x89705)))
% 28.73/28.52 [9174]~P1(f319(f319(f227(a925),f319(x91744,x91742)),f319(x91744,x91743)))+P1(f319(f319(f321(f931(x91741,x91741)),f319(f319(f244(x91741,x91741),x91742),x91743)),f145(x91741,f319(f319(f143(f932(x91741,a925)),x91744),x91745))))
% 28.73/28.52 [9175]~P1(f319(f319(f227(a925),f319(x91754,x91752)),f319(x91754,x91753)))+P1(f319(f319(f321(f931(x91751,x91751)),f319(f319(f244(x91751,x91751),x91752),x91753)),f145(x91751,f319(f319(f143(f932(x91751,a925)),x91754),x91755))))
% 28.73/28.52 [9426]~P41(f932(x94265,a923),f932(x94261,a923),x94262)+P1(f319(f319(f226(f932(x94261,a923)),f319(f319(f102(f932(x94261,a923)),f319(x94262,x94263)),f319(x94262,x94264))),f319(x94262,f319(f319(f102(f932(x94265,a923)),x94263),x94264))))
% 28.73/28.52 [9445]~P26(x94452,x94451,x94453,f319(f319(f102(f932(x94452,a923)),x94454),x94455))+E(f319(f319(f93(f932(x94451,a923)),f319(f302(x94452,x94451,x94453),f319(f319(f23(f932(x94452,a923)),x94454),x94455))),f319(f302(x94452,x94451,x94453),f319(f319(f23(f932(x94452,a923)),x94455),x94454))),f180(f932(x94451,a923)))
% 28.73/28.52 [9703]~P26(x97033,x97031,x97035,f234(f932(x97033,a923)))+E(f319(f66(x97031,x97032,x97033,f319(f66(x97033,x97032,x97031,x97034),f85(x97033,x97031,f234(f932(x97033,a923)),x97035))),x97035),x97034)
% 28.73/28.52 [9733]~P1(f319(f319(f226(f932(x97333,a923)),f319(f277(x97331,x97333,x97334),x97332)),x97335))+P1(f319(f319(f226(f932(x97331,a923)),x97332),f319(f73(f932(x97331,a923)),f319(f277(x97333,x97331,f319(f278(x97331,x97333),x97334)),f319(f73(f932(x97333,a923)),x97335)))))
% 28.73/28.52 [9758]~P26(x97581,x97582,x97583,f319(f319(f301(x97581),x97584),x97585))+~P1(f319(f319(f321(x97582),f319(x97583,x97584)),f319(f302(x97581,x97582,x97583),f319(f319(f23(f932(x97581,a923)),x97585),f319(f319(f301(x97581),x97584),f180(f932(x97581,a923)))))))
% 28.73/28.52 [9813]P1(f319(f319(f226(f932(x98131,a923)),f319(f277(x98132,x98131,x98133),x98134)),x98135))+~P1(f319(f319(f226(f932(x98132,a923)),x98134),f319(f73(f932(x98132,a923)),f319(f277(x98131,x98132,f319(f278(x98132,x98131),x98133)),f319(f73(f932(x98131,a923)),x98135)))))
% 28.73/28.52 [9887]~P92(x98871)+P1(f319(f319(f226(x98871),f319(f69(x98871),f319(f319(f23(x98871),f319(f319(f74(x98871),x98872),x98873)),f319(f319(f74(x98871),x98874),x98875)))),f319(f319(f74(x98871),f319(f69(x98871),f319(f319(f23(x98871),x98872),x98874))),f319(f69(x98871),f319(f319(f23(x98871),x98873),x98875)))))
% 28.73/28.52 [10008]P1(f319(f319(f321(x100081),f900(x100082,x100083,x100084,x100081,x100085)),x100084))+P1(f319(f319(f226(f932(x100085,a923)),f319(f319(f33(x100081,f932(x100085,a923)),x100084),x100083)),x100082))
% 28.73/28.52 [10009]P1(f319(f319(f321(x100091),f537(x100092,x100093,x100094,x100095,x100091)),x100095))+P1(f319(f319(f226(f932(x100094,a923)),f319(f319(f33(x100091,f932(x100094,a923)),x100095),x100093)),x100092))
% 28.73/28.52 [10196]~P1(f319(f319(f226(f932(x101961,a923)),f319(x101964,f900(x101965,x101964,x101963,x101962,x101961))),x101965))+P1(f319(f319(f226(f932(x101961,a923)),f319(f319(f33(x101962,f932(x101961,a923)),x101963),x101964)),x101965))
% 28.73/28.52 [10197]~P1(f319(f319(f226(f932(x101971,a923)),f319(x101974,f537(x101975,x101974,x101971,x101973,x101972))),x101975))+P1(f319(f319(f226(f932(x101971,a923)),f319(f319(f33(x101972,f932(x101971,a923)),x101973),x101974)),x101975))
% 28.73/28.52 [8781]E(f319(f319(f126(x87811),x87812),f319(f319(f151(x87811,x87813),f319(f319(f23(a925),x87814),f319(f181(f926(x87811)),x87812))),x87815)),f319(f319(f151(x87811,f319(f319(f126(x87811),x87812),x87813)),x87814),x87815))+P1(f319(f319(f227(a925),x87814),f319(f181(f926(x87811)),x87812)))
% 28.73/28.52 [8810]~P146(x88101)+E(f319(f319(f74(x88101),f319(f319(f75(x88101),x88102),x88103)),f319(f319(f74(x88101),f319(f319(f75(x88101),x88104),x88103)),x88105)),f319(f319(f74(x88101),f319(f319(f75(x88101),f319(f319(f74(x88101),x88102),x88104)),x88103)),x88105))
% 28.73/28.52 [9398]~P143(x93981)+E(f319(f157(x93981),f319(f319(f146(x93982,x93981),f319(f319(f8(x93981,x93981,x93982),f319(f75(x93981),x93983)),x93984)),x93985)),f319(f319(f75(x93981),x93983),f319(f157(x93981),f319(f319(f146(x93982,x93981),x93984),x93985))))
% 28.73/28.52 [9574]E(f319(f181(f926(x95741)),f319(f319(f167(x95741),f319(f319(f224(a925),f319(f181(f926(x95741)),x95742)),f319(f181(f926(x95743)),x95744))),x95742)),f319(f181(f926(x95743)),f319(f319(f167(x95743),f319(f319(f224(a925),f319(f181(f926(x95741)),x95742)),f319(f181(f926(x95743)),x95744))),x95744)))+P1(f319(x95745,f319(f319(f173(x95741,x95743),x95742),x95744)))
% 28.73/28.52 [9823]~P143(x98232)+E(f319(f319(f6(x98231,x98232),f319(f319(f7(x98231,x98232,x98232),f319(f319(f8(x98232,f932(x98232,x98232),x98231),f75(x98232)),x98233)),x98234)),x98235),f319(f319(f75(x98232),f319(f319(f6(x98231,x98232),x98233),x98235)),x98234))
% 28.73/28.52 [9824]~P73(x98242)+E(f319(f319(f6(x98241,x98242),f319(f319(f7(x98241,x98242,x98242),f319(f319(f8(x98242,f932(x98242,x98242),x98241),f283(x98242)),x98243)),x98244)),x98245),f319(f319(f283(x98242),f319(f319(f6(x98241,x98242),x98243),x98245)),x98244))
% 28.73/28.52 [9831]~P70(x98312)+E(f319(f319(f6(x98311,x98312),f319(f319(f18(x98311,x98312,x98312),f319(f319(f8(x98312,f932(x98312,x98312),x98311),f23(x98312)),x98313)),x98314)),x98315),f319(f319(f23(x98312),f319(f319(f6(x98311,x98312),x98313),x98315)),f319(f319(f6(x98311,x98312),x98314),x98315)))
% 28.73/28.52 [9832]~P79(x98322)+E(f319(f319(f6(x98321,x98322),f319(f319(f18(x98321,x98322,x98322),f319(f319(f8(x98322,f932(x98322,x98322),x98321),f74(x98322)),x98323)),x98324)),x98325),f319(f319(f74(x98322),f319(f319(f6(x98321,x98322),x98323),x98325)),f319(f319(f6(x98321,x98322),x98324),x98325)))
% 28.73/28.52 [9833]~P78(x98332)+E(f319(f319(f9(x98331,x98332),f319(f319(f18(x98331,x98332,x98332),f319(f319(f8(x98332,f932(x98332,x98332),x98331),f75(x98332)),x98333)),x98334)),x98335),f319(f319(f75(x98332),f319(f319(f9(x98331,x98332),x98333),x98335)),f319(f319(f9(x98331,x98332),x98334),x98335)))
% 28.73/28.52 [9872]~E(x98723,f180(f932(x98721,a923)))+E(f319(f319(f33(x98721,f932(x98722,a923)),x98723),f319(f319(f7(x98721,f932(x98722,a923),f932(x98722,a923)),f319(f319(f8(f932(x98722,a923),f932(f932(x98722,a923),f932(x98722,a923)),x98721),f102(f932(x98722,a923))),x98724)),x98725)),f180(f932(x98722,a923)))
% 28.73/28.52 [9873]~E(x98733,f180(f932(x98731,a923)))+E(f319(f319(f34(x98731,f932(x98732,a923)),x98733),f319(f319(f7(x98731,f932(x98732,a923),f932(x98732,a923)),f319(f319(f8(f932(x98732,a923),f932(f932(x98732,a923),f932(x98732,a923)),x98731),f93(f932(x98732,a923))),x98734)),x98735)),f234(f932(x98732,a923)))
% 28.73/28.52 [9874]~E(x98743,f180(f932(x98741,a923)))+E(f319(f319(f34(x98741,f932(x98742,a923)),x98743),f319(f319(f7(x98741,f932(x98742,a923),f932(x98742,a923)),f319(f319(f8(f932(x98742,a923),f932(f932(x98742,a923),f932(x98742,a923)),x98741),f23(f932(x98742,a923))),x98744)),x98745)),f234(f932(x98742,a923)))
% 28.73/28.52 [9892]E(x98921,f180(f932(x98922,a923)))+E(f319(f319(f33(x98922,f932(x98923,a923)),x98921),f319(f319(f7(x98922,f932(x98923,a923),f932(x98923,a923)),f319(f319(f8(f932(x98923,a923),f932(f932(x98923,a923),f932(x98923,a923)),x98922),f102(f932(x98923,a923))),x98924)),x98925)),f319(f319(f102(f932(x98923,a923)),f319(f319(f33(x98922,f932(x98923,a923)),x98921),x98924)),x98925))
% 28.73/28.52 [9893]E(x98931,f180(f932(x98932,a923)))+E(f319(f319(f34(x98932,f932(x98933,a923)),x98931),f319(f319(f7(x98932,f932(x98933,a923),f932(x98933,a923)),f319(f319(f8(f932(x98933,a923),f932(f932(x98933,a923),f932(x98933,a923)),x98932),f93(f932(x98933,a923))),x98934)),x98935)),f319(f319(f93(f932(x98933,a923)),f319(f319(f34(x98932,f932(x98933,a923)),x98931),x98934)),x98935))
% 28.73/28.52 [9894]E(x98941,f180(f932(x98942,a923)))+E(f319(f319(f34(x98942,f932(x98943,a923)),x98941),f319(f319(f7(x98942,f932(x98943,a923),f932(x98943,a923)),f319(f319(f8(f932(x98943,a923),f932(f932(x98943,a923),f932(x98943,a923)),x98942),f23(f932(x98943,a923))),x98944)),x98945)),f319(f319(f23(f932(x98943,a923)),f319(f319(f34(x98942,f932(x98943,a923)),x98941),x98944)),x98945))
% 28.73/28.52 [9895]E(x98951,f180(f932(x98952,a923)))+E(f319(f319(f33(x98952,f932(x98953,a923)),x98951),f319(f319(f7(x98952,f932(x98953,a923),f932(x98953,a923)),f319(f319(f8(f932(x98953,a923),f932(f932(x98953,a923),f932(x98953,a923)),x98952),f102(f932(x98953,a923))),x98954)),x98955)),f319(f319(f102(f932(x98953,a923)),f319(f319(f33(x98952,f932(x98953,a923)),x98951),x98954)),x98955))
% 28.73/28.52 [9896]E(x98961,f180(f932(x98962,a923)))+E(f319(f319(f34(x98962,f932(x98963,a923)),x98961),f319(f319(f7(x98962,f932(x98963,a923),f932(x98963,a923)),f319(f319(f8(f932(x98963,a923),f932(f932(x98963,a923),f932(x98963,a923)),x98962),f93(f932(x98963,a923))),x98964)),x98965)),f319(f319(f93(f932(x98963,a923)),f319(f319(f34(x98962,f932(x98963,a923)),x98961),x98964)),x98965))
% 28.73/28.52 [9897]E(x98971,f180(f932(x98972,a923)))+E(f319(f319(f34(x98972,f932(x98973,a923)),x98971),f319(f319(f7(x98972,f932(x98973,a923),f932(x98973,a923)),f319(f319(f8(f932(x98973,a923),f932(f932(x98973,a923),f932(x98973,a923)),x98972),f23(f932(x98973,a923))),x98974)),x98975)),f319(f319(f23(f932(x98973,a923)),f319(f319(f34(x98972,f932(x98973,a923)),x98971),x98974)),x98975))
% 28.73/28.52 [9450]~P1(f319(f319(f226(a925),x94501),x94504))+E(f319(f319(f23(a925),f319(f319(f74(a925),f319(f319(f75(a925),x94501),x94502)),x94503)),f319(f319(f74(a925),f319(f319(f75(a925),x94504),x94502)),x94505)),f319(f319(f23(a925),x94503),f319(f319(f74(a925),f319(f319(f75(a925),f319(f319(f23(a925),x94504),x94501)),x94502)),x94505)))
% 28.73/28.52 [10062]~P143(x100621)+E(f319(f157(x100621),f319(f319(f146(x100622,x100621),f319(f319(f7(x100622,x100621,x100621),f319(f319(f8(x100621,f932(x100621,x100621),x100622),f75(x100621)),x100623)),x100624)),x100625)),f319(f319(f75(x100621),f319(f157(x100621),f319(f319(f146(x100622,x100621),x100623),x100625))),x100624))
% 28.73/28.52 [10068]~P70(x100681)+E(f319(f157(x100681),f319(f319(f146(x100682,x100681),f319(f319(f18(x100682,x100681,x100681),f319(f319(f8(x100681,f932(x100681,x100681),x100682),f23(x100681)),x100683)),x100684)),x100685)),f319(f319(f23(x100681),f319(f157(x100681),f319(f319(f146(x100682,x100681),x100683),x100685))),f319(f157(x100681),f319(f319(f146(x100682,x100681),x100684),x100685))))
% 28.73/28.52 [10069]~P79(x100691)+E(f319(f157(x100691),f319(f319(f146(x100692,x100691),f319(f319(f18(x100692,x100691,x100691),f319(f319(f8(x100691,f932(x100691,x100691),x100692),f74(x100691)),x100693)),x100694)),x100695)),f319(f319(f74(x100691),f319(f157(x100691),f319(f319(f146(x100692,x100691),x100693),x100695))),f319(f157(x100691),f319(f319(f146(x100692,x100691),x100694),x100695))))
% 28.73/28.52 [10220]P1(f319(x102201,f319(f319(f173(x102202,x102203),x102204),x102205)))+~P1(f319(x102201,f319(f319(f173(x102202,x102203),f319(f319(f167(x102202),f319(f319(f224(a925),f319(f181(f926(x102202)),x102204)),f319(f181(f926(x102203)),x102205))),x102204)),f319(f319(f167(x102203),f319(f319(f224(a925),f319(f181(f926(x102202)),x102204)),f319(f181(f926(x102203)),x102205))),x102205))))
% 28.73/28.52 [10482]~P1(f319(f319(f321(f931(x104822,x104821)),f319(f319(f244(x104822,x104821),x104824),x104825)),f319(f278(x104821,x104822),x104823)))+P1(f319(f319(f235(x104821,x104822,f319(f319(f7(x104821,f932(f931(x104821,x104822),a923),f932(x104822,a923)),f319(f319(f8(f932(x104822,f932(f932(f931(x104821,x104822),a923),a923)),f932(f932(f931(x104821,x104822),a923),f932(x104822,a923)),x104821),f7(x104822,f932(f931(x104821,x104822),a923),a923)),f319(f319(f8(f932(x104822,f931(x104821,x104822)),f932(x104822,f932(f932(f931(x104821,x104822),a923),a923)),x104821),f319(f8(f931(x104821,x104822),f932(f932(f931(x104821,x104822),a923),a923),x104822),f321(f931(x104821,x104822)))),f244(x104821,x104822)))),x104823)),x104824),x104825))
% 28.73/28.52 [10494]P1(f319(f319(f321(f931(x104941,x104942)),f319(f319(f244(x104941,x104942),x104943),x104944)),f319(f278(x104942,x104941),x104945)))+~P1(f319(f319(f235(x104942,x104941,f319(f319(f7(x104942,f932(f931(x104942,x104941),a923),f932(x104941,a923)),f319(f319(f8(f932(x104941,f932(f932(f931(x104942,x104941),a923),a923)),f932(f932(f931(x104942,x104941),a923),f932(x104941,a923)),x104942),f7(x104941,f932(f931(x104942,x104941),a923),a923)),f319(f319(f8(f932(x104941,f931(x104942,x104941)),f932(x104941,f932(f932(f931(x104942,x104941),a923),a923)),x104942),f319(f8(f931(x104942,x104941),f932(f932(f931(x104942,x104941),a923),a923),x104941),f321(f931(x104942,x104941)))),f244(x104942,x104941)))),x104945)),x104943),x104944))
% 28.73/28.52 [9702]~P1(f319(f319(f226(a925),x97024),x97021))+E(f319(f319(f23(a925),f319(f319(f74(a925),f319(f319(f75(a925),x97021),x97022)),x97023)),f319(f319(f74(a925),f319(f319(f75(a925),x97024),x97022)),x97025)),f319(f319(f23(a925),f319(f319(f74(a925),f319(f319(f75(a925),f319(f319(f23(a925),x97021),x97024)),x97022)),x97023)),x97025))
% 28.73/28.52 [7495]E(x74951,x74952)+~E(f212(x74953,x74954,x74955,x74951),f212(x74953,x74954,x74956,x74952))
% 28.73/28.52 [7496]E(x74961,x74962)+~E(f212(x74963,x74964,x74961,x74965),f212(x74963,x74964,x74962,x74966))
% 28.73/28.52 [8614]~P21(x86145,x86141,x86142,x86146)+E(f319(f66(x86141,x86141,x86141,f319(x86142,x86143)),f319(x86142,x86144)),f319(f66(x86141,x86141,x86141,f319(x86142,x86144)),f319(x86142,x86143)))
% 28.73/28.52 [8854]~P61(x88544,x88545,x88542,x88541,x88546)+E(f319(x88541,f319(x88542,x88543)),x88543)
% 28.73/28.52 [9022]P26(x90221,x90222,x90223,x90224)+~P26(x90221,x90225,f319(f66(x90222,x90225,x90221,x90226),x90223),x90224)
% 28.73/28.52 [9094]~E(x90946,x90944)+E(f319(f68(x90941,x90942,x90943,x90944,x90945),x90946),x90945)
% 28.73/28.52 [9095]~E(x90956,x90954)+E(f319(f68(x90951,x90952,x90953,x90954,x90955),x90956),x90955)
% 28.73/28.52 [9100]E(x91001,x91002)+E(f319(f68(x91003,x91004,x91005,x91002,x91006),x91001),f319(x91005,x91001))
% 28.73/28.52 [9101]E(x91011,x91012)+E(f319(f68(x91013,x91014,x91015,x91012,x91016),x91011),f319(x91015,x91011))
% 28.73/28.52 [9102]E(x91021,x91022)+E(f319(f68(x91023,x91024,x91025,x91022,x91026),x91021),f319(x91025,x91021))
% 28.73/28.52 [9114]~P26(x91144,x91142,f319(f66(x91141,x91142,x91144,x91143),x91145),x91146)+P26(x91141,x91142,x91143,f319(f302(x91144,x91141,x91145),x91146))
% 28.73/28.52 [9772]P53(x97721,x97722,x97723,x97724,x97725,x97726)+~P1(f319(f319(x97723,f319(x97724,x97725)),f319(x97724,x97726)))
% 28.73/28.52 [9773]P53(x97731,x97732,x97733,x97734,x97735,x97736)+~P1(f319(f319(x97733,f319(x97734,x97735)),f319(x97734,x97736)))
% 28.73/28.52 [9834]P1(f319(f55(x98341),x98342))+~P1(f319(f60(x98341,x98343,x98344,x98345,x98342),x98346))
% 28.73/28.52 [9843]~P1(f319(f319(f321(x98434),x98433),f292(x98434,x98435,x98431,x98432,x98436)))+P1(f319(f319(x98431,x98432),x98433))
% 28.73/28.52 [9844]~P1(f319(f319(f321(x98444),x98443),f289(x98444,x98441,x98445,x98442,x98446)))+P1(f319(f319(x98441,x98442),x98443))
% 28.73/28.52 [9845]~P1(f319(f319(f321(x98454),x98452),f292(x98454,x98451,x98455,x98456,x98453)))+P1(f319(f319(x98451,x98452),x98453))
% 28.73/28.52 [9846]~P1(f319(f319(f321(x98464),x98462),f289(x98464,x98465,x98461,x98466,x98463)))+P1(f319(f319(x98461,x98462),x98463))
% 28.73/28.52 [9908]~P53(x99085,x99086,x99081,x99082,x99083,x99084)+P1(f319(f319(x99081,f319(x99082,x99083)),f319(x99082,x99084)))
% 28.73/28.52 [9909]~P53(x99095,x99096,x99091,x99092,x99093,x99094)+P1(f319(f319(x99091,f319(x99092,x99093)),f319(x99092,x99094)))
% 28.73/28.52 [10373]P13(x103731,x103732,x103733,x103734,x103735,x103736)+~E(f319(f319(x103736,f860(x103733,x103736,x103735,x103732,x103734,x103731)),f864(x103733,x103736,x103735,x103732,x103734,x103731)),f319(f319(x103736,f861(x103733,x103736,x103735,x103732,x103734,x103731)),f865(x103733,x103736,x103735,x103732,x103734,x103731)))
% 28.73/28.52 [5978]E(x59781,x59782)+~E(f319(f319(f244(x59783,x59784),x59785),x59781),f319(f319(f244(x59783,x59784),x59786),x59782))
% 28.73/28.52 [5979]E(x59791,x59792)+~E(f319(f319(f244(x59793,x59794),x59795),x59791),f319(f319(f244(x59793,x59794),x59796),x59792))
% 28.73/28.52 [5980]E(x59801,x59802)+~E(f319(f319(f244(x59803,x59804),x59801),x59805),f319(f319(f244(x59803,x59804),x59802),x59806))
% 28.73/28.52 [5981]E(x59811,x59812)+~E(f319(f319(f244(x59813,x59814),x59811),x59815),f319(f319(f244(x59813,x59814),x59812),x59816))
% 28.73/28.52 [6119]~P18(x61195,x61196,x61191)+E(f319(f319(x61191,x61192),f319(f319(x61191,x61193),x61194)),f319(f319(x61191,x61193),f319(f319(x61191,x61192),x61194)))
% 28.73/28.52 [7559]~P33(x75594,x75591,f319(f319(f143(x75594),x75592),x75595),f319(f319(f143(x75594),x75593),x75596))+P1(f319(f319(x75591,x75592),x75593))
% 28.73/28.52 [7912]P33(x79121,x79122,x79123,x79124)+~P33(x79121,x79122,f319(f319(f143(x79121),x79125),x79123),f319(f319(f143(x79121),x79126),x79124))
% 28.73/28.52 [8958]~P61(x89585,x89581,x89582,x89586,x89584)+P1(f319(f319(f321(x89581),f319(x89582,x89583)),x89584))
% 28.73/28.52 [9141]E(f319(f70(x91411,x91412,x91413,x91414,x91415),x91416),f319(x91413,x91416))+P1(f319(f319(f321(x91411),x91416),x91415))
% 28.73/28.52 [9142]E(f319(f70(x91421,x91422,x91423,x91424,x91425),x91426),f319(x91423,x91426))+P1(f319(f319(f321(x91421),x91426),x91425))
% 28.73/28.52 [9164]~E(x91643,f319(f319(f143(x91641),x91645),x91646))+P1(f319(f319(f321(f931(f926(x91641),f926(x91641))),f319(f319(f244(f926(x91641),f926(x91641)),x91642),f319(f319(f126(x91641),x91642),x91643))),f139(x91641,x91644)))
% 28.73/28.52 [9168]E(f319(f70(x91681,x91682,x91683,x91684,x91685),x91686),f319(x91684,x91686))+~P1(f319(f319(f321(x91681),x91686),x91685))
% 28.73/28.52 [9169]E(f319(f70(x91691,x91692,x91693,x91694,x91695),x91696),f319(x91694,x91696))+~P1(f319(f319(f321(x91691),x91696),x91695))
% 28.73/28.52 [9404]~P35(x94041,x94042,x94043,x94045,x94046)+P35(x94041,x94042,x94043,f319(f319(f167(x94041),x94044),x94045),f319(f319(f167(x94042),x94044),x94046))
% 28.73/28.52 [9405]~P35(x94051,x94052,x94053,x94055,x94056)+P35(x94051,x94052,x94053,f319(f319(f130(x94051),x94054),x94055),f319(f319(f130(x94052),x94054),x94056))
% 28.73/28.52 [9668]E(f319(f302(x96681,x96682,f68(x96681,x96682,x96683,x96684,x96685)),x96686),f319(f302(x96681,x96682,x96683),x96686))+P1(f319(f319(f321(x96681),x96684),x96686))
% 28.73/28.52 [9671]E(f319(f319(f146(x96711,x96712),f68(x96711,x96712,x96713,x96714,x96715)),x96716),f319(f319(f146(x96711,x96712),x96713),x96716))+P1(f319(f319(f321(x96711),x96714),f319(f164(x96711),x96716)))
% 28.73/28.52 [9907]~P25(x99074,x99072,x99075,x99073,x99076,x99071)+E(f319(x99071,f180(f932(x99072,a923))),x99073)
% 28.73/28.52 [10160]~E(f319(x101604,f319(f243(x101601,x101603),x101605)),f319(x101606,f319(f243(x101601,x101603),x101605)))+E(f319(f250(x101601,x101602,x101603,x101603,x101604,f25(x101603)),x101605),f319(f250(x101601,x101602,x101603,x101603,x101606,f25(x101603)),x101605))
% 28.73/28.52 [10161]~E(f319(x101614,f319(f248(x101611,x101612),x101615)),f319(x101616,f319(f248(x101611,x101612),x101615)))+E(f319(f250(x101611,x101611,x101612,x101613,f25(x101611),x101614),x101615),f319(f250(x101611,x101611,x101612,x101613,f25(x101611),x101616),x101615))
% 28.73/28.52 [10215]~E(f319(f250(x102152,x102156,x102153,x102153,x102151,f25(x102153)),x102154),f319(f250(x102152,x102156,x102153,x102153,x102155,f25(x102153)),x102154))+E(f319(x102151,f319(f243(x102152,x102153),x102154)),f319(x102155,f319(f243(x102152,x102153),x102154)))
% 28.73/28.52 [10216]~E(f319(f250(x102162,x102162,x102163,x102166,f25(x102162),x102161),x102164),f319(f250(x102162,x102162,x102163,x102166,f25(x102162),x102165),x102164))+E(f319(x102161,f319(f248(x102162,x102163),x102164)),f319(x102165,f319(f248(x102162,x102163),x102164)))
% 28.73/28.52 [9060]P1(f319(f319(f321(x90601),x90602),x90603))+~P1(f319(f319(f321(f931(x90601,x90604)),f319(f319(f244(x90601,x90604),x90602),x90605)),f319(f319(f246(x90601,x90604),x90603),x90606)))
% 28.73/28.52 [9061]P1(f319(f319(f321(x90611),x90612),x90613))+~P1(f319(f319(f321(f931(x90611,x90614)),f319(f319(f244(x90611,x90614),x90612),x90615)),f319(f319(f246(x90611,x90614),x90613),x90616)))
% 28.73/28.52 [9062]P1(f319(f319(f321(x90621),x90622),x90623))+~P1(f319(f319(f321(f931(x90621,x90624)),f319(f319(f244(x90621,x90624),x90622),x90625)),f319(f319(f246(x90621,x90624),x90623),x90626)))
% 28.73/28.52 [9076]P1(f319(f319(f321(x90761),x90762),f319(x90763,x90764)))+~P1(f319(f319(f321(f931(x90765,x90761)),f319(f319(f244(x90765,x90761),x90764),x90762)),f319(f319(f246(x90765,x90761),x90766),x90763)))
% 28.73/28.52 [9077]P1(f319(f319(f321(x90771),x90772),f319(x90773,x90774)))+~P1(f319(f319(f321(f931(x90775,x90771)),f319(f319(f244(x90775,x90771),x90774),x90772)),f319(f319(f246(x90775,x90771),x90776),x90773)))
% 28.73/28.52 [9078]P1(f319(f319(f321(x90781),x90782),f319(x90783,x90784)))+~P1(f319(f319(f321(f931(x90785,x90781)),f319(f319(f244(x90785,x90781),x90784),x90782)),f319(f319(f246(x90785,x90781),x90786),x90783)))
% 28.73/28.52 [9523]P1(f319(f319(f321(f931(x95231,x95231)),f319(f319(f244(x95231,x95231),f319(x95232,x95233)),f319(x95232,x95234))),x95235))+~P1(f319(f319(f321(f931(x95236,x95236)),f319(f319(f244(x95236,x95236),x95233),x95234)),f319(f319(f280(x95231,x95236),x95235),x95232)))
% 28.73/28.52 [9543]~P1(f319(f319(f321(f931(x95434,x95434)),f319(f319(f244(x95434,x95434),f319(x95436,x95432)),f319(x95436,x95433))),x95435))+P1(f319(f319(f321(f931(x95431,x95431)),f319(f319(f244(x95431,x95431),x95432),x95433)),f319(f319(f280(x95434,x95431),x95435),x95436)))
% 28.73/28.52 [10219]E(f319(f319(f244(x102191,x102192),f666(x102193,x102194,x102195,x102196,x102192,x102191)),f667(x102193,x102194,x102195,x102196,x102192,x102191)),x102196)+~P1(f319(f319(f321(f931(x102191,x102192)),x102196),f319(f319(f281(x102191,x102195,x102192),x102194),x102193)))
% 28.73/28.52 [10224]~E(f319(x102243,f907(x102244,x102242,x102246,x102243,x102245,x102241)),f319(x102246,f907(x102244,x102242,x102246,x102243,x102245,x102241)))+E(f319(f319(f93(f932(x102241,a923)),f319(f303(x102241,x102242,x102243),x102244)),x102245),f319(f319(f93(f932(x102241,a923)),f319(f303(x102241,x102242,x102246),x102244)),x102245))
% 28.73/28.52 [10286]E(f319(f319(f93(f932(x102861,a923)),f319(f303(x102861,x102862,x102863),x102864)),x102865),f319(f319(f93(f932(x102861,a923)),f319(f303(x102861,x102862,x102866),x102864)),x102865))+P1(f319(f319(f321(x102861),f907(x102864,x102862,x102863,x102866,x102865,x102861)),x102865))
% 28.73/28.52 [10439]~P1(f319(f319(f321(f931(x104391,x104396)),x104395),f319(f319(f281(x104391,x104392,x104396),x104394),x104393)))+P1(f319(f319(f321(f931(x104391,x104392)),f319(f319(f244(x104391,x104392),f666(x104393,x104394,x104392,x104395,x104396,x104391)),f668(x104393,x104394,x104392,x104395,x104396,x104391))),x104394))
% 28.73/28.52 [10440]~P1(f319(f319(f321(f931(x104406,x104402)),x104405),f319(f319(f281(x104406,x104401,x104402),x104404),x104403)))+P1(f319(f319(f321(f931(x104401,x104402)),f319(f319(f244(x104401,x104402),f668(x104403,x104404,x104401,x104405,x104402,x104406)),f667(x104403,x104404,x104401,x104405,x104402,x104406))),x104403))
% 28.73/28.52 [10441]P13(x104411,x104412,x104413,x104414,x104415,x104416)+P1(f319(f319(f321(f931(x104412,x104412)),f319(f319(f244(x104412,x104412),f865(x104413,x104416,x104415,x104412,x104414,x104411)),f864(x104413,x104416,x104415,x104412,x104414,x104411))),x104415))
% 28.73/28.52 [10442]P13(x104421,x104422,x104423,x104424,x104425,x104426)+P1(f319(f319(f321(f931(x104421,x104421)),f319(f319(f244(x104421,x104421),f861(x104423,x104426,x104425,x104422,x104424,x104421)),f860(x104423,x104426,x104425,x104422,x104424,x104421))),x104424))
% 28.73/28.52 [7982]~P6(x79822)+E(f319(f319(f33(x79821,x79822),x79823),f319(f319(f7(x79821,x79824,x79822),x79825),x79826)),f319(f319(f319(f33(x79821,f932(x79824,x79822)),x79823),x79825),x79826))
% 28.73/28.52 [7983]~P6(x79832)+E(f319(f319(f34(x79831,x79832),x79833),f319(f319(f7(x79831,x79834,x79832),x79835),x79836)),f319(f319(f319(f34(x79831,f932(x79834,x79832)),x79833),x79835),x79836))
% 28.73/28.52 [8763]E(f319(f319(f33(x87631,f932(x87632,a923)),x87633),f319(f319(f8(f932(x87632,a923),f932(x87632,a923),x87631),f319(f301(x87632),x87634)),x87635)),f319(f319(f301(x87632),x87634),f319(f319(f33(x87631,f932(x87632,a923)),x87633),x87635)))+~P1(f319(f319(f321(x87631),x87636),x87633))
% 28.73/28.52 [8764]E(f319(f319(f34(x87641,f932(x87642,a923)),x87643),f319(f319(f8(f932(x87642,a923),f932(x87642,a923),x87641),f319(f301(x87642),x87644)),x87645)),f319(f319(f301(x87642),x87644),f319(f319(f34(x87641,f932(x87642,a923)),x87643),x87645)))+~P1(f319(f319(f321(x87641),x87646),x87643))
% 28.73/28.52 [9220]~P6(x92202)+E(f319(f319(f33(x92201,x92202),x92203),f319(f319(f8(f932(x92204,x92202),x92202,x92201),f319(f33(x92204,x92202),x92205)),f319(f7(x92204,x92201,x92202),x92206))),f319(f319(f33(x92204,x92202),x92205),f319(f319(f8(f932(x92201,x92202),x92202,x92204),f319(f33(x92201,x92202),x92203)),x92206)))
% 28.73/28.52 [9221]~P6(x92212)+E(f319(f319(f34(x92211,x92212),x92213),f319(f319(f8(f932(x92214,x92212),x92212,x92211),f319(f34(x92214,x92212),x92215)),f319(f7(x92214,x92211,x92212),x92216))),f319(f319(f34(x92214,x92212),x92215),f319(f319(f8(f932(x92211,x92212),x92212,x92214),f319(f34(x92211,x92212),x92213)),x92216)))
% 28.73/28.52 [9428]P1(f319(f319(f321(x94281),x94282),f319(f164(x94281),x94283)))+~P1(f319(f319(f321(f931(x94284,x94281)),f319(f319(f244(x94284,x94281),x94285),x94282)),f319(f164(f931(x94284,x94281)),f319(f319(f173(x94284,x94281),x94286),x94283))))
% 28.73/28.52 [9429]P1(f319(f319(f321(x94291),x94292),f319(f164(x94291),x94293)))+~P1(f319(f319(f321(f931(x94291,x94294)),f319(f319(f244(x94291,x94294),x94292),x94295)),f319(f164(f931(x94291,x94294)),f319(f319(f173(x94291,x94294),x94293),x94296))))
% 28.73/28.52 [9430]P1(f319(f319(f321(x94301),x94302),f319(f164(x94301),x94303)))+~P1(f319(f319(f321(f931(x94304,x94301)),f319(f319(f244(x94304,x94301),x94305),x94302)),f319(f164(f931(x94304,x94301)),f319(f319(f173(x94304,x94301),x94306),x94303))))
% 28.73/28.52 [9431]P1(f319(f319(f321(x94311),x94312),f319(f164(x94311),x94313)))+~P1(f319(f319(f321(f931(x94311,x94314)),f319(f319(f244(x94311,x94314),x94312),x94315)),f319(f164(f931(x94311,x94314)),f319(f319(f173(x94311,x94314),x94313),x94316))))
% 28.73/28.52 [9539]P1(f319(f319(f226(f932(x95391,a923)),f319(f277(x95392,x95391,x95393),x95394)),x95395))+~P1(f319(f319(f226(f932(f931(x95392,x95391),a923)),x95393),f319(f319(f246(x95392,x95391),x95396),f319(f16(f932(x95391,a923),x95392),x95395))))
% 28.73/28.52 [9544]~P27(x95444,x95442,x95445,f234(f932(x95444,a923)),f234(f932(x95442,a923)))+E(f319(f319(f34(x95441,f932(x95442,a923)),x95443),f319(f319(f8(f932(x95444,a923),f932(x95442,a923),x95441),f302(x95444,x95442,x95445)),x95446)),f319(f302(x95444,x95442,x95445),f319(f319(f34(x95441,f932(x95444,a923)),x95443),x95446)))
% 28.73/28.52 [9736]P1(f319(f319(f321(f931(f926(x97361),f926(x97361))),f319(f319(f244(f926(x97361),f926(x97361)),f319(f319(f143(x97361),x97362),x97363)),f319(f319(f143(x97361),x97364),x97365))),f139(x97361,x97366)))+~P1(f319(f319(f321(f931(x97361,x97361)),f319(f319(f244(x97361,x97361),x97362),x97364)),x97366))
% 28.73/28.52 [10214]E(f319(f319(f244(x102141,x102142),f604(x102143,x102144,x102145,x102142,x102141,x102146)),f607(x102143,x102144,x102145,x102142,x102141,x102146)),x102146)+P1(f319(f319(f321(x102145),x102144),f319(f319(f249(x102141,x102142,f932(x102145,a923)),x102143),x102146)))
% 28.73/28.52 [10221]E(f319(f319(f244(x102211,x102212),f605(x102213,x102214,x102212,x102211,x102215,x102216)),f606(x102213,x102214,x102212,x102211,x102215,x102216)),x102213)+~P1(f319(f319(f321(x102216),x102215),f319(f319(f249(x102211,x102212,f932(x102216,a923)),x102214),x102213)))
% 28.73/28.52 [10386]P1(f319(f319(f321(x103861),x103862),f319(f319(x103863,f605(x103864,x103863,x103865,x103866,x103862,x103861)),f606(x103864,x103863,x103865,x103866,x103862,x103861))))+~P1(f319(f319(f321(x103861),x103862),f319(f319(f249(x103866,x103865,f932(x103861,a923)),x103863),x103864)))
% 28.73/28.52 [10411]~P1(f319(f319(f321(x104111),x104112),f319(f319(x104115,f604(x104115,x104112,x104111,x104114,x104113,x104116)),f607(x104115,x104112,x104111,x104114,x104113,x104116))))+P1(f319(f319(f321(x104111),x104112),f319(f319(f249(x104113,x104114,f932(x104111,a923)),x104115),x104116)))
% 28.73/28.52 [8660]E(x86601,x86602)+E(f319(f319(f151(x86603,f319(f319(f151(x86603,x86604),x86601),x86605)),x86602),x86606),f319(f319(f151(x86603,f319(f319(f151(x86603,x86604),x86602),x86606)),x86601),x86605))
% 28.73/28.52 [9798]~P1(f319(f319(f321(x97983),x97986),x97985))+E(f319(f319(f301(x97981),x97982),f319(f302(x97983,x97981,x97984),f319(f319(f23(f932(x97983,a923)),x97985),f319(f319(f301(x97983),x97986),f180(f932(x97983,a923)))))),f319(f302(x97983,x97981,f68(x97983,x97981,x97984,x97986,x97982)),x97985))
% 28.73/28.52 [9299]~P1(f319(f319(x92994,x92995),x92996))+P1(f319(f319(f319(f319(f102(f932(x92991,f932(x92992,a923))),x92993),x92994),x92995),x92996))
% 28.73/28.52 [9300]~P1(f319(f319(x93004,x93005),x93006))+P1(f319(f319(f319(f319(f102(f932(x93001,f932(x93002,a923))),x93003),x93004),x93005),x93006))
% 28.73/28.52 [9301]~P1(f319(f319(x93013,x93015),x93016))+P1(f319(f319(f319(f319(f102(f932(x93011,f932(x93012,a923))),x93013),x93014),x93015),x93016))
% 28.73/28.52 [9302]~P1(f319(f319(x93023,x93025),x93026))+P1(f319(f319(f319(f319(f102(f932(x93021,f932(x93022,a923))),x93023),x93024),x93025),x93026))
% 28.73/28.52 [9593]P1(f319(f319(x95931,x95932),x95933))+~P1(f319(f319(f319(f319(f93(f932(x95934,f932(x95935,a923))),x95936),x95931),x95932),x95933))
% 28.73/28.52 [9594]P1(f319(f319(x95941,x95942),x95943))+~P1(f319(f319(f319(f319(f93(f932(x95944,f932(x95945,a923))),x95941),x95946),x95942),x95943))
% 28.73/28.52 [9595]P1(f319(f319(x95951,x95952),x95953))+~P1(f319(f319(f319(f319(f93(f932(x95954,f932(x95955,a923))),x95956),x95951),x95952),x95953))
% 28.73/28.52 [9596]P1(f319(f319(x95961,x95962),x95963))+~P1(f319(f319(f319(f319(f93(f932(x95964,f932(x95965,a923))),x95961),x95966),x95962),x95963))
% 28.73/28.52 [10050]~P79(x100502)+E(f319(f319(f6(x100501,x100502),f319(f319(f7(x100501,f932(x100503,a923),x100502),f319(f319(f8(f932(x100503,x100502),f932(f932(x100503,a923),x100502),x100501),f6(x100503,x100502)),x100504)),x100505)),x100506),f319(f319(f6(f931(x100501,x100503),x100502),f319(f249(x100501,x100503,x100502),x100504)),f319(f319(f246(x100501,x100503),x100506),f319(f16(f932(x100503,a923),x100501),x100505))))
% 28.73/28.52 [10051]~P78(x100512)+E(f319(f319(f9(x100511,x100512),f319(f319(f7(x100511,f932(x100513,a923),x100512),f319(f319(f8(f932(x100513,x100512),f932(f932(x100513,a923),x100512),x100511),f9(x100513,x100512)),x100514)),x100515)),x100516),f319(f319(f9(f931(x100511,x100513),x100512),f319(f249(x100511,x100513,x100512),x100514)),f319(f319(f246(x100511,x100513),x100516),f319(f16(f932(x100513,a923),x100511),x100515))))
% 28.73/28.52 [10185]~P79(x101852)+E(f319(f319(f6(x101851,x101852),f319(f319(f7(x101851,f932(x101853,a923),x101852),f319(f319(f8(f932(x101853,x101852),f932(f932(x101853,a923),x101852),x101851),f6(x101853,x101852)),f319(f7(x101853,x101851,x101852),x101854))),x101855)),x101856),f319(f319(f6(x101853,x101852),f319(f319(f7(x101853,f932(x101851,a923),x101852),f319(f319(f8(f932(x101851,x101852),f932(f932(x101851,a923),x101852),x101853),f6(x101851,x101852)),x101854)),x101856)),x101855))
% 28.73/28.52 [10506]~P1(f319(f319(f321(f931(x105061,x105062)),f319(f319(f244(x105061,x105062),x105065),x105066)),f319(f319(f102(f932(f931(x105061,x105062),a923)),x105063),x105064)))+P1(f319(f319(f319(f319(f102(f932(x105061,f932(x105062,a923))),f319(f319(f7(x105061,f932(f931(x105061,x105062),a923),f932(x105062,a923)),f319(f319(f8(f932(x105062,f932(f932(f931(x105061,x105062),a923),a923)),f932(f932(f931(x105061,x105062),a923),f932(x105062,a923)),x105061),f7(x105062,f932(f931(x105061,x105062),a923),a923)),f319(f319(f8(f932(x105062,f931(x105061,x105062)),f932(x105062,f932(f932(f931(x105061,x105062),a923),a923)),x105061),f319(f8(f931(x105061,x105062),f932(f932(f931(x105061,x105062),a923),a923),x105062),f321(f931(x105061,x105062)))),f244(x105061,x105062)))),x105063)),f319(f319(f7(x105061,f932(f931(x105061,x105062),a923),f932(x105062,a923)),f319(f319(f8(f932(x105062,f932(f932(f931(x105061,x105062),a923),a923)),f932(f932(f931(x105061,x105062),a923),f932(x105062,a923)),x105061),f7(x105062,f932(f931(x105061,x105062),a923),a923)),f319(f319(f8(f932(x105062,f931(x105061,x105062)),f932(x105062,f932(f932(f931(x105061,x105062),a923),a923)),x105061),f319(f8(f931(x105061,x105062),f932(f932(f931(x105061,x105062),a923),a923),x105062),f321(f931(x105061,x105062)))),f244(x105061,x105062)))),x105064)),x105065),x105066))
% 28.73/28.52 [10507]~P1(f319(f319(f321(f931(x105071,x105072)),f319(f319(f244(x105071,x105072),x105075),x105076)),f319(f319(f93(f932(f931(x105071,x105072),a923)),x105073),x105074)))+P1(f319(f319(f319(f319(f93(f932(x105071,f932(x105072,a923))),f319(f319(f7(x105071,f932(f931(x105071,x105072),a923),f932(x105072,a923)),f319(f319(f8(f932(x105072,f932(f932(f931(x105071,x105072),a923),a923)),f932(f932(f931(x105071,x105072),a923),f932(x105072,a923)),x105071),f7(x105072,f932(f931(x105071,x105072),a923),a923)),f319(f319(f8(f932(x105072,f931(x105071,x105072)),f932(x105072,f932(f932(f931(x105071,x105072),a923),a923)),x105071),f319(f8(f931(x105071,x105072),f932(f932(f931(x105071,x105072),a923),a923),x105072),f321(f931(x105071,x105072)))),f244(x105071,x105072)))),x105073)),f319(f319(f7(x105071,f932(f931(x105071,x105072),a923),f932(x105072,a923)),f319(f319(f8(f932(x105072,f932(f932(f931(x105071,x105072),a923),a923)),f932(f932(f931(x105071,x105072),a923),f932(x105072,a923)),x105071),f7(x105072,f932(f931(x105071,x105072),a923),a923)),f319(f319(f8(f932(x105072,f931(x105071,x105072)),f932(x105072,f932(f932(f931(x105071,x105072),a923),a923)),x105071),f319(f8(f931(x105071,x105072),f932(f932(f931(x105071,x105072),a923),a923),x105072),f321(f931(x105071,x105072)))),f244(x105071,x105072)))),x105074)),x105075),x105076))
% 28.73/28.52 [10517]P1(f319(f319(f321(f931(x105171,x105172)),f319(f319(f244(x105171,x105172),x105173),x105174)),f319(f319(f102(f932(f931(x105171,x105172),a923)),x105175),x105176)))+~P1(f319(f319(f319(f319(f102(f932(x105171,f932(x105172,a923))),f319(f319(f7(x105171,f932(f931(x105171,x105172),a923),f932(x105172,a923)),f319(f319(f8(f932(x105172,f932(f932(f931(x105171,x105172),a923),a923)),f932(f932(f931(x105171,x105172),a923),f932(x105172,a923)),x105171),f7(x105172,f932(f931(x105171,x105172),a923),a923)),f319(f319(f8(f932(x105172,f931(x105171,x105172)),f932(x105172,f932(f932(f931(x105171,x105172),a923),a923)),x105171),f319(f8(f931(x105171,x105172),f932(f932(f931(x105171,x105172),a923),a923),x105172),f321(f931(x105171,x105172)))),f244(x105171,x105172)))),x105175)),f319(f319(f7(x105171,f932(f931(x105171,x105172),a923),f932(x105172,a923)),f319(f319(f8(f932(x105172,f932(f932(f931(x105171,x105172),a923),a923)),f932(f932(f931(x105171,x105172),a923),f932(x105172,a923)),x105171),f7(x105172,f932(f931(x105171,x105172),a923),a923)),f319(f319(f8(f932(x105172,f931(x105171,x105172)),f932(x105172,f932(f932(f931(x105171,x105172),a923),a923)),x105171),f319(f8(f931(x105171,x105172),f932(f932(f931(x105171,x105172),a923),a923),x105172),f321(f931(x105171,x105172)))),f244(x105171,x105172)))),x105176)),x105173),x105174))
% 28.73/28.52 [10518]P1(f319(f319(f321(f931(x105181,x105182)),f319(f319(f244(x105181,x105182),x105183),x105184)),f319(f319(f93(f932(f931(x105181,x105182),a923)),x105185),x105186)))+~P1(f319(f319(f319(f319(f93(f932(x105181,f932(x105182,a923))),f319(f319(f7(x105181,f932(f931(x105181,x105182),a923),f932(x105182,a923)),f319(f319(f8(f932(x105182,f932(f932(f931(x105181,x105182),a923),a923)),f932(f932(f931(x105181,x105182),a923),f932(x105182,a923)),x105181),f7(x105182,f932(f931(x105181,x105182),a923),a923)),f319(f319(f8(f932(x105182,f931(x105181,x105182)),f932(x105182,f932(f932(f931(x105181,x105182),a923),a923)),x105181),f319(f8(f931(x105181,x105182),f932(f932(f931(x105181,x105182),a923),a923),x105182),f321(f931(x105181,x105182)))),f244(x105181,x105182)))),x105185)),f319(f319(f7(x105181,f932(f931(x105181,x105182),a923),f932(x105182,a923)),f319(f319(f8(f932(x105182,f932(f932(f931(x105181,x105182),a923),a923)),f932(f932(f931(x105181,x105182),a923),f932(x105182,a923)),x105181),f7(x105182,f932(f931(x105181,x105182),a923),a923)),f319(f319(f8(f932(x105182,f931(x105181,x105182)),f932(x105182,f932(f932(f931(x105181,x105182),a923),a923)),x105181),f319(f8(f931(x105181,x105182),f932(f932(f931(x105181,x105182),a923),a923),x105182),f321(f931(x105181,x105182)))),f244(x105181,x105182)))),x105186)),x105183),x105184))
% 28.73/28.52 [10500]~P1(f319(f319(f321(f931(x105002,x105003)),f319(f319(f244(x105002,x105003),x105005),x105006)),f319(f319(f33(x105001,f932(f931(x105002,x105003),a923)),f234(f932(x105001,a923))),x105004)))+P1(f319(f319(f319(f319(f33(x105001,f932(x105002,f932(x105003,a923))),f234(f932(x105001,a923))),f319(f319(f8(f932(f931(x105002,x105003),a923),f932(x105002,f932(x105003,a923)),x105001),f319(f7(x105002,f932(f931(x105002,x105003),a923),f932(x105003,a923)),f319(f319(f8(f932(x105003,f932(f932(f931(x105002,x105003),a923),a923)),f932(f932(f931(x105002,x105003),a923),f932(x105003,a923)),x105002),f7(x105003,f932(f931(x105002,x105003),a923),a923)),f319(f319(f8(f932(x105003,f931(x105002,x105003)),f932(x105003,f932(f932(f931(x105002,x105003),a923),a923)),x105002),f319(f8(f931(x105002,x105003),f932(f932(f931(x105002,x105003),a923),a923),x105003),f321(f931(x105002,x105003)))),f244(x105002,x105003))))),x105004)),x105005),x105006))
% 28.73/28.52 [10501]~P1(f319(f319(f321(f931(x105012,x105013)),f319(f319(f244(x105012,x105013),x105015),x105016)),f319(f319(f34(x105011,f932(f931(x105012,x105013),a923)),f234(f932(x105011,a923))),x105014)))+P1(f319(f319(f319(f319(f34(x105011,f932(x105012,f932(x105013,a923))),f234(f932(x105011,a923))),f319(f319(f8(f932(f931(x105012,x105013),a923),f932(x105012,f932(x105013,a923)),x105011),f319(f7(x105012,f932(f931(x105012,x105013),a923),f932(x105013,a923)),f319(f319(f8(f932(x105013,f932(f932(f931(x105012,x105013),a923),a923)),f932(f932(f931(x105012,x105013),a923),f932(x105013,a923)),x105012),f7(x105013,f932(f931(x105012,x105013),a923),a923)),f319(f319(f8(f932(x105013,f931(x105012,x105013)),f932(x105013,f932(f932(f931(x105012,x105013),a923),a923)),x105012),f319(f8(f931(x105012,x105013),f932(f932(f931(x105012,x105013),a923),a923),x105013),f321(f931(x105012,x105013)))),f244(x105012,x105013))))),x105014)),x105015),x105016))
% 28.73/28.52 [10511]P1(f319(f319(f321(f931(x105111,x105112)),f319(f319(f244(x105111,x105112),x105113),x105114)),f319(f319(f33(x105115,f932(f931(x105111,x105112),a923)),f234(f932(x105115,a923))),x105116)))+~P1(f319(f319(f319(f319(f33(x105115,f932(x105111,f932(x105112,a923))),f234(f932(x105115,a923))),f319(f319(f8(f932(f931(x105111,x105112),a923),f932(x105111,f932(x105112,a923)),x105115),f319(f7(x105111,f932(f931(x105111,x105112),a923),f932(x105112,a923)),f319(f319(f8(f932(x105112,f932(f932(f931(x105111,x105112),a923),a923)),f932(f932(f931(x105111,x105112),a923),f932(x105112,a923)),x105111),f7(x105112,f932(f931(x105111,x105112),a923),a923)),f319(f319(f8(f932(x105112,f931(x105111,x105112)),f932(x105112,f932(f932(f931(x105111,x105112),a923),a923)),x105111),f319(f8(f931(x105111,x105112),f932(f932(f931(x105111,x105112),a923),a923),x105112),f321(f931(x105111,x105112)))),f244(x105111,x105112))))),x105116)),x105113),x105114))
% 28.73/28.52 [10512]P1(f319(f319(f321(f931(x105121,x105122)),f319(f319(f244(x105121,x105122),x105123),x105124)),f319(f319(f34(x105125,f932(f931(x105121,x105122),a923)),f234(f932(x105125,a923))),x105126)))+~P1(f319(f319(f319(f319(f34(x105125,f932(x105121,f932(x105122,a923))),f234(f932(x105125,a923))),f319(f319(f8(f932(f931(x105121,x105122),a923),f932(x105121,f932(x105122,a923)),x105125),f319(f7(x105121,f932(f931(x105121,x105122),a923),f932(x105122,a923)),f319(f319(f8(f932(x105122,f932(f932(f931(x105121,x105122),a923),a923)),f932(f932(f931(x105121,x105122),a923),f932(x105122,a923)),x105121),f7(x105122,f932(f931(x105121,x105122),a923),a923)),f319(f319(f8(f932(x105122,f931(x105121,x105122)),f932(x105122,f932(f932(f931(x105121,x105122),a923),a923)),x105121),f319(f8(f931(x105121,x105122),f932(f932(f931(x105121,x105122),a923),a923),x105122),f321(f931(x105121,x105122)))),f244(x105121,x105122))))),x105126)),x105123),x105124))
% 28.73/28.52 [7662]E(f319(x76621,f319(x76622,x76623)),f319(x76624,x76623))+~E(f319(f66(x76625,x76626,x76627,x76621),x76622),x76624)
% 28.73/28.52 [9814]E(x98141,x98142)+E(f68(x98143,x98144,f68(x98143,x98144,x98145,x98141,x98146),x98142,x98147),f68(x98143,x98144,f68(x98143,x98144,x98145,x98142,x98147),x98141,x98146))
% 28.73/28.52 [9906]~P24(x99063,x99064,x99061,x99065,x99066,x99067)+E(f319(f319(x99061,x99062),x99062),x99062)
% 28.73/28.52 [6224]~E(f319(f319(f146(x62241,x62245),x62246),x62242),f319(f319(f146(x62243,x62245),x62247),x62244))+E(f319(f181(f926(x62241)),x62242),f319(f181(f926(x62243)),x62244))
% 28.73/28.52 [8693]E(f319(x86931,f319(x86932,x86933)),f319(x86934,x86933))+~E(f319(f66(x86935,x86936,x86937,x86931),x86932),f319(f66(x86936,x86936,x86937,f25(x86936)),x86934))
% 28.73/28.52 [9051]~P35(x90514,x90515,x90511,f319(f319(f143(x90514),x90512),x90516),f319(f319(f143(x90515),x90513),x90517))+P1(f319(f319(x90511,x90512),x90513))
% 28.73/28.52 [9437]P35(x94371,x94372,x94373,x94374,x94375)+~P35(x94371,x94372,x94373,f319(f319(f143(x94371),x94376),x94374),f319(f319(f143(x94372),x94377),x94375))
% 28.73/28.52 [10086]P1(f319(f319(x100861,x100862),f563(x100863,x100862,x100864,x100861)))+~P1(f319(f319(f245(x100865,x100866,x100867,x100861,x100864),x100862),x100863))
% 28.73/28.52 [10110]P1(f319(f319(x101101,f563(x101102,x101103,x101101,x101104)),x101102))+~P1(f319(f319(f245(x101105,x101106,x101107,x101104,x101101),x101103),x101102))
% 28.73/28.52 [9173]~P22(x91736,x91731,x91733,x91737)+E(f319(f66(x91731,x91731,x91732,f319(x91733,x91734)),f319(f66(x91731,x91731,x91732,f319(x91733,x91734)),x91735)),f319(f66(x91731,x91731,x91732,f319(x91733,x91734)),x91735))
% 28.73/28.52 [9547]~P35(x95473,x95472,x95474,f319(f319(f146(x95471,x95473),x95475),x95476),x95477)+P35(x95471,x95472,f319(f319(f8(x95473,f932(x95472,a923),x95471),x95474),x95475),x95476,x95477)
% 28.73/28.52 [9571]P35(x95711,x95712,x95713,f319(f319(f146(x95714,x95711),x95715),x95716),x95717)+~P35(x95714,x95712,f319(f319(f8(x95711,f932(x95712,a923),x95714),x95713),x95715),x95716,x95717)
% 28.73/28.52 [9172]~P1(f319(f319(f321(x91721),x91722),f319(f319(x91725,x91726),x91727)))+P1(f319(f319(f321(x91721),x91722),f319(f319(f249(x91723,x91724,f932(x91721,a923)),x91725),f319(f319(f244(x91723,x91724),x91726),x91727))))
% 28.73/28.52 [9462]P1(f319(f319(f319(x94621,x94622),x94623),x94624))+~P1(f319(f319(f319(f249(x94625,x94626,f932(x94627,a923)),x94621),f319(f319(f244(x94625,x94626),x94622),x94623)),x94624))
% 28.73/28.52 [9610]P1(f319(f319(f321(x96101),f319(f319(x96102,x96103),x96104)),f319(f302(f931(x96105,x96106),x96101,f319(f249(x96105,x96106,x96101),x96102)),x96107)))+~P1(f319(f319(f321(f931(x96105,x96106)),f319(f319(f244(x96105,x96106),x96103),x96104)),x96107))
% 28.73/28.52 [9961]P1(f319(f319(f321(f931(f926(x99611),f926(x99611))),f319(f319(f244(f926(x99611),f926(x99611)),f319(f319(f126(x99611),x99612),f319(f319(f143(x99611),x99613),x99614))),f319(f319(f126(x99611),x99612),f319(f319(f143(x99611),x99615),x99616)))),f139(x99611,x99617)))+~P1(f319(f319(f321(f931(x99611,x99611)),f319(f319(f244(x99611,x99611),x99613),x99615)),x99617))
% 28.73/28.52 [10033]~P35(x100331,x100333,x100334,x100336,f319(f319(f146(x100332,x100333),x100335),x100337))+P35(x100331,x100332,f319(f319(f7(x100331,f932(x100332,x100333),f932(x100332,a923)),f319(f319(f8(f932(x100333,a923),f932(f932(x100332,x100333),f932(x100332,a923)),x100331),f8(x100333,a923,x100332)),x100334)),x100335),x100336,x100337)
% 28.73/28.52 [10114]P35(x101141,x101142,x101143,x101144,f319(f319(f146(x101145,x101142),x101146),x101147))+~P35(x101141,x101145,f319(f319(f7(x101141,f932(x101145,x101142),f932(x101145,a923)),f319(f319(f8(f932(x101142,a923),f932(f932(x101145,x101142),f932(x101145,a923)),x101141),f8(x101142,a923,x101145)),x101143)),x101146),x101144,x101147)
% 28.73/28.52 [10426]P1(f319(f319(f321(x104261),f465(x104262,x104263,x104264,x104265,x104266,x104267,x104261)),x104265))+P1(f319(f319(f319(f319(f34(x104261,f932(x104267,f932(x104266,a923))),x104265),x104264),x104263),x104262))
% 28.73/28.52 [10427]P1(f319(f319(f321(x104271),f507(x104272,x104273,x104274,x104275,x104276,x104277,x104271)),x104277))+P1(f319(f319(f319(f319(f34(x104271,f932(x104273,f932(x104272,a923))),x104277),x104276),x104275),x104274))
% 28.73/28.52 [10428]P1(f319(f319(f321(x104281),f450(x104282,x104283,x104284,x104285,x104286,x104287,x104281)),x104285))+~P1(f319(f319(f319(f319(f33(x104281,f932(x104287,f932(x104286,a923))),x104285),x104284),x104283),x104282))
% 28.73/28.52 [10429]P1(f319(f319(f321(x104291),f497(x104292,x104293,x104294,x104295,x104296,x104297,x104291)),x104295))+~P1(f319(f319(f319(f319(f33(x104291,f932(x104297,f932(x104296,a923))),x104295),x104294),x104293),x104292))
% 28.73/28.52 [10463]P1(f319(f319(f319(x104631,f450(x104632,x104633,x104631,x104634,x104635,x104636,x104637)),x104633),x104632))+~P1(f319(f319(f319(f319(f33(x104637,f932(x104636,f932(x104635,a923))),x104634),x104631),x104633),x104632))
% 28.73/28.52 [10464]P1(f319(f319(f319(x104641,f497(x104642,x104643,x104641,x104644,x104645,x104646,x104647)),x104643),x104642))+~P1(f319(f319(f319(f319(f33(x104647,f932(x104646,f932(x104645,a923))),x104644),x104641),x104643),x104642))
% 28.73/28.52 [10479]~P1(f319(f319(f319(x104795,f465(x104797,x104796,x104795,x104794,x104793,x104792,x104791)),x104796),x104797))+P1(f319(f319(f319(f319(f34(x104791,f932(x104792,f932(x104793,a923))),x104794),x104795),x104796),x104797))
% 28.73/28.52 [10480]~P1(f319(f319(f319(x104805,f507(x104803,x104802,x104807,x104806,x104805,x104804,x104801)),x104806),x104807))+P1(f319(f319(f319(f319(f34(x104801,f932(x104802,f932(x104803,a923))),x104804),x104805),x104806),x104807))
% 28.73/28.52 [10499]~P1(f319(f319(f321(f931(x104991,x104993)),f319(f319(f244(x104991,x104993),x104996),x104997)),f319(f319(f281(x104991,x104992,x104993),x104994),x104995)))+P1(f319(f319(f245(x104991,x104992,x104993,f319(f319(f7(x104991,f932(f931(x104991,x104992),a923),f932(x104992,a923)),f319(f319(f8(f932(x104992,f932(f932(f931(x104991,x104992),a923),a923)),f932(f932(f931(x104991,x104992),a923),f932(x104992,a923)),x104991),f7(x104992,f932(f931(x104991,x104992),a923),a923)),f319(f319(f8(f932(x104992,f931(x104991,x104992)),f932(x104992,f932(f932(f931(x104991,x104992),a923),a923)),x104991),f319(f8(f931(x104991,x104992),f932(f932(f931(x104991,x104992),a923),a923),x104992),f321(f931(x104991,x104992)))),f244(x104991,x104992)))),x104994),f319(f319(f7(x104992,f932(f931(x104992,x104993),a923),f932(x104993,a923)),f319(f319(f8(f932(x104993,f932(f932(f931(x104992,x104993),a923),a923)),f932(f932(f931(x104992,x104993),a923),f932(x104993,a923)),x104992),f7(x104993,f932(f931(x104992,x104993),a923),a923)),f319(f319(f8(f932(x104993,f931(x104992,x104993)),f932(x104993,f932(f932(f931(x104992,x104993),a923),a923)),x104992),f319(f8(f931(x104992,x104993),f932(f932(f931(x104992,x104993),a923),a923),x104993),f321(f931(x104992,x104993)))),f244(x104992,x104993)))),x104995)),x104996),x104997))
% 28.73/28.52 [10510]P1(f319(f319(f321(f931(x105101,x105102)),f319(f319(f244(x105101,x105102),x105103),x105104)),f319(f319(f281(x105101,x105105,x105102),x105106),x105107)))+~P1(f319(f319(f245(x105101,x105105,x105102,f319(f319(f7(x105101,f932(f931(x105101,x105105),a923),f932(x105105,a923)),f319(f319(f8(f932(x105105,f932(f932(f931(x105101,x105105),a923),a923)),f932(f932(f931(x105101,x105105),a923),f932(x105105,a923)),x105101),f7(x105105,f932(f931(x105101,x105105),a923),a923)),f319(f319(f8(f932(x105105,f931(x105101,x105105)),f932(x105105,f932(f932(f931(x105101,x105105),a923),a923)),x105101),f319(f8(f931(x105101,x105105),f932(f932(f931(x105101,x105105),a923),a923),x105105),f321(f931(x105101,x105105)))),f244(x105101,x105105)))),x105106),f319(f319(f7(x105105,f932(f931(x105105,x105102),a923),f932(x105102,a923)),f319(f319(f8(f932(x105102,f932(f932(f931(x105105,x105102),a923),a923)),f932(f932(f931(x105105,x105102),a923),f932(x105102,a923)),x105105),f7(x105102,f932(f931(x105105,x105102),a923),a923)),f319(f319(f8(f932(x105102,f931(x105105,x105102)),f932(x105102,f932(f932(f931(x105105,x105102),a923),a923)),x105105),f319(f8(f931(x105105,x105102),f932(f932(f931(x105105,x105102),a923),a923),x105102),f321(f931(x105105,x105102)))),f244(x105105,x105102)))),x105107)),x105103),x105104))
% 28.73/28.52 [10438]~P143(x104382)+E(f319(f319(f6(x104381,x104382),f319(f319(f7(x104381,f932(x104383,a923),x104382),f319(f319(f8(f932(x104383,x104382),f932(f932(x104383,a923),x104382),x104381),f6(x104383,x104382)),f319(f319(f7(x104381,f932(x104383,x104382),f932(x104383,x104382)),f319(f319(f8(f932(x104382,x104382),f932(f932(x104383,x104382),f932(x104383,x104382)),x104381),f8(x104382,x104382,x104383)),f319(f319(f8(x104382,f932(x104382,x104382),x104381),f75(x104382)),x104384))),x104385))),x104386)),x104387),f319(f319(f75(x104382),f319(f319(f6(x104381,x104382),x104384),x104387)),f319(f319(f6(x104383,x104382),x104385),x104386)))
% 28.73/28.52 [9495]~P21(x94957,x94951,x94953,x94958)+E(f319(f66(x94951,x94951,x94952,f319(x94953,x94954)),f319(f66(x94951,x94951,x94952,f319(x94953,x94955)),x94956)),f319(f66(x94951,x94951,x94952,f319(x94953,x94955)),f319(f66(x94951,x94951,x94952,f319(x94953,x94954)),x94956)))
% 28.73/28.52 [10504]E(f319(f319(f244(x105041,x105042),f319(x105043,f586(x105044,x105045,x105043,x105046,x105047,x105048,x105042,x105041))),f319(x105045,f587(x105044,x105045,x105043,x105046,x105047,x105048,x105042,x105041))),x105048)+~P1(f319(f319(f321(f931(x105041,x105042)),x105048),f319(f302(f931(x105047,x105046),f931(x105041,x105042),f250(x105047,x105041,x105046,x105042,x105043,x105045)),x105044)))
% 28.73/28.52 [10523]~P1(f319(f319(f321(f931(x105238,x105237)),x105236),f319(f302(f931(x105231,x105232),f931(x105238,x105237),f250(x105231,x105238,x105232,x105237,x105235,x105234)),x105233)))+P1(f319(f319(f321(f931(x105231,x105232)),f319(f319(f244(x105231,x105232),f586(x105233,x105234,x105235,x105232,x105231,x105236,x105237,x105238)),f587(x105233,x105234,x105235,x105232,x105231,x105236,x105237,x105238))),x105233))
% 28.73/28.52 [9948]P1(f319(f319(f321(f931(f931(x99481,x99482),f931(x99481,x99482))),f319(f319(f244(f931(x99481,x99482),f931(x99481,x99482)),f319(f319(f244(x99481,x99482),x99483),x99484)),f319(f319(f244(x99481,x99482),x99485),x99486))),f312(x99481,x99482,x99487,x99488)))+~P1(f319(f319(f321(f931(x99481,x99481)),f319(f319(f244(x99481,x99481),x99483),x99485)),x99487))
% 28.73/28.52 [10493]E(f319(f134(x104931,x104932,f319(f7(x104932,x104931,x104931),x104933),f319(x104934,x104935)),x104936),f319(x104934,f319(f134(x104937,x104932,f319(f7(x104932,x104937,x104937),x104938),x104935),x104936)))+P1(f319(f319(f321(x104932),f754(x104935,x104938,x104934,x104933,x104937,x104931,x104936,x104932)),f319(f164(x104932),x104936)))
% 28.73/28.52 [10513]~E(f319(f66(x105131,x105131,x105137,f319(x105133,f754(x105135,x105138,x105134,x105133,x105137,x105131,x105136,x105132))),x105134),f319(f66(x105137,x105131,x105137,x105134),f319(x105138,f754(x105135,x105138,x105134,x105133,x105137,x105131,x105136,x105132))))+E(f319(f134(x105131,x105132,f319(f7(x105132,x105131,x105131),x105133),f319(x105134,x105135)),x105136),f319(x105134,f319(f134(x105137,x105132,f319(f7(x105132,x105137,x105137),x105138),x105135),x105136)))
% 28.73/28.52 [8697]E(f319(x86971,f319(x86972,x86973)),f319(x86974,f319(x86975,x86973)))+~E(f319(f66(x86976,x86977,x86978,x86971),x86972),f319(f66(x86979,x86977,x86978,x86974),x86975))
% 28.73/28.52 [8698]E(f319(x86981,f319(x86982,x86983)),f319(x86984,f319(x86985,x86983)))+~E(f319(f66(x86986,x86987,x86988,x86981),x86982),f319(f66(x86989,x86987,x86988,x86984),x86985))
% 28.73/28.52 [10351]P1(f319(f319(f321(f931(x103511,x103512)),f319(f319(f244(x103511,x103512),f319(x103513,x103514)),f319(x103515,x103516))),f319(f302(f931(x103517,x103518),f931(x103511,x103512),f250(x103517,x103511,x103518,x103512,x103513,x103515)),x103519)))+~P1(f319(f319(f321(f931(x103517,x103518)),f319(f319(f244(x103517,x103518),x103514),x103516)),x103519))
% 28.73/28.52 [8996]~E(f319(x89964,f319(x89965,x89966)),f319(x89969,f319(x899610,x899611)))+E(f319(f319(f66(x89961,x89962,x89963,x89964),x89965),x89966),f319(f319(f66(x89967,x89962,x89968,x89969),x899610),x899611))
% 28.73/28.52 [9581]~P21(x95818,x95819,x958110,x958111)+E(f319(f66(x95811,x95812,x95813,x95814),f319(f66(x95815,x95811,x95813,x95816),x95817)),f319(f66(x95815,x95812,x95813,f319(f66(x95811,x95812,x95815,x95814),x95816)),x95817))
% 28.73/28.52 [4793]~P4(x47931)+~P108(x47931)+E(f93(x47931),f224(x47931))
% 28.73/28.52 [4794]~P4(x47941)+~P107(x47941)+E(f102(x47941),f225(x47941))
% 28.73/28.52 [5039]~P126(x50391)+~P99(x50391)+E(f319(f69(x50391),f319(f95(x50391),a89)),f72(x50391))
% 28.73/28.52 [5330]E(x53301,f2(a1))+E(f76(a1,x53301),f319(f73(a1),f72(a1)))+P1(f319(f319(f227(a1),f2(a1)),x53301))
% 28.73/28.52 [5535]E(x55351,f2(a1))+E(f76(a1,x55351),f72(a1))+~P1(f319(f319(f227(a1),f2(a1)),x55351))
% 28.73/28.52 [6856]~P42(x68561)+~P1(f319(f55(a1),x68561))+P1(f319(f55(a925),f319(f302(a1,a925,a96),x68561)))
% 28.73/28.52 [7221]E(f41(f72(a1),f319(f95(a1),x72211)),f319(f319(f244(a1,a1),f2(a1)),f72(a1)))+~P1(f319(f319(f227(a1),f2(a1)),f319(f95(a1),x72211)))+~P1(f319(f319(f227(a1),f72(a1)),f319(f95(a1),x72211)))
% 28.73/28.52 [7563]~P42(x75631)+P1(f319(f55(a1),x75631))+~P1(f319(f55(a925),f319(f302(a1,a925,a96),x75631)))
% 28.73/28.52 [8399]E(f319(f319(f244(a1,a1),f319(f95(a1),a89)),f319(f319(f74(a1),f72(a1)),f319(f95(a1),x83991))),f44(f72(a1),f319(f95(a1),x83991)))+~P1(f319(f319(f227(a1),f2(a1)),f319(f95(a1),x83991)))+~P1(f319(f319(f226(a1),f2(a1)),f319(f319(f74(a1),f72(a1)),f319(f95(a1),x83991))))
% 28.73/28.52 [10239]E(f319(f37(f319(f95(a1),x102391)),f41(f72(a1),f319(f319(f75(a1),f319(f95(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),f319(f95(a1),x102391)))),f41(f72(a1),f319(f95(a1),x102391)))+~P1(f319(f319(f227(a1),f2(a1)),f319(f95(a1),x102391)))+P1(f319(f319(f227(a1),f72(a1)),f319(f95(a1),x102391)))
% 28.73/28.52 [10245]E(f319(f37(f319(f95(a1),x102451)),f44(f72(a1),f319(f319(f75(a1),f319(f95(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),f319(f95(a1),x102451)))),f44(f72(a1),f319(f95(a1),x102451)))+~P1(f319(f319(f227(a1),f2(a1)),f319(f95(a1),x102451)))+P1(f319(f319(f226(a1),f2(a1)),f319(f319(f74(a1),f72(a1)),f319(f95(a1),x102451))))
% 28.73/28.52 [9905]E(x99051,f180(f932(f931(a925,a925),a923)))+~P1(f319(f55(f931(a925,a925)),x99051))+P1(f319(f319(f321(f931(f932(f931(a925,a925),a923),f932(f931(a925,a925),a923))),f319(f319(f244(f932(f931(a925,a925),a923),f932(f931(a925,a925),a923)),f180(f932(f931(a925,a925),a923))),x99051)),a28))
% 28.73/28.52 [10087]E(x100871,f2(a925))+E(x100871,f319(a104,f2(a925)))+~P1(f319(f319(f227(a925),x100871),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))))
% 28.73/28.52 [10381]E(x103811,f2(a91))+E(f319(f319(f74(a1),f319(f319(f75(a1),f319(f95(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),f319(a22,f319(f319(f30(a91),x103811),f319(f95(a91),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))))))),f72(a1)),f319(a22,x103811))+E(f39(a91,x103811,f319(f95(a91),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),f2(a91))
% 28.73/28.52 [10226]E(x102261,f2(a91))+~E(f39(a91,x102261,f319(f95(a91),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),f2(a91))+E(f319(f319(f75(a1),f319(f95(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),f319(a22,f319(f319(f30(a91),x102261),f319(f95(a91),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))))),f319(a22,x102261))
% 28.73/28.52 [4874]~P62(x48741,x48742)+P45(x48741,x48742)+~P46(a923)
% 28.73/28.52 [4803]~P149(x48031)+P29(x48031,x48032)+~E(x48032,f2(x48031))
% 28.73/28.52 [4804]~P4(x48041)+P14(x48041,x48042)+~E(x48042,f105(x48041))
% 28.73/28.52 [4813]~P126(x48131)+~E(x48132,f2(x48131))+E(f76(x48131,x48132),f2(x48131))
% 28.73/28.52 [4814]~P94(x48141)+~E(x48142,f2(x48141))+E(f76(x48141,x48142),f2(x48141))
% 28.73/28.52 [4822]~P149(x48222)+~P29(x48222,x48221)+E(x48221,f2(x48222))
% 28.73/28.52 [4867]~P126(x48672)+~E(f76(x48672,x48671),f2(x48672))+E(x48671,f2(x48672))
% 28.73/28.52 [4881]~P5(x48812)+~P5(x48811)+P5(f932(x48811,x48812))
% 28.73/28.52 [4882]~P5(x48822)+~P5(x48821)+P5(f931(x48821,x48822))
% 28.73/28.52 [4883]~P5(x48832)+~P5(x48831)+P5(f933(x48831,x48832))
% 28.73/28.52 [4884]~P71(x48842)+~P71(x48841)+P71(f932(x48841,x48842))
% 28.73/28.52 [4885]~P71(x48852)+~P71(x48851)+P71(f931(x48851,x48852))
% 28.73/28.52 [4886]~P71(x48862)+~P71(x48861)+P71(f933(x48861,x48862))
% 28.73/28.52 [4887]~P7(x48872)+~P7(x48871)+P7(f186(x48871,x48872))
% 28.73/28.52 [4888]~P111(x48882)+~P111(x48881)+P111(f931(x48881,x48882))
% 28.73/28.52 [5011]~P4(x50111)+~P14(x50111,x50112)+P14(x50111,f144(x50111,x50112))
% 28.73/28.52 [5254]~P7(x52542)+~P7(x52541)+P7(f39(a1,x52541,x52542))
% 28.73/28.52 [4823]~P84(x48231)+~E(x48232,f2(x48231))+E(f319(f73(x48231),x48232),x48232)
% 28.73/28.52 [4824]~P84(x48241)+~E(x48242,f2(x48241))+E(f319(f73(x48241),x48242),x48242)
% 28.73/28.52 [4838]~P98(x48381)+~E(x48382,f2(a1))+E(f319(f94(x48381),x48382),f2(x48381))
% 28.73/28.52 [4839]~P145(x48391)+~E(x48392,f2(a1))+E(f319(f94(x48391),x48392),f2(x48391))
% 28.73/28.52 [4840]~P98(x48401)+~E(x48402,f2(a1))+E(f319(f94(x48401),x48402),f2(x48401))
% 28.73/28.52 [4864]~P69(x48641)+~E(f2(x48641),x48642)+E(f319(f73(x48641),x48642),f2(x48641))
% 28.73/28.52 [4865]~P69(x48651)+~E(x48652,f2(x48651))+E(f319(f73(x48651),x48652),f2(x48651))
% 28.73/28.52 [4866]~P92(x48661)+~E(x48662,f2(x48661))+E(f319(f69(x48661),x48662),f2(x48661))
% 28.73/28.52 [4889]~P84(x48892)+E(x48891,f2(x48892))+~E(f319(f73(x48892),x48891),x48891)
% 28.73/28.52 [4890]~P84(x48902)+E(x48901,f2(x48902))+~E(f319(f73(x48902),x48901),x48901)
% 28.73/28.52 [4892]E(x48921,f319(a96,x48922))+~E(x48921,f2(a925))+~E(x48922,f319(f92(a1),x48921))
% 28.73/28.52 [4893]E(f319(a96,x48931),x48932)+~E(x48932,f2(a925))+~E(x48931,f319(f92(a1),x48932))
% 28.73/28.52 [4896]~P98(x48962)+E(x48961,f2(a1))+~E(f319(f94(x48962),x48961),f2(x48962))
% 28.73/28.52 [4897]~P98(x48972)+E(x48971,f2(a1))+~E(f319(f94(x48972),x48971),f2(x48972))
% 28.73/28.52 [4901]~P69(x49012)+E(x49011,f2(x49012))+~E(f319(f73(x49012),x49011),f2(x49012))
% 28.73/28.52 [4902]~P92(x49022)+E(x49021,f2(x49022))+~E(f319(f69(x49022),x49021),f2(x49022))
% 28.73/28.52 [4903]~P69(x49031)+E(f2(x49031),x49032)+~E(f319(f73(x49031),x49032),f2(x49031))
% 28.73/28.52 [5086]~P4(x50861)+~P14(x50861,x50862)+P14(x50861,f319(f163(x50861),x50862))
% 28.73/28.52 [5113]~P1(x51132)+~P1(x51131)+P1(f319(f319(a317,x51131),x51132))
% 28.73/28.52 [5147]~E(f72(a925),f2(a925))+E(f319(f29(x51471),x51472),f2(a925))+~P1(f319(f55(x51471),x51472))
% 28.73/28.52 [5184]~P143(x51841)+~P119(x51841)+E(f319(f319(f236(x51841),f2(x51841)),f319(a104,x51842)),f2(x51841))
% 28.73/28.52 [5222]~P4(x52221)+P14(x52221,f131(x52221,x52222))+~P1(f319(f55(x52221),x52222))
% 28.73/28.52 [5223]~P4(x52231)+P14(x52231,f747(x52232,x52231))+~P1(f319(f55(x52231),x52232))
% 28.73/28.52 [5246]~P4(x52461)+E(f319(f164(x52461),f131(x52461,x52462)),x52462)+~P1(f319(f55(x52461),x52462))
% 28.73/28.52 [5247]~P4(x52471)+E(f319(f164(x52471),f747(x52472,x52471)),x52472)+~P1(f319(f55(x52471),x52472))
% 28.73/28.52 [5276]P1(x52761)+P1(x52762)+~P1(f319(f319(a318,x52762),x52761))
% 28.73/28.52 [5289]E(x52891,f180(f932(x52892,a923)))+~E(f319(f29(x52892),x52891),f2(a925))+~P1(f319(f55(x52892),x52891))
% 28.73/28.52 [5294]P1(x52941)+~P1(x52942)+~P1(f319(f319(a322,x52942),x52941))
% 28.73/28.52 [5349]~P82(x53491)+E(f319(f69(x53491),x53492),x53492)+P1(f319(f319(f227(x53491),x53492),f2(x53491)))
% 28.73/28.52 [5350]~P6(x53502)+~P41(x53502,x53502,x53501)+E(f319(x53501,f88(x53502,x53501)),f88(x53502,x53501))
% 28.73/28.52 [5351]~P6(x53512)+~P41(x53512,x53512,x53511)+E(f319(x53511,f87(x53512,x53511)),f87(x53512,x53511))
% 28.73/28.52 [5412]~P5(x54122)+~P1(f319(f50(x54122),x54121))+P1(f319(x54121,f835(x54121,x54122)))
% 28.73/28.52 [5413]~P5(x54132)+~P1(f319(f50(x54132),x54131))+P1(f319(x54131,f902(x54131,x54132)))
% 28.73/28.52 [5453]E(x54531,f105(x54532))+P1(f319(f129(x54532),f106(x54532,x54531)))+~P1(f319(f129(x54532),x54531))
% 28.73/28.52 [5458]~P4(x54581)+~P1(f319(f55(x54581),x54582))+P1(f319(f129(x54581),f131(x54581,x54582)))
% 28.73/28.52 [5459]~P4(x54591)+~P1(f319(f55(x54591),x54592))+P1(f319(f129(x54591),f747(x54592,x54591)))
% 28.73/28.52 [5464]~P145(x54641)+E(f319(f92(x54641),f319(a96,x54642)),f319(f94(x54641),x54642))+P1(f319(f319(f227(a1),x54642),f2(a1)))
% 28.73/28.52 [5485]P8(x54852,x54851)+E(f319(x54851,f516(x54851)),f319(x54851,f554(x54851)))+P1(f319(f319(x54851,f516(x54851)),f554(x54851)))
% 28.73/28.52 [5497]E(f319(f92(a1),f430(x54971,x54972)),x54971)+P1(f319(x54972,f319(a96,x54971)))+~P1(f319(x54972,f2(a925)))
% 28.73/28.52 [5509]~P5(x55091)+~P1(f319(x55092,f758(x55092,x55091)))+P1(f319(f51(x55091),x55092))
% 28.73/28.52 [5510]~P5(x55101)+~P1(f319(x55102,f836(x55102,x55101)))+P1(f319(f51(x55101),x55102))
% 28.73/28.52 [5545]~P126(x55451)+~E(f76(x55451,x55452),f319(f73(x55451),f72(x55451)))+P1(f319(f319(f227(x55451),x55452),f2(x55451)))
% 28.73/28.52 [5619]~E(x56192,f2(a1))+E(f207(x56191,x56192),f319(f319(f244(a1,a1),f2(a1)),f72(a1)))+P1(f319(f319(f227(a1),x56192),f2(a1)))
% 28.73/28.52 [5620]~E(x56201,f2(a1))+E(f207(x56201,x56202),f319(f319(f244(a1,a1),f2(a1)),f72(a1)))+P1(f319(f319(f227(a1),x56202),f2(a1)))
% 28.73/28.52 [5672]E(f319(f92(a1),f430(x56721,x56722)),x56721)+P1(f319(x56722,f319(a96,x56721)))+P1(f319(f319(f227(a1),x56721),f2(a1)))
% 28.73/28.52 [5738]~P126(x57381)+E(f76(x57381,x57382),f319(f73(x57381),f72(x57381)))+~P1(f319(f319(f227(x57381),x57382),f2(x57381)))
% 28.73/28.52 [5739]~P126(x57391)+E(f76(x57391,x57392),f319(f73(x57391),f72(x57391)))+~P1(f319(f319(f227(x57391),x57392),f2(x57391)))
% 28.73/28.52 [5740]~P92(x57401)+E(f319(f69(x57401),x57402),f319(f73(x57401),x57402))+~P1(f319(f319(f226(x57401),x57402),f2(x57401)))
% 28.73/28.52 [5741]~P92(x57411)+E(f319(f69(x57411),x57412),f319(f73(x57411),x57412))+~P1(f319(f319(f227(x57411),x57412),f2(x57411)))
% 28.73/28.52 [5742]~P82(x57421)+E(f319(f69(x57421),x57422),f319(f73(x57421),x57422))+~P1(f319(f319(f227(x57421),x57422),f2(x57421)))
% 28.73/28.52 [5841]~P1(f319(x58411,f430(x58412,x58411)))+P1(f319(x58411,f319(a96,x58412)))+~P1(f319(x58411,f2(a925)))
% 28.73/28.52 [5848]E(x58481,f2(a925))+E(f319(a104,f372(x58482,x58481)),x58481)+~P1(f319(f319(f227(a925),x58481),f319(a104,x58482)))
% 28.73/28.52 [5852]P8(x58521,x58522)+~E(f319(x58522,f516(x58522)),f319(x58522,f554(x58522)))+~P1(f319(f319(x58522,f516(x58522)),f554(x58522)))
% 28.73/28.52 [5871]~P4(x58711)+P14(x58711,x58712)+P1(f319(f319(f226(a925),f730(x58712,x58711)),f731(x58712,x58711)))
% 28.73/28.52 [5872]~P4(x58721)+P14(x58721,x58722)+P1(f319(f319(f226(a925),f738(x58722,x58721)),f742(x58722,x58721)))
% 28.73/28.52 [5958]~P92(x59581)+~E(x59582,f2(x59581))+P1(f319(f319(f226(x59581),f319(f69(x59581),x59582)),f2(x59581)))
% 28.73/28.52 [6047]~P1(f319(x60471,f430(x60472,x60471)))+P1(f319(x60471,f319(a96,x60472)))+P1(f319(f319(f227(a1),x60472),f2(a1)))
% 28.73/28.52 [6073]~P1(f319(x60731,f319(a96,x60732)))+P1(f319(x60731,f2(a925)))+~P1(f319(f319(f227(a1),x60732),f2(a1)))
% 28.73/28.52 [6419]~P126(x64191)+~P1(f319(f319(f227(x64191),x64192),f2(x64191)))+P1(f319(f319(f227(x64191),f76(x64191,x64192)),f2(x64191)))
% 28.73/28.52 [6533]~P126(x65331)+P1(f319(f319(f226(x65331),f319(f94(x65331),x65332)),f2(x65331)))+~P1(f319(f319(f226(a1),x65332),f2(a1)))
% 28.73/28.52 [6534]~P126(x65341)+P1(f319(f319(f227(x65341),f319(f94(x65341),x65342)),f2(x65341)))+~P1(f319(f319(f227(a1),x65342),f2(a1)))
% 28.73/28.52 [6543]~P92(x65432)+E(x65431,f2(x65432))+~P1(f319(f319(f226(x65432),f319(f69(x65432),x65431)),f2(x65432)))
% 28.73/28.52 [6621]~P145(x66211)+~P1(f319(f319(f321(x66211),x66212),f101(x66211)))+P1(f319(f319(f321(x66211),f319(f73(x66211),x66212)),f101(x66211)))
% 28.73/28.52 [6654]~P126(x66541)+~P1(f319(f319(f227(x66541),f76(x66541,x66542)),f2(x66541)))+P1(f319(f319(f227(x66541),x66542),f2(x66541)))
% 28.73/28.52 [6830]~P126(x68302)+~P1(f319(f319(f226(x68302),f319(f94(x68302),x68301)),f2(x68302)))+P1(f319(f319(f226(a1),x68301),f2(a1)))
% 28.73/28.52 [6831]~P126(x68312)+~P1(f319(f319(f227(x68312),f319(f94(x68312),x68311)),f2(x68312)))+P1(f319(f319(f227(a1),x68311),f2(a1)))
% 28.73/28.52 [6917]~P6(x69171)+~P41(x69171,x69171,x69172)+P1(f319(f319(f226(x69171),f319(x69172,f88(x69171,x69172))),f88(x69171,x69172)))
% 28.73/28.52 [6918]~P6(x69181)+~P41(x69181,x69181,x69182)+P1(f319(f319(f226(x69181),f319(x69182,f87(x69181,x69182))),f87(x69181,x69182)))
% 28.73/28.52 [7338]~P84(x73381)+~P1(f319(f319(f226(x73381),x73382),f2(x73381)))+P1(f319(f319(f226(x73381),f319(f319(f74(x73381),x73382),x73382)),f2(x73381)))
% 28.73/28.52 [7340]~P126(x73401)+~P1(f319(f319(f227(x73401),x73402),f2(x73401)))+P1(f319(f319(f227(x73401),f319(f319(f74(x73401),x73402),x73402)),f2(x73401)))
% 28.73/28.52 [7341]~P84(x73411)+~P1(f319(f319(f227(x73411),x73412),f2(x73411)))+P1(f319(f319(f227(x73411),f319(f319(f74(x73411),x73412),x73412)),f2(x73411)))
% 28.73/28.52 [7906]~P84(x79061)+~P1(f319(f319(f226(x79061),f319(f319(f74(x79061),x79062),x79062)),f2(x79061)))+P1(f319(f319(f226(x79061),x79062),f2(x79061)))
% 28.73/28.52 [7907]~P126(x79071)+~P1(f319(f319(f227(x79071),f319(f319(f74(x79071),x79072),x79072)),f2(x79071)))+P1(f319(f319(f227(x79071),x79072),f2(x79071)))
% 28.73/28.52 [7908]~P84(x79081)+~P1(f319(f319(f227(x79081),f319(f319(f74(x79081),x79082),x79082)),f2(x79081)))+P1(f319(f319(f227(x79081),x79082),f2(x79081)))
% 28.73/28.52 [4937]~E(x49372,f72(a925))+~E(x49371,f72(a925))+E(f319(f319(f75(a925),x49371),x49372),f72(a925))
% 28.73/28.52 [4938]~E(x49382,f72(a925))+~E(x49381,f72(a925))+E(f319(f319(f75(a925),x49381),x49382),f72(a925))
% 28.73/28.52 [4939]~E(x49392,f72(a1))+~E(x49391,f72(a1))+E(f319(f319(f75(a1),x49391),x49392),f72(a1))
% 28.73/28.52 [4940]~E(x49402,f2(a925))+~E(x49401,f2(a925))+E(f319(f319(f74(a925),x49401),x49402),f2(a925))
% 28.73/28.52 [4995]~P124(x49952)+E(x49951,f2(x49952))+E(f319(f319(f283(x49952),x49951),x49951),f72(x49952))
% 28.73/28.52 [4996]~P65(x49962)+E(x49961,f2(x49962))+E(f319(f319(f30(x49962),x49961),x49961),f72(x49962))
% 28.73/28.52 [4997]~P125(x49972)+E(x49971,f2(x49972))+E(f319(f319(f283(x49972),x49971),x49971),f72(x49972))
% 28.73/28.52 [5014]~P84(x50141)+~E(x50142,f2(x50141))+E(f319(f319(f74(x50141),x50142),x50142),f2(x50141))
% 28.73/28.52 [5017]~P144(x50171)+~E(x50172,f72(x50171))+E(f319(f319(f75(x50171),x50172),x50172),f72(x50171))
% 28.73/28.52 [5018]~P84(x50181)+~E(x50182,f2(x50181))+E(f319(f319(f74(x50181),x50182),x50182),f2(x50181))
% 28.73/28.52 [5019]~P125(x50191)+~E(x50192,f2(x50191))+E(f319(f319(f283(x50191),x50192),x50192),f2(x50191))
% 28.73/28.52 [5064]~E(x50642,f2(a925))+~E(x50641,f2(a925))+E(f319(f73(a1),f319(f92(a1),x50641)),f319(f92(a1),x50642))
% 28.73/28.52 [5083]E(x50831,f72(a925))+E(x50832,f2(a925))+~E(f319(f319(f75(a925),x50832),x50831),x50832)
% 28.73/28.52 [5095]E(x50951,f2(a925))+E(x50952,f2(a925))+~E(f319(f319(f75(a925),x50952),x50951),f2(a925))
% 28.73/28.52 [5120]~E(x51202,f2(a925))+~E(x51201,f319(a104,f2(a925)))+E(f319(f319(f74(a925),x51201),x51202),f319(a104,f2(a925)))
% 28.73/28.52 [5121]~E(x51211,f2(a925))+~E(x51212,f319(a104,f2(a925)))+E(f319(f319(f74(a925),x51211),x51212),f319(a104,f2(a925)))
% 28.73/28.52 [5122]~E(x51222,f2(a925))+~E(x51221,f319(a104,f2(a925)))+E(f319(f319(f74(a925),x51221),x51222),f319(a104,f2(a925)))
% 28.73/28.52 [5123]~E(x51231,f2(a925))+~E(x51232,f319(a104,f2(a925)))+E(f319(f319(f74(a925),x51231),x51232),f319(a104,f2(a925)))
% 28.73/28.52 [5130]E(x51301,f72(a1))+E(x51302,f319(f95(a1),a89))+~E(f319(f319(f75(a1),x51301),x51302),f72(a1))
% 28.73/28.52 [5131]E(x51311,f72(a1))+E(x51312,f319(f95(a1),a89))+~E(f319(f319(f75(a1),x51312),x51311),f72(a1))
% 28.73/28.52 [5132]E(x51321,f72(a1))+E(x51321,f319(f95(a1),a89))+~E(f319(f319(f75(a1),x51322),x51321),f72(a1))
% 28.73/28.52 [5133]E(x51331,f72(a1))+E(x51331,f319(f95(a1),a89))+~E(f319(f319(f75(a1),x51331),x51332),f72(a1))
% 28.73/28.52 [5134]E(x51341,f72(a1))+E(x51341,f319(f95(a1),a89))+~E(f319(f319(f75(a1),x51341),x51342),f72(a1))
% 28.73/28.52 [5155]~P84(x51552)+E(x51551,f2(x51552))+~E(f319(f319(f74(x51552),x51551),x51551),f2(x51552))
% 28.73/28.52 [5156]~P84(x51562)+E(x51561,f2(x51562))+~E(f319(f319(f74(x51562),x51561),x51561),f2(x51562))
% 28.73/28.52 [5162]~E(x51621,f319(f95(a1),a89))+~E(x51622,f319(f95(a1),a89))+E(f319(f319(f75(a1),x51621),x51622),f72(a1))
% 28.73/28.52 [5172]E(x51721,f2(a925))+E(x51722,f2(a925))+~E(f319(f319(f74(a925),x51722),x51721),f319(a104,f2(a925)))
% 28.73/28.52 [5173]E(x51731,f2(a925))+E(x51732,f2(a925))+~E(f319(f319(f74(a925),x51732),x51731),f319(a104,f2(a925)))
% 28.73/28.52 [5183]~P72(x51831)+~P99(x51831)+E(f319(f319(f283(x51831),x51832),f319(f95(x51831),a77)),f2(x51831))
% 28.73/28.52 [5189]~P144(x51891)+~E(x51892,f319(f73(x51891),f72(x51891)))+E(f319(f319(f75(x51891),x51892),x51892),f72(x51891))
% 28.73/28.52 [5194]~P7(x51942)+~P7(x51941)+P7(f319(f319(f75(a1),x51941),x51942))
% 28.73/28.52 [5195]~P7(x51952)+~P7(x51951)+P7(f319(f319(f74(a1),x51951),x51952))
% 28.73/28.52 [5196]~P7(x51962)+~P7(x51961)+P7(f319(f319(f30(a1),x51961),x51962))
% 28.73/28.52 [5197]~E(x51972,f2(a1))+E(x51971,f2(a1))+E(f40(x51971,x51972),f319(f319(f244(a1,a1),f2(a1)),x51971))
% 28.73/28.52 [5198]~E(x51982,f2(a1))+E(x51981,f2(a1))+E(f40(x51981,x51982),f319(f319(f244(a1,a1),f2(a1)),x51981))
% 28.73/28.52 [5220]~E(x52202,f319(a104,f2(a925)))+~E(x52201,f319(a104,f2(a925)))+E(f319(f319(f75(a925),x52201),x52202),f319(a104,f2(a925)))
% 28.73/28.52 [5235]E(x52351,f2(a925))+E(x52351,f319(a104,f2(a925)))+~E(f319(f319(f74(a925),x52352),x52351),f319(a104,f2(a925)))
% 28.73/28.52 [5236]E(x52361,f2(a925))+E(x52361,f319(a104,f2(a925)))+~E(f319(f319(f74(a925),x52361),x52362),f319(a104,f2(a925)))
% 28.73/28.52 [5237]E(x52371,f2(a925))+E(x52372,f319(a104,f2(a925)))+~E(f319(f319(f236(a925),x52372),x52371),f319(a104,f2(a925)))
% 28.73/28.52 [5238]E(x52381,f2(a925))+E(x52381,f319(a104,f2(a925)))+~E(f319(f319(f74(a925),x52382),x52381),f319(a104,f2(a925)))
% 28.73/28.52 [5239]E(x52391,f2(a925))+E(x52391,f319(a104,f2(a925)))+~E(f319(f319(f74(a925),x52391),x52392),f319(a104,f2(a925)))
% 28.73/28.52 [5248]~P72(x52481)+~P99(x52481)+E(f319(f319(f283(x52481),x52482),f319(f95(x52481),a89)),f319(f73(x52481),x52482))
% 28.73/28.52 [5268]E(x52681,f319(a96,x52682))+~E(x52681,f2(a925))+P1(f319(f319(f226(a1),f2(a1)),x52682))
% 28.73/28.52 [5269]E(f319(a96,x52691),x52692)+~E(x52692,f2(a925))+P1(f319(f319(f226(a1),f2(a1)),x52691))
% 28.73/28.52 [5284]E(x52841,f319(a104,f2(a925)))+E(x52842,f319(a104,f2(a925)))+~E(f319(f319(f74(a925),x52841),x52842),f319(a104,f2(a925)))
% 28.73/28.52 [5285]E(x52851,f319(a104,f2(a925)))+E(x52852,f319(a104,f2(a925)))+~E(f319(f319(f74(a925),x52851),x52852),f319(a104,f2(a925)))
% 28.73/28.52 [5296]~E(x52961,f319(a96,x52962))+E(x52961,f2(a925))+P1(f319(f319(f226(a1),f2(a1)),x52962))
% 28.73/28.52 [5297]~E(f319(a96,x52972),x52971)+E(x52971,f2(a925))+P1(f319(f319(f226(a1),f2(a1)),x52972))
% 28.73/28.52 [5323]~P102(x53231)+E(f319(f57(x53231,f93(x53231)),x53232),f10(x53231,x53232))+~P1(f319(f55(x53231),x53232))
% 28.73/28.52 [5324]~P102(x53241)+E(f319(f57(x53241,f102(x53241)),x53242),f13(x53241,x53242))+~P1(f319(f55(x53241),x53242))
% 28.73/28.52 [5325]~P4(x53251)+E(f319(f57(x53251,f224(x53251)),x53252),f14(x53251,x53252))+~P1(f319(f55(x53251),x53252))
% 28.73/28.52 [5326]~P4(x53261)+E(f319(f57(x53261,f225(x53261)),x53262),f15(x53261,x53262))+~P1(f319(f55(x53261),x53262))
% 28.73/28.52 [5407]E(x54071,x54072)+~E(f319(f319(f23(a925),x54072),x54071),f2(a925))+~E(f319(f319(f23(a925),x54071),x54072),f2(a925))
% 28.73/28.52 [5424]P7(x54241)+~P42(x54242)+~P1(f319(f319(f321(a1),x54241),x54242))
% 28.73/28.52 [5454]~P126(x54541)+~E(f76(x54541,x54542),f72(x54541))+P1(f319(f319(f227(x54541),f2(x54541)),x54542))
% 28.73/28.52 [5465]~P99(x54651)+E(f319(f92(x54651),f319(f95(a925),x54652)),f319(f95(x54651),x54652))+P1(f319(a185,f319(f95(a1),x54652)))
% 28.73/28.52 [5470]~P45(x54701,x54702)+P46(a923)+P1(f319(f55(f931(x54701,x54701)),x54702))
% 28.73/28.52 [5537]~P4(x55371)+E(f319(f57(x55371,f224(x55371)),x55372),f11(x55371,f224(x55371),x55372))+~P1(f319(f55(x55371),x55372))
% 28.73/28.52 [5538]~P4(x55381)+E(f319(f57(x55381,f225(x55381)),x55382),f12(x55381,f225(x55381),x55382))+~P1(f319(f55(x55381),x55382))
% 28.73/28.52 [5551]E(x55511,x55512)+P1(f319(f319(f227(a925),x55512),x55511))+P1(f319(f319(f227(a925),x55511),x55512))
% 28.73/28.52 [5552]E(x55521,x55522)+P1(f319(f319(f227(a925),x55522),x55521))+P1(f319(f319(f227(a925),x55521),x55522))
% 28.73/28.52 [5553]E(x55531,x55532)+P1(f319(f319(f227(a1),x55532),x55531))+P1(f319(f319(f227(a1),x55531),x55532))
% 28.73/28.52 [5606]~P99(x56061)+E(f319(f92(x56061),f319(f95(a925),x56062)),f2(x56061))+~P1(f319(a185,f319(f95(a1),x56062)))
% 28.73/28.52 [5609]~E(x56092,f319(a96,x56091))+E(x56091,f319(f92(a1),x56092))+~P1(f319(f319(f226(a1),f2(a1)),x56091))
% 28.73/28.52 [5610]~E(f319(a96,x56101),x56102)+E(x56101,f319(f92(a1),x56102))+~P1(f319(f319(f226(a1),f2(a1)),x56101))
% 28.73/28.52 [5611]~E(x56111,f319(a96,x56112))+E(f319(f92(a1),x56111),x56112)+~P1(f319(f319(f226(a1),f2(a1)),x56112))
% 28.73/28.52 [5621]E(x56211,f319(a96,x56212))+~E(x56212,f319(f92(a1),x56211))+~P1(f319(f319(f226(a1),f2(a1)),x56212))
% 28.73/28.52 [5622]E(f319(a96,x56221),x56222)+~E(x56221,f319(f92(a1),x56222))+~P1(f319(f319(f226(a1),f2(a1)),x56221))
% 28.73/28.52 [5663]~P92(x56632)+E(x56631,f2(x56632))+P1(f319(f319(f227(x56632),f2(x56632)),f319(f69(x56632),x56631)))
% 28.73/28.52 [5727]~P126(x57271)+E(f76(x57271,x57272),f72(x57271))+~P1(f319(f319(f227(x57271),f2(x57271)),x57272))
% 28.73/28.52 [5728]~P126(x57281)+E(f76(x57281,x57282),f72(x57281))+~P1(f319(f319(f227(x57281),f2(x57281)),x57282))
% 28.73/28.52 [5732]~P99(x57321)+E(f319(f92(x57321),f319(f95(a925),x57322)),f2(x57321))+P1(f319(f319(f226(a1),f2(a1)),f319(f95(a1),x57322)))
% 28.73/28.52 [5743]~P92(x57431)+E(f319(f69(x57431),x57432),x57432)+~P1(f319(f319(f226(x57431),f2(x57431)),x57432))
% 28.73/28.52 [5744]~P92(x57441)+E(f319(f69(x57441),x57442),x57442)+~P1(f319(f319(f227(x57441),f2(x57441)),x57442))
% 28.73/28.52 [5753]E(x57531,f2(a925))+~E(f131(a925,f319(f294(a925,x57532),x57531)),f105(a925))+P1(f319(f319(f226(a925),x57531),x57532))
% 28.73/28.52 [5763]~P79(x57631)+E(f319(f319(f6(x57631,x57631),f5(x57631)),f319(f164(x57631),x57632)),f319(f157(x57631),x57632))+~P1(f319(f129(x57631),x57632))
% 28.73/28.52 [5766]~P145(x57661)+E(f319(f92(x57661),f319(a96,x57662)),f319(f94(x57661),x57662))+~P1(f319(f319(f226(a1),f2(a1)),x57662))
% 28.73/28.52 [5768]~E(x57681,x57682)+P1(f319(f319(f227(a925),x57681),f319(a104,x57682)))+P1(f319(f319(f227(a925),x57681),x57682))
% 28.73/28.52 [5791]E(x57911,x57912)+P1(f319(f319(f227(a925),x57911),x57912))+~P1(f319(f319(f226(a925),x57911),x57912))
% 28.73/28.52 [5792]E(x57921,x57922)+P1(f319(f319(f227(a925),x57921),x57922))+~P1(f319(f319(f226(a925),x57921),x57922))
% 28.73/28.52 [5793]E(x57931,x57932)+P1(f319(f319(f227(a925),x57931),x57932))+~P1(f319(f319(f226(a925),x57931),x57932))
% 28.73/28.52 [5794]E(x57941,x57942)+P1(f319(f319(f227(a1),x57941),x57942))+~P1(f319(f319(f226(a1),x57941),x57942))
% 28.73/28.52 [5797]E(x57971,f72(a1))+~E(f319(f319(f75(a1),x57972),x57971),f72(a1))+~P1(f319(f319(f227(a1),f2(a1)),x57972))
% 28.73/28.52 [5798]E(x57981,f72(a1))+~E(f319(f319(f75(a1),x57981),x57982),f72(a1))+~P1(f319(f319(f227(a1),f2(a1)),x57981))
% 28.73/28.52 [5837]~P42(x58372)+P1(f319(f319(f226(a1),f2(a1)),x58371))+~P1(f319(f319(f321(a1),x58371),x58372))
% 28.73/28.52 [5838]~P42(x58382)+P1(f319(f319(f226(a1),f2(a1)),x58381))+~P1(f319(f319(f321(a1),x58381),x58382))
% 28.73/28.52 [5857]~P62(x58571,x58572)+P38(x58571,x58572)+~P1(f319(f55(f931(x58571,x58571)),x58572))
% 28.73/28.52 [5858]~P62(x58581,x58582)+P38(x58581,x58582)+~P1(f319(f55(f931(x58581,x58581)),x58582))
% 28.73/28.52 [5859]~P38(x58591,x58592)+P62(x58591,x58592)+~P1(f319(f55(f931(x58591,x58591)),x58592))
% 28.73/28.52 [5860]~P62(x58601,x58602)+P45(x58601,x58602)+~P1(f319(f55(f931(x58601,x58601)),x58602))
% 28.73/28.52 [5902]E(x59021,f180(f932(x59022,a923)))+~P1(f319(f55(x59022),x59021))+P1(f319(f319(f227(a925),f2(a925)),f319(f29(x59022),x59021)))
% 28.73/28.52 [5929]~P1(f319(x59291,x59292))+P1(f319(x59291,f2(a925)))+P1(f319(f319(f227(a925),f440(x59292,x59291)),x59292))
% 28.73/28.52 [5952]E(x59521,f2(a925))+~E(f319(f157(a925),x59522),f2(a925))+~P1(f319(f319(f321(a925),x59521),f319(f164(a925),x59522)))
% 28.73/28.52 [5988]~E(x59881,x59882)+P1(f319(f319(f227(a925),x59881),f319(a104,x59882)))+~P1(f319(f319(f226(a925),x59882),x59881))
% 28.73/28.52 [6020]E(x60201,x60202)+~P1(f319(f319(f226(a925),x60202),x60201))+~P1(f319(f319(f226(a925),x60201),x60202))
% 28.73/28.52 [6021]E(x60211,x60212)+~P1(f319(f319(f226(a1),x60212),x60211))+~P1(f319(f319(f226(a1),x60211),x60212))
% 28.73/28.52 [6023]E(f319(f29(x60231),x60232),f2(a925))+~P1(f319(f55(x60231),x60232))+P1(f319(f319(f321(x60231),f517(x60232,x60231)),x60232))
% 28.73/28.52 [6032]E(f44(x60321,x60322),f40(x60321,x60322))+P1(f319(f319(f226(a1),f2(a1)),x60321))+~P1(f319(f319(f227(a1),f2(a1)),x60322))
% 28.73/28.52 [6059]~P1(f319(x60591,f427(x60591)))+P1(f319(x60591,f319(a96,x60592)))+~P1(f319(f319(f226(a1),f2(a1)),x60592))
% 28.73/28.52 [6062]P1(f319(f319(f226(a925),x60621),f333(x60622)))+~P1(f319(f55(a925),x60622))+~P1(f319(f319(f321(a925),x60621),x60622))
% 28.73/28.52 [6063]P1(f319(f319(f227(a925),x60631),f352(x60632)))+~P1(f319(f55(a925),x60632))+~P1(f319(f319(f321(a925),x60631),x60632))
% 28.73/28.52 [6092]E(x60921,x60922)+~P1(f319(f319(f227(a925),x60921),f319(a104,x60922)))+P1(f319(f319(f227(a925),x60921),x60922))
% 28.73/28.52 [6093]E(x60931,x60932)+~P1(f319(f319(f227(a925),x60931),f319(a104,x60932)))+P1(f319(f319(f227(a925),x60931),x60932))
% 28.73/28.52 [6094]E(x60941,x60942)+~P1(f319(f319(f227(a925),x60941),f319(a104,x60942)))+P1(f319(f319(f227(a925),x60941),x60942))
% 28.73/28.52 [6095]E(x60951,x60952)+~P1(f319(f319(f227(a925),x60951),f319(a104,x60952)))+P1(f319(f319(f227(a925),x60951),x60952))
% 28.73/28.52 [6130]E(x61301,f319(a104,x61302))+~P1(f319(f319(f226(a925),x61301),f319(a104,x61302)))+P1(f319(f319(f226(a925),x61301),x61302))
% 28.73/28.52 [6131]E(x61311,f319(a104,x61312))+~P1(f319(f319(f226(a925),x61311),f319(a104,x61312)))+P1(f319(f319(f226(a925),x61311),x61312))
% 28.73/28.52 [6147]P1(f319(x61471,f431(x61471)))+~P1(f319(x61471,f319(a96,x61472)))+~P1(f319(f319(f226(a1),f2(a1)),x61472))
% 28.73/28.52 [6163]~P1(f319(x61631,x61632))+~P1(f319(f319(f226(a1),f2(a1)),x61632))+P1(f319(x61631,f319(f92(a1),f370(x61631))))
% 28.73/28.52 [6174]~P92(x61742)+~E(x61741,f2(x61742))+~P1(f319(f319(f227(x61742),f2(x61742)),f319(f69(x61742),x61741)))
% 28.73/28.52 [6199]~P62(x61991,x61992)+P38(x61991,f319(f278(x61991,x61991),x61992))+~P1(f319(f55(f931(x61991,x61991)),x61992))
% 28.73/28.52 [6210]~P99(x62101)+E(f319(f92(x62101),f319(f95(a925),x62102)),f319(f95(x62101),x62102))+~P1(f319(f319(f226(a1),f2(a1)),f319(f95(a1),x62102)))
% 28.73/28.52 [6213]E(f319(a104,x62131),x62132)+~P1(f319(f319(f227(a925),x62131),x62132))+P1(f319(f319(f227(a925),f319(a104,x62131)),x62132))
% 28.73/28.52 [6229]E(f319(f319(f30(a1),x62291),x62292),f2(a1))+~P1(f319(f319(f226(a1),x62291),f2(a1)))+~P1(f319(f319(f227(a1),x62292),x62291))
% 28.73/28.52 [6230]E(f319(f319(f30(a1),x62301),x62302),f2(a1))+~P1(f319(f319(f226(a1),x62301),f2(a1)))+~P1(f319(f319(f227(a1),x62302),x62301))
% 28.73/28.52 [6240]E(f39(a1,x62401,x62402),x62401)+~P1(f319(f319(f226(a1),x62401),f2(a1)))+~P1(f319(f319(f227(a1),x62402),x62401))
% 28.73/28.52 [6254]E(f41(x62541,x62542),f40(x62541,x62542))+~P1(f319(f319(f226(a1),f2(a1)),x62541))+~P1(f319(f319(f226(a1),f2(a1)),x62542))
% 28.73/28.52 [6262]E(f319(f319(f30(a925),x62621),x62622),f2(a925))+~P1(f319(f319(f227(a925),f2(a925)),x62622))+~P1(f319(f319(f227(a925),x62621),x62622))
% 28.73/28.52 [6263]E(f319(f319(f30(a1),x62631),x62632),f2(a1))+~P1(f319(f319(f226(a1),f2(a1)),x62631))+~P1(f319(f319(f227(a1),x62631),x62632))
% 28.73/28.52 [6264]E(f319(f319(f30(a1),x62641),x62642),f2(a1))+~P1(f319(f319(f226(a1),f2(a1)),x62641))+~P1(f319(f319(f227(a1),x62641),x62642))
% 28.73/28.52 [6273]E(f39(a925,f319(f95(a925),x62731),f319(f95(a925),x62732)),f319(f95(a925),x62731))+P1(f319(a185,f319(f95(a1),x62731)))+~P1(f319(a185,f319(f95(a1),x62732)))
% 28.73/28.52 [6275]E(f39(a1,x62751,x62752),x62751)+~P1(f319(f319(f226(a1),f2(a1)),x62751))+~P1(f319(f319(f227(a1),x62751),x62752))
% 28.73/28.52 [6276]E(x62761,x62762)+~P1(f319(f319(f227(a925),x62761),f319(a104,x62762)))+~P1(f319(f319(f226(a925),x62762),x62761))
% 28.73/28.52 [6286]E(f319(f95(a1),x62861),f319(f92(a1),x62862))+~E(x62862,f319(a96,f319(f95(a1),x62861)))+~P1(f319(f319(f226(a1),f2(a1)),f319(f95(a1),x62861)))
% 28.73/28.52 [6290]~P84(x62901)+~P1(f319(f319(f226(x62901),x62902),f2(x62901)))+P1(f319(f319(f226(x62901),x62902),f319(f73(x62901),x62902)))
% 28.73/28.52 [6291]~P126(x62911)+~P1(f319(f319(f227(x62911),x62912),f2(x62911)))+P1(f319(f319(f227(x62911),x62912),f319(f73(x62911),x62912)))
% 28.73/28.52 [6300]~P6(x63001)+E(f319(f319(f58(x63001,x63001,f93(x63001)),f234(x63001)),x63002),f32(x63001,x63002))+~P1(f319(f55(x63001),x63002))
% 28.73/28.52 [6301]~P6(x63011)+E(f319(f319(f58(x63011,x63011,f102(x63011)),f180(x63011)),x63012),f31(x63011,x63012))+~P1(f319(f55(x63011),x63012))
% 28.73/28.52 [6318]~P126(x63181)+~P1(f319(f319(f226(a1),f2(a1)),x63182))+P1(f319(f319(f226(x63181),f2(x63181)),f319(f94(x63181),x63182)))
% 28.73/28.52 [6319]~P129(x63191)+~P1(f319(f319(f227(a925),f2(a925)),x63192))+P1(f319(f319(f227(x63191),f2(x63191)),f319(f92(x63191),x63192)))
% 28.73/28.52 [6320]~P126(x63201)+~P1(f319(f319(f227(a1),f2(a1)),x63202))+P1(f319(f319(f227(x63201),f2(x63201)),f319(f94(x63201),x63202)))
% 28.73/28.52 [6323]~P7(x63232)+~P7(x63231)+E(f319(f302(a925,a1,f92(a1)),f295(a925,f319(a96,x63231),f319(a96,x63232))),f295(a1,x63231,x63232))
% 28.73/28.52 [6329]P1(f319(x63291,x63292))+~P1(f319(f319(f226(a1),f2(a1)),x63292))+~P1(f319(x63291,f319(f92(a1),f373(x63291))))
% 28.73/28.52 [6358]E(f319(f319(f74(a925),f319(f95(a925),x63581)),f319(f95(a925),x63582)),f319(f95(a925),x63581))+P1(f319(f319(f227(a1),x63581),a77))+~P1(f319(f319(f227(a1),x63582),a77))
% 28.73/28.52 [6362]~P126(x63621)+P1(f319(f319(f227(x63621),f2(x63621)),f76(x63621,x63622)))+~P1(f319(f319(f227(x63621),f2(x63621)),x63622))
% 28.73/28.52 [6374]~P68(x63741)+~P1(f319(f319(f226(x63741),x63742),f2(x63741)))+P1(f319(f319(f226(x63741),f2(x63741)),f319(f73(x63741),x63742)))
% 28.73/28.52 [6375]~P68(x63751)+~P1(f319(f319(f227(x63751),x63752),f2(x63751)))+P1(f319(f319(f227(x63751),f2(x63751)),f319(f73(x63751),x63752)))
% 28.73/28.52 [6378]E(x63781,f234(f932(x63782,a923)))+~E(f319(f29(x63782),x63781),f319(f29(x63782),f234(f932(x63782,a923))))+~P1(f319(f55(x63782),f234(f932(x63782,a923))))
% 28.73/28.52 [6410]~P84(x64101)+P1(f319(f319(f226(x64101),x64102),f2(x64101)))+~P1(f319(f319(f226(x64101),x64102),f319(f73(x64101),x64102)))
% 28.73/28.52 [6411]~P126(x64111)+P1(f319(f319(f227(x64111),x64112),f2(x64111)))+~P1(f319(f319(f227(x64111),x64112),f319(f73(x64111),x64112)))
% 28.73/28.52 [6418]E(f41(x64181,x64182),f319(f319(f244(a1,a1),f2(a1)),x64181))+~P1(f319(f319(f227(a1),f2(a1)),x64182))+~P1(f319(f319(f227(a1),x64181),x64182))
% 28.73/28.52 [6421]~P99(x64211)+P1(f319(f319(f321(x64211),f319(f95(x64211),x64212)),f178(x64211)))+~P1(f319(f319(f226(a1),a77),x64212))
% 28.73/28.52 [6450]E(x64501,f2(a925))+~P1(f319(f319(f227(a925),x64501),f319(a104,x64502)))+P1(f319(f319(f227(a925),f372(x64502,x64501)),x64502))
% 28.73/28.52 [6472]~P126(x64721)+~P1(f319(f319(f227(x64721),f2(x64721)),f76(x64721,x64722)))+P1(f319(f319(f227(x64721),f2(x64721)),x64722))
% 28.73/28.52 [6474]~E(f319(f95(a925),x64742),f319(f95(a925),x64741))+P1(f319(f319(f226(a1),f319(f95(a1),x64741)),f2(a1)))+~P1(f319(a185,f319(f95(a1),x64742)))
% 28.73/28.52 [6503]E(f319(f243(a1,a1),f44(x65031,x65032)),f319(f319(f30(a1),x65031),x65032))+~P1(f319(f319(f227(a1),x65031),f2(a1)))+~P1(f319(f319(f227(a1),f2(a1)),x65032))
% 28.73/28.52 [6541]E(f319(f248(a1,a1),f44(x65411,x65412)),f39(a1,x65411,x65412))+~P1(f319(f319(f227(a1),x65411),f2(a1)))+~P1(f319(f319(f227(a1),f2(a1)),x65412))
% 28.73/28.52 [6544]~P126(x65442)+~P1(f319(f319(f226(x65442),f2(x65442)),f319(f94(x65442),x65441)))+P1(f319(f319(f226(a1),f2(a1)),x65441))
% 28.73/28.52 [6545]~P129(x65452)+~P1(f319(f319(f227(x65452),f2(x65452)),f319(f92(x65452),x65451)))+P1(f319(f319(f227(a925),f2(a925)),x65451))
% 28.73/28.52 [6546]~P126(x65462)+~P1(f319(f319(f227(x65462),f2(x65462)),f319(f94(x65462),x65461)))+P1(f319(f319(f227(a1),f2(a1)),x65461))
% 28.73/28.52 [6549]E(f319(f243(a1,a1),f41(x65491,x65492)),f319(f319(f30(a1),x65491),x65492))+~P1(f319(f319(f226(a1),f2(a1)),x65492))+~P1(f319(f319(f227(a1),f2(a1)),x65491))
% 28.73/28.52 [6564]E(f319(f248(a1,a1),f41(x65641,x65642)),f39(a1,x65641,x65642))+~P1(f319(f319(f226(a1),f2(a1)),x65642))+~P1(f319(f319(f227(a1),f2(a1)),x65641))
% 28.73/28.52 [6579]~P68(x65791)+P1(f319(f319(f226(x65791),x65792),f2(x65791)))+~P1(f319(f319(f226(x65791),f2(x65791)),f319(f73(x65791),x65792)))
% 28.73/28.52 [6580]~P68(x65801)+P1(f319(f319(f227(x65801),x65802),f2(x65801)))+~P1(f319(f319(f227(x65801),f2(x65801)),f319(f73(x65801),x65802)))
% 28.73/28.52 [6603]~P6(x66031)+~P41(x66031,x66031,x66032)+P1(f319(f319(f226(x66031),f88(x66031,x66032)),f319(x66032,f88(x66031,x66032))))
% 28.73/28.52 [6604]~P6(x66041)+~P41(x66041,x66041,x66042)+P1(f319(f319(f226(x66041),f87(x66041,x66042)),f319(x66042,f87(x66041,x66042))))
% 28.73/28.52 [6609]P1(f319(f43(x66091,x66092),f44(x66091,x66092)))+~P1(f319(f319(f227(a1),x66091),f2(a1)))+~P1(f319(f319(f227(a1),f2(a1)),x66092))
% 28.73/28.52 [6633]P1(f319(f43(x66331,x66332),f41(x66331,x66332)))+~P1(f319(f319(f226(a1),f2(a1)),x66331))+~P1(f319(f319(f227(a1),f2(a1)),x66332))
% 28.73/28.52 [6677]~P68(x66771)+P1(f319(f319(f226(x66771),f319(f73(x66771),x66772)),f2(x66771)))+~P1(f319(f319(f226(x66771),f2(x66771)),x66772))
% 28.73/28.52 [6678]~P68(x66781)+P1(f319(f319(f227(x66781),f319(f73(x66781),x66782)),f2(x66781)))+~P1(f319(f319(f227(x66781),f2(x66781)),x66782))
% 28.73/28.52 [6696]E(f319(f319(f23(a925),f319(a96,x66961)),f319(a96,x66962)),f319(a96,f186(x66961,x66962)))+~P1(f319(f319(f226(a1),f2(a1)),x66962))+~P1(f319(f319(f226(a1),f2(a1)),x66961))
% 28.73/28.52 [6714]P1(f319(f319(f226(a1),f2(a1)),f186(x67141,x67142)))+~P1(f319(f319(f226(a1),f2(a1)),x67142))+~P1(f319(f319(f226(a1),f2(a1)),x67141))
% 28.73/28.52 [6751]~P1(f319(x67511,x67512))+P1(f319(x67511,f2(a925)))+P1(f319(x67511,f319(f319(f74(a925),f440(x67512,x67511)),f72(a925))))
% 28.73/28.52 [6837]E(f319(f95(a925),x68371),f319(f95(a925),x68372))+~P1(f319(f319(f226(a1),f319(f95(a1),x68372)),f2(a1)))+~P1(f319(a185,f319(f95(a1),x68371)))
% 28.73/28.52 [6849]~E(x68491,f2(a925))+~E(f697(x68492,x68491),f2(a925))+E(f319(f134(a925,a925,f74(a925),x68491),x68492),f2(a925))
% 28.73/28.52 [6873]~P1(f319(f55(x68731),f903(x68732,x68731)))+~P1(f319(f55(f932(x68731,a923)),x68732))+P1(f319(f55(x68731),f31(f932(x68731,a923),x68732)))
% 28.73/28.52 [6879]E(x68791,x68792)+P1(f319(f319(f227(a1),x68791),x68792))+~P1(f319(f319(f227(a1),x68791),f319(f319(f74(a1),x68792),f72(a1))))
% 28.73/28.52 [6880]P1(f319(f319(f226(a925),f319(a96,x68801)),f319(a96,x68802)))+~P1(f319(f319(f226(a1),f2(a1)),x68802))+~P1(f319(f319(f226(a1),x68801),x68802))
% 28.73/28.52 [6881]P1(f319(f319(f226(a925),f319(a96,x68811)),f319(a96,x68812)))+~P1(f319(f319(f227(a1),f2(a1)),x68811))+~P1(f319(f319(f226(a1),x68811),x68812))
% 28.73/28.52 [6882]P1(f319(f319(f227(a925),f319(a96,x68821)),f319(a96,x68822)))+~P1(f319(f319(f227(a1),f2(a1)),x68822))+~P1(f319(f319(f227(a1),x68821),x68822))
% 28.73/28.52 [6883]P1(f319(f319(f227(a925),f319(a96,x68831)),f319(a96,x68832)))+~P1(f319(f319(f226(a1),f2(a1)),x68831))+~P1(f319(f319(f227(a1),x68831),x68832))
% 28.73/28.52 [6884]P1(f319(f319(f227(a925),f319(a96,x68841)),f319(a96,x68842)))+~P1(f319(f319(f227(a1),f2(a1)),x68842))+~P1(f319(f319(f227(a1),x68841),x68842))
% 28.73/28.52 [6895]E(f39(a925,f319(a96,x68951),f319(a96,x68952)),f319(a96,f39(a1,x68951,x68952)))+~P1(f319(f319(f226(a1),f2(a1)),x68952))+~P1(f319(f319(f226(a1),f2(a1)),x68951))
% 28.73/28.52 [6896]E(f39(a925,f319(a96,x68961),f319(a96,x68962)),f319(a96,f39(a1,x68961,x68962)))+~P1(f319(f319(f226(a1),f2(a1)),x68962))+~P1(f319(f319(f226(a1),f2(a1)),x68961))
% 28.73/28.52 [6922]~P68(x69221)+~P1(f319(f319(f226(x69221),f319(f73(x69221),x69222)),f2(x69221)))+P1(f319(f319(f226(x69221),f2(x69221)),x69222))
% 28.73/28.52 [6923]~P68(x69231)+~P1(f319(f319(f227(x69231),f319(f73(x69231),x69232)),f2(x69231)))+P1(f319(f319(f227(x69231),f2(x69231)),x69232))
% 28.73/28.52 [6938]~P1(f319(f319(f227(a1),a77),x69382))+~P1(f319(f319(f227(a1),x69381),x69382))+P1(f319(f319(f227(a925),f319(f95(a925),x69381)),f319(f95(a925),x69382)))
% 28.73/28.52 [7027]~P1(f319(f319(f226(a1),f2(a1)),x70271))+P1(f319(f319(f227(a925),f319(a96,x70271)),x70272))+~P1(f319(f319(f227(a1),x70271),f319(f92(a1),x70272)))
% 28.73/28.52 [7032]P1(f319(x70321,x70322))+~P1(f319(x70321,f319(a20,f834(x70321,x70322))))+~P1(f319(f319(f321(a925),x70322),f234(f932(a925,a923))))
% 28.73/28.52 [7043]E(x70431,f2(a1))+E(f39(a1,x70432,x70431),f2(a1))+E(f319(f319(f23(a1),f319(f73(a1),f319(f319(f30(a1),x70432),x70431))),f72(a1)),f319(f319(f30(a1),x70432),f319(f73(a1),x70431)))
% 28.73/28.52 [7057]~P1(f319(f319(f226(a1),f2(a1)),x70571))+~P1(f319(f319(f227(a925),f319(a96,x70571)),x70572))+P1(f319(f319(f227(a1),x70571),f319(f92(a1),x70572)))
% 28.73/28.52 [7095]~P1(f319(f319(f226(a925),f319(a96,x70951)),f319(a96,x70952)))+~P1(f319(f319(f226(a1),f2(a1)),x70952))+P1(f319(f319(f226(a1),x70951),x70952))
% 28.73/28.52 [7096]~P1(f319(f319(f226(a925),f319(a96,x70961)),f319(a96,x70962)))+~P1(f319(f319(f227(a1),f2(a1)),x70961))+P1(f319(f319(f226(a1),x70961),x70962))
% 28.73/28.52 [7097]~P1(f319(f319(f227(a925),f319(a96,x70971)),f319(a96,x70972)))+~P1(f319(f319(f226(a1),f2(a1)),x70971))+P1(f319(f319(f227(a1),x70971),x70972))
% 28.73/28.52 [7098]~P1(f319(f319(f227(a925),f319(a96,x70981)),f319(a96,x70982)))+~P1(f319(f319(f227(a1),f2(a1)),x70982))+P1(f319(f319(f227(a1),x70981),x70982))
% 28.73/28.52 [7125]P1(f319(f319(f226(a1),x71251),x71252))+~P1(f319(f319(f226(a925),f319(f95(a925),x71251)),f319(f95(a925),x71252)))+P1(f319(f319(f226(a1),x71251),a77))
% 28.73/28.52 [7151]P1(f319(f319(f226(a1),f2(a1)),f39(a1,x71511,x71512)))+~P1(f319(f319(f226(a1),f2(a1)),x71512))+~P1(f319(f319(f226(a1),f2(a1)),x71511))
% 28.73/28.52 [7246]P1(f319(f319(f227(a1),a77),x72461))+~P1(f319(f319(f227(a1),x72462),x72461))+~P1(f319(f319(f227(a925),f319(f95(a925),x72462)),f319(f95(a925),x72461)))
% 28.73/28.52 [7301]E(f319(f319(f244(a1,a1),f319(f319(f30(a1),x73011),x73012)),f39(a1,x73011,x73012)),f44(x73011,x73012))+~P1(f319(f319(f227(a1),x73011),f2(a1)))+~P1(f319(f319(f227(a1),f2(a1)),x73012))
% 28.73/28.52 [7321]E(f319(f319(f244(a1,a1),f319(f319(f30(a1),x73211),x73212)),f39(a1,x73211,x73212)),f41(x73211,x73212))+~P1(f319(f319(f226(a1),f2(a1)),x73212))+~P1(f319(f319(f226(a1),f2(a1)),x73211))
% 28.73/28.52 [7375]~P101(x73752)+E(x73751,f105(x73752))+E(f319(f134(x73752,x73752,f75(x73752),f319(f133(x73752),x73751)),f319(f163(x73752),x73751)),f319(f57(x73752,f75(x73752)),f319(f164(x73752),x73751)))
% 28.73/28.52 [7492]~E(x74921,f2(a925))+E(f319(f134(a925,a925,f74(a925),x74921),x74922),f2(a925))+P1(f319(f319(f321(a925),f697(x74922,x74921)),f319(f164(a925),x74922)))
% 28.73/28.52 [7543]~P1(f319(f319(f226(a1),x75431),f2(a1)))+P1(f319(f319(f226(a1),f319(f319(f30(a1),x75431),x75432)),f2(a1)))+~P1(f319(f319(f227(a1),f2(a1)),x75432))
% 28.73/28.52 [7544]~P1(f319(f319(f227(a1),x75442),f2(a1)))+P1(f319(f319(f226(a1),f319(f319(f30(a1),x75441),x75442)),f2(a1)))+~P1(f319(f319(f226(a1),f2(a1)),x75441))
% 28.73/28.52 [7545]~P1(f319(f319(f227(a1),x75452),f2(a1)))+P1(f319(f319(f227(a1),f319(f319(f30(a1),x75451),x75452)),f2(a1)))+~P1(f319(f319(f227(a1),f2(a1)),x75451))
% 28.73/28.52 [7546]~P1(f319(f319(f227(a1),x75461),f2(a1)))+P1(f319(f319(f227(a1),f319(f319(f30(a1),x75461),x75462)),f2(a1)))+~P1(f319(f319(f227(a1),f2(a1)),x75462))
% 28.73/28.52 [7547]~P1(f319(f319(f227(a1),x75471),f2(a1)))+P1(f319(f319(f227(a1),f319(f319(f30(a1),x75471),x75472)),f2(a1)))+~P1(f319(f319(f227(a1),f2(a1)),x75472))
% 28.73/28.52 [7553]P1(f319(f319(f321(f932(x75531,a923)),f903(x75532,x75531)),x75532))+~P1(f319(f55(f932(x75531,a923)),x75532))+P1(f319(f55(x75531),f31(f932(x75531,a923),x75532)))
% 28.73/28.52 [7641]P26(x76411,x76411,x76412,f234(f932(x76411,a923)))+~E(f319(f302(x76411,x76411,x76412),f234(f932(x76411,a923))),f234(f932(x76411,a923)))+~P1(f319(f55(x76411),f234(f932(x76411,a923))))
% 28.73/28.52 [7760]~P26(x77601,x77601,x77602,f234(f932(x77601,a923)))+E(f319(f302(x77601,x77601,x77602),f234(f932(x77601,a923))),f234(f932(x77601,a923)))+~P1(f319(f55(x77601),f234(f932(x77601,a923))))
% 28.73/28.52 [7783]E(f41(f319(f95(a1),x77831),f319(f95(a1),x77832)),f319(f319(f244(a1,a1),f2(a1)),f319(f95(a1),x77831)))+~P1(f319(f319(f227(a1),f2(a1)),f319(f95(a1),x77832)))+~P1(f319(f319(f227(a1),f319(f95(a1),x77831)),f319(f95(a1),x77832)))
% 28.73/28.52 [7899]E(f319(f319(f30(a1),x78991),x78992),f319(f95(a1),a89))+~P1(f319(f319(f226(a1),f319(f319(f74(a1),x78991),x78992)),f2(a1)))+~P1(f319(f319(f227(a1),f2(a1)),x78991))
% 28.73/28.52 [7956]~P1(f319(f319(f227(a1),x79562),f2(a1)))+~P1(f319(f319(f227(a1),f319(f319(f30(a1),x79561),x79562)),f2(a1)))+P1(f319(f319(f227(a1),f2(a1)),x79561))
% 28.73/28.52 [7961]E(f319(f319(f74(a1),x79611),x79612),f39(a1,x79611,x79612))+~P1(f319(f319(f226(a1),f319(f319(f74(a1),x79611),x79612)),f2(a1)))+~P1(f319(f319(f227(a1),f2(a1)),x79611))
% 28.73/28.52 [7964]P1(f319(f319(f227(a1),x79641),f2(a1)))+~P1(f319(f319(f227(a1),f319(f319(f30(a1),x79641),x79642)),f2(a1)))+~P1(f319(f319(f227(a1),f2(a1)),x79642))
% 28.73/28.52 [8665]~P4(x86651)+P14(x86651,x86652)+~P1(f319(f319(f226(x86651),f319(f319(f156(x86651),x86652),f730(x86652,x86651))),f319(f319(f156(x86651),x86652),f731(x86652,x86651))))
% 28.73/28.52 [8666]~P4(x86661)+P14(x86661,x86662)+~P1(f319(f319(f226(x86661),f319(f319(f156(x86661),x86662),f738(x86662,x86661))),f319(f319(f156(x86661),x86662),f742(x86662,x86661))))
% 28.73/28.52 [5895]E(x58951,f2(a1))+~E(f39(a1,x58952,x58951),f2(a1))+E(f319(f319(f30(a1),x58952),f319(f73(a1),x58951)),f319(f73(a1),f319(f319(f30(a1),x58952),x58951)))
% 28.73/28.52 [5913]~P42(x59132)+~P42(x59131)+P42(f319(f319(f102(f932(a1,a923)),x59131),x59132))
% 28.73/28.52 [5914]~P42(x59142)+~P42(x59141)+P42(f319(f319(f93(f932(a1,a923)),x59141),x59142))
% 28.73/28.52 [5932]~P72(x59321)+~P99(x59321)+E(f319(f73(x59321),f319(f319(f283(x59321),f72(x59321)),x59322)),f319(f319(f283(x59321),f319(f95(x59321),a89)),x59322))
% 28.73/28.52 [6051]E(x60511,f2(a1))+~E(f39(a1,x60512,x60511),f2(a1))+E(f319(f319(f30(a1),f319(f73(a1),x60512)),x60511),f319(f73(a1),f319(f319(f30(a1),x60512),x60511)))
% 28.73/28.52 [6193]~P4(x61931)+P14(x61931,x61932)+P1(f319(f319(f227(a925),f731(x61932,x61931)),f319(f181(f926(x61931)),x61932)))
% 28.73/28.52 [6194]~P4(x61941)+P14(x61941,x61942)+P1(f319(f319(f227(a925),f742(x61942,x61941)),f319(f181(f926(x61941)),x61942)))
% 28.73/28.52 [6352]~P99(x63521)+~E(f319(f95(x63521),x63522),f2(x63521))+P29(x63521,f319(f95(x63521),f319(f319(f74(a1),x63522),f319(f73(a1),a77))))
% 28.73/28.52 [6353]~P99(x63531)+~E(f319(f95(x63531),x63532),f2(x63531))+P29(x63531,f319(f95(x63531),f319(f319(f74(a1),a77),f319(f73(a1),x63532))))
% 28.73/28.52 [6355]E(f319(a45,f41(f319(f73(a1),x63551),f319(f73(a1),x63552))),f40(x63551,x63552))+P1(f319(f319(f226(a1),f2(a1)),x63551))+P1(f319(f319(f227(a1),f2(a1)),x63552))
% 28.73/28.52 [6480]~E(x64802,f2(a925))+~E(x64801,f2(a925))+P1(f319(f319(f226(a1),f319(f92(a1),x64801)),f319(f73(a1),f319(f92(a1),x64802))))
% 28.73/28.52 [6509]E(f319(f319(f74(a925),f319(f95(a925),x65091)),f319(f95(a925),x65092)),f319(f95(a925),f319(f319(f74(a1),x65091),x65092)))+P1(f319(f319(f227(a1),x65091),a77))+P1(f319(f319(f227(a1),x65092),a77))
% 28.73/28.52 [6643]~P84(x66431)+~P1(f319(f319(f226(x66431),f2(x66431)),x66432))+P1(f319(f319(f226(x66431),f319(f73(x66431),x66432)),x66432))
% 28.73/28.52 [6644]~P84(x66441)+~P1(f319(f319(f227(x66441),f2(x66441)),x66442))+P1(f319(f319(f227(x66441),f319(f73(x66441),x66442)),x66442))
% 28.73/28.52 [6823]E(f319(f319(f23(a925),f319(a96,x68231)),f319(a96,x68232)),f319(a96,f319(f319(f23(a1),x68231),x68232)))+~P1(f319(f319(f226(a1),f2(a1)),x68232))+~P1(f319(f319(f226(a1),x68232),x68231))
% 28.73/28.52 [6857]E(f319(a96,f39(a1,f319(f95(a1),x68571),f319(f95(a1),x68572))),f39(a925,f319(f95(a925),x68571),f319(f95(a925),x68572)))+P1(f319(a185,f319(f95(a1),x68571)))+P1(f319(a185,f319(f95(a1),x68572)))
% 28.73/28.52 [6874]~P84(x68741)+P1(f319(f319(f226(x68741),f2(x68741)),x68742))+~P1(f319(f319(f226(x68741),f319(f73(x68741),x68742)),x68742))
% 28.73/28.52 [6875]~P84(x68751)+P1(f319(f319(f227(x68751),f2(x68751)),x68752))+~P1(f319(f319(f227(x68751),f319(f73(x68751),x68752)),x68752))
% 28.73/28.52 [6888]~P84(x68881)+~P1(f319(f319(f226(x68881),f2(x68881)),x68882))+P1(f319(f319(f226(x68881),f2(x68881)),f319(f319(f74(x68881),x68882),x68882)))
% 28.73/28.52 [6890]~P84(x68901)+~P1(f319(f319(f227(x68901),f2(x68901)),x68902))+P1(f319(f319(f227(x68901),f2(x68901)),f319(f319(f74(x68901),x68902),x68902)))
% 28.73/28.52 [6901]E(f319(f319(f74(a925),f319(a96,x69011)),f319(a96,x69012)),f319(a96,f319(f319(f74(a1),x69011),x69012)))+~P1(f319(f319(f226(a1),f2(a1)),x69012))+~P1(f319(f319(f226(a1),f2(a1)),x69011))
% 28.73/28.52 [6902]E(f319(f319(f75(a925),f319(a96,x69021)),f319(a96,x69022)),f319(a96,f319(f319(f75(a1),x69021),x69022)))+~P1(f319(f319(f226(a1),f2(a1)),x69022))+~P1(f319(f319(f226(a1),f2(a1)),x69021))
% 28.73/28.52 [6903]E(f319(f319(f74(a925),f319(a96,x69031)),f319(a96,x69032)),f319(a96,f319(f319(f74(a1),x69031),x69032)))+~P1(f319(f319(f226(a1),f2(a1)),x69032))+~P1(f319(f319(f226(a1),f2(a1)),x69031))
% 28.73/28.52 [6904]E(f319(f319(f30(a925),f319(a96,x69041)),f319(a96,x69042)),f319(a96,f319(f319(f30(a1),x69041),x69042)))+~P1(f319(f319(f226(a1),f2(a1)),x69042))+~P1(f319(f319(f226(a1),f2(a1)),x69041))
% 28.73/28.52 [6914]E(x69141,f2(a925))+P1(f319(f319(f227(a925),f2(a925)),x69142))+~P1(f319(f319(f227(a925),f2(a925)),f319(f319(f236(a925),x69142),x69141)))
% 28.73/28.52 [6948]~P99(x69481)+E(f319(f95(x69481),x69482),f2(x69481))+~P29(x69481,f319(f95(x69481),f319(f319(f74(a1),a77),f319(f73(a1),x69482))))
% 28.73/28.52 [6949]~P99(x69491)+E(f319(f95(x69491),x69492),f2(x69491))+~P29(x69491,f319(f95(x69491),f319(f319(f74(a1),x69492),f319(f73(a1),a77))))
% 28.73/28.52 [7005]~P1(f319(f55(x70051),x70052))+~P1(f319(f55(x70051),f234(f932(x70051,a923))))+P1(f319(f55(x70051),f319(f73(f932(x70051,a923)),x70052)))
% 28.73/28.52 [7028]~P1(f319(f319(f227(a1),f2(a1)),x70282))+~P1(f319(f319(f226(a1),x70282),x70281))+P1(f319(f319(f227(a1),f2(a1)),f319(f319(f30(a1),x70281),x70282)))
% 28.73/28.52 [7029]~P1(f319(f319(f226(a1),x70291),f2(a1)))+~P1(f319(f319(f227(a1),x70292),f2(a1)))+P1(f319(f319(f226(a1),f2(a1)),f319(f319(f30(a1),x70291),x70292)))
% 28.73/28.52 [7069]~P1(f319(f319(f226(a1),f2(a1)),x70692))+~P1(f319(f319(f226(a1),f2(a1)),x70691))+P1(f319(f319(f226(a1),f2(a1)),f319(f319(f75(a1),x70691),x70692)))
% 28.73/28.52 [7070]~P1(f319(f319(f226(a1),f2(a1)),x70702))+~P1(f319(f319(f226(a1),f2(a1)),x70701))+P1(f319(f319(f226(a1),f2(a1)),f319(f319(f74(a1),x70701),x70702)))
% 28.73/28.52 [7071]~P1(f319(f319(f226(a1),f2(a1)),x70712))+~P1(f319(f319(f226(a1),f2(a1)),x70711))+P1(f319(f319(f226(a1),f2(a1)),f319(f319(f30(a1),x70711),x70712)))
% 28.73/28.52 [7072]~P1(f319(f319(f226(a1),f2(a1)),x70721))+~P1(f319(f319(f227(a1),f2(a1)),x70722))+P1(f319(f319(f226(a1),f2(a1)),f319(f319(f30(a1),x70721),x70722)))
% 28.73/28.52 [7073]~P1(f319(f319(f227(a925),f2(a925)),x70732))+~P1(f319(f319(f227(a925),f2(a925)),x70731))+P1(f319(f319(f227(a925),f2(a925)),f319(f319(f75(a925),x70731),x70732)))
% 28.73/28.52 [7138]E(x71381,f2(a1))+E(f39(a1,x71382,x71381),f2(a1))+E(f319(f319(f23(a1),f319(f73(a1),f319(f319(f30(a1),x71382),x71381))),f72(a1)),f319(f319(f30(a1),f319(f73(a1),x71382)),x71381))
% 28.73/28.52 [7192]P1(f319(f319(f227(a925),f2(a925)),x71921))+P1(f319(f319(f227(a925),f2(a925)),x71922))+~P1(f319(f319(f227(a925),f2(a925)),f319(f319(f74(a925),x71922),x71921)))
% 28.73/28.52 [7196]~P84(x71961)+P1(f319(f319(f226(x71961),f2(x71961)),x71962))+~P1(f319(f319(f226(x71961),f2(x71961)),f319(f319(f74(x71961),x71962),x71962)))
% 28.73/28.52 [7197]~P84(x71971)+P1(f319(f319(f227(x71971),f2(x71971)),x71972))+~P1(f319(f319(f227(x71971),f2(x71971)),f319(f319(f74(x71971),x71972),x71972)))
% 28.73/28.52 [7247]~P1(f319(f55(x72471),x72472))+P1(f319(f55(x72471),f234(f932(x72471,a923))))+~P1(f319(f55(x72471),f319(f73(f932(x72471,a923)),x72472)))
% 28.73/28.52 [7313]P1(f319(f319(f226(a1),x73131),f2(a1)))+~P1(f319(f319(f227(a1),x73132),f2(a1)))+~P1(f319(f319(f226(a1),f2(a1)),f319(f319(f30(a1),x73131),x73132)))
% 28.73/28.52 [7319]~P1(f319(f319(f227(a1),f2(a1)),x73191))+P1(f319(f319(f226(a1),x73191),x73192))+~P1(f319(f319(f227(a1),f2(a1)),f319(f319(f30(a1),x73192),x73191)))
% 28.73/28.52 [7320]~P1(f319(f319(f226(a1),f2(a1)),x73202))+P1(f319(f319(f226(a1),x73201),x73202))+~P1(f319(f319(f227(a1),f2(a1)),f319(f319(f30(a1),x73202),x73201)))
% 28.73/28.52 [7350]P1(f319(f319(f226(a1),f2(a1)),x73501))+~P1(f319(f319(f227(a1),f2(a1)),x73502))+~P1(f319(f319(f226(a1),f2(a1)),f319(f319(f30(a1),x73501),x73502)))
% 28.73/28.52 [7351]P1(f319(f319(f227(a1),f2(a1)),x73511))+~P1(f319(f319(f226(a1),f2(a1)),x73512))+~P1(f319(f319(f227(a1),f2(a1)),f319(f319(f30(a1),x73512),x73511)))
% 28.73/28.52 [7454]E(f208(x74541,x74542),x74541)+~E(x74542,f2(a925))+~P1(f319(f307(f931(a925,a925),a211),f319(f319(f244(a925,a925),x74541),x74542)))
% 28.73/28.52 [7660]E(f170(x76601,x76602),f105(a1))+P1(f319(f319(f226(a1),x76601),x76602))+~P1(f319(f307(f931(a1,a1),a174),f319(f319(f244(a1,a1),x76601),x76602)))
% 28.73/28.52 [7681]E(f319(f319(f244(a1,a1),f319(f95(a1),a89)),f319(f319(f74(a1),x76811),x76812)),f44(x76811,x76812))+~P1(f319(f319(f227(a1),f2(a1)),x76812))+~P1(f319(f319(f226(a1),f2(a1)),f319(f319(f74(a1),x76811),x76812)))
% 28.73/28.52 [7711]E(x77111,f2(a925))+E(f208(x77111,f39(a925,x77112,x77111)),f208(x77112,x77111))+~P1(f319(f307(f931(a925,a925),a211),f319(f319(f244(a925,a925),x77112),x77111)))
% 28.73/28.52 [7762]E(f120(x77621,x77622),f107(a1))+~P1(f319(f319(f227(a1),x77621),x77622))+~P1(f319(f307(f931(a1,a1),a125),f319(f319(f244(a1,a1),x77621),x77622)))
% 28.73/28.52 [7791]~P1(f319(f55(x77912),f234(f932(x77912,a923))))+~P1(f319(f55(x77911),f234(f932(x77911,a923))))+P1(f319(f55(f931(x77911,x77912)),f234(f932(f931(x77911,x77912),a923))))
% 28.73/28.52 [7792]~P1(f319(f55(x77922),f234(f932(x77922,a923))))+~P1(f319(f55(x77921),f234(f932(x77921,a923))))+P1(f319(f55(f933(x77921,x77922)),f234(f932(f933(x77921,x77922),a923))))
% 28.73/28.52 [7864]~P1(f319(f319(f227(a925),f319(a104,f2(a925))),x78641))+~P1(f319(f319(f227(a925),f319(a104,f2(a925))),x78642))+P1(f319(f319(f227(a925),x78641),f319(f319(f75(a925),x78642),x78641)))
% 28.73/28.52 [7865]~P1(f319(f319(f227(a925),f319(a104,f2(a925))),x78651))+~P1(f319(f319(f227(a925),f319(a104,f2(a925))),x78652))+P1(f319(f319(f227(a925),x78651),f319(f319(f75(a925),x78651),x78652)))
% 28.73/28.52 [7898]E(f319(f29(x78981),f234(f932(x78981,a923))),f319(a104,f2(a925)))+P1(f319(f55(x78982),f234(f932(x78982,a923))))+~P1(f319(f55(f932(x78982,x78981)),f234(f932(f932(x78982,x78981),a923))))
% 28.73/28.52 [7949]E(f41(x79491,x79492),f319(f319(f244(a1,a1),f2(a1)),x79491))+~P1(f319(f319(f227(a1),x79491),x79492))+~P1(f319(f307(f931(a1,a1),a52),f319(f319(f244(a1,a1),x79491),x79492)))
% 28.73/28.52 [7953]E(f207(f319(f73(a1),x79531),f319(f73(a1),x79532)),f207(x79531,x79532))+~P1(f319(f319(f227(a1),x79532),f2(a1)))+~P1(f319(f307(f931(a1,a1),a213),f319(f319(f244(a1,a1),x79531),x79532)))
% 28.73/28.52 [7974]E(f41(x79741,x79742),f319(f319(f244(a1,a1),f2(a1)),x79741))+~P1(f319(f319(f226(a1),x79742),f2(a1)))+~P1(f319(f307(f931(a1,a1),a52),f319(f319(f244(a1,a1),x79741),x79742)))
% 28.73/28.52 [8024]~P1(f319(f319(f226(a925),f319(a104,f2(a925))),x80241))+~P1(f319(f319(f226(a925),f319(a104,f2(a925))),x80242))+P1(f319(f319(f226(a925),f319(a104,f2(a925))),f319(f319(f75(a925),x80241),x80242)))
% 28.73/28.52 [8025]~P1(f319(f319(f227(a925),f319(a104,f2(a925))),x80252))+~P1(f319(f319(f227(a925),f319(a104,f2(a925))),x80251))+P1(f319(f319(f227(a925),f319(a104,f2(a925))),f319(f319(f75(a925),x80251),x80252)))
% 28.73/28.52 [8189]E(f319(f319(f244(a1,a1),f319(f95(a1),a89)),f319(f319(f74(a1),x81891),x81892)),f44(x81891,x81892))+~P1(f319(f319(f226(a1),x81892),f2(a1)))+~P1(f319(f307(f931(a1,a1),a46),f319(f319(f244(a1,a1),x81891),x81892)))
% 28.73/28.52 [8213]E(f108(a1,f319(f121(a1),x82131),f120(x82132,f319(f319(f74(a1),x82131),f72(a1)))),f120(x82132,x82131))+P1(f319(f319(f227(a1),x82132),x82131))+~P1(f319(f307(f931(a1,a1),a125),f319(f319(f244(a1,a1),x82132),x82131)))
% 28.73/28.52 [8226]E(f319(f319(f143(a1),x82261),f170(f319(f319(f74(a1),x82261),f72(a1)),x82262)),f170(x82261,x82262))+~P1(f319(f319(f226(a1),x82261),x82262))+~P1(f319(f307(f931(a1,a1),a174),f319(f319(f244(a1,a1),x82261),x82262)))
% 28.73/28.52 [8372]~P113(x83721)+P41(a925,x83721,x83722)+~P1(f319(f319(f226(x83721),f319(x83722,f374(x83722,x83721))),f319(x83722,f319(a104,f374(x83722,x83721)))))
% 28.73/28.52 [8510]E(f319(f319(f244(a1,a1),f319(f95(a1),a89)),f319(f319(f74(a1),x85101),x85102)),f44(x85101,x85102))+~P1(f319(f319(f226(a1),f2(a1)),f319(f319(f74(a1),x85101),x85102)))+~P1(f319(f307(f931(a1,a1),a46),f319(f319(f244(a1,a1),x85101),x85102)))
% 28.73/28.52 [8714]E(x87141,f105(x87142))+~P1(f319(f129(x87142),x87141))+E(f169(x87142,f319(f319(f8(a923,a923,x87142),a314),f319(f319(f7(x87142,x87142,a923),a316),f136(x87142,x87141))),x87141),f106(x87142,x87141))
% 28.73/28.52 [8787]E(f319(f319(f244(a1,a1),f319(f95(a1),a89)),f319(f319(f74(a1),f319(f95(a1),x87871)),f319(f95(a1),x87872))),f44(f319(f95(a1),x87871),f319(f95(a1),x87872)))+~P1(f319(f319(f227(a1),f2(a1)),f319(f95(a1),x87872)))+~P1(f319(f319(f226(a1),f2(a1)),f319(f319(f74(a1),f319(f95(a1),x87871)),f319(f95(a1),x87872))))
% 28.73/28.52 [8812]~P42(x88122)+~P42(x88121)+E(f319(f302(a925,a1,f92(a1)),f319(f319(f102(f932(a925,a923)),f319(f302(a1,a925,a96),x88121)),f319(f302(a1,a925,a96),x88122))),f319(f319(f102(f932(a1,a923)),x88121),x88122))
% 28.73/28.52 [8813]~P42(x88132)+~P42(x88131)+E(f319(f302(a925,a1,f92(a1)),f319(f319(f93(f932(a925,a923)),f319(f302(a1,a925,a96),x88131)),f319(f302(a1,a925,a96),x88132))),f319(f319(f93(f932(a1,a923)),x88131),x88132))
% 28.73/28.52 [9488]~P99(x94881)+~E(f319(f95(x94881),x94882),f72(x94881))+P29(x94881,f319(f95(x94881),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f73(a1),x94882))))
% 28.73/28.52 [9734]~P99(x97341)+E(f319(f95(x97341),x97342),f72(x97341))+~P29(x97341,f319(f95(x97341),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f73(a1),x97342))))
% 28.73/28.52 [10520]E(x105201,f2(a1))+E(x105202,f2(a1))+E(f319(f250(a1,a1,a1,a1,f25(a1),f319(f75(a1),f76(a1,x105202))),f319(f319(f319(f86(f931(a1,a1)),f319(f319(a316,f76(a1,x105201)),f76(a1,x105202))),f47(x105201,x105202)),f319(f319(f249(a1,a1,f931(a1,a1)),f319(f319(f18(a1,f932(a1,f931(a1,a1)),f932(a1,f931(a1,a1))),f319(f319(f8(f932(a1,f932(f931(a1,a1),f931(a1,a1))),f932(f932(a1,f931(a1,a1)),f932(a1,f931(a1,a1))),a1),f18(a1,f931(a1,a1),f931(a1,a1))),f319(f319(f8(f931(a1,a1),f932(a1,f932(f931(a1,a1),f931(a1,a1))),a1),f319(f7(a1,f931(a1,a1),f932(f931(a1,a1),f931(a1,a1))),f319(f319(f8(a923,f932(f931(a1,a1),f932(f931(a1,a1),f931(a1,a1))),a1),f86(f931(a1,a1))),f319(f319(f7(a1,a1,a923),a316),f2(a1))))),f319(f319(f7(a1,a1,f931(a1,a1)),f319(f319(f8(a1,f932(a1,f931(a1,a1)),a1),f244(a1,a1)),f73(a1))),f2(a1))))),f319(f319(f7(a1,f932(a1,a1),f932(a1,f931(a1,a1))),f319(f319(f8(f932(a1,f931(a1,a1)),f932(f932(a1,a1),f932(a1,f931(a1,a1))),a1),f8(a1,f931(a1,a1),a1)),f319(f319(f8(a1,f932(a1,f931(a1,a1)),a1),f244(a1,a1)),f319(f319(f7(a1,a1,a1),f319(f319(f8(a1,f932(a1,a1),a1),f23(a1)),f73(a1))),f72(a1))))),f319(f23(a1),f319(f69(a1),x105202))))),f47(x105201,x105202)))),f40(x105201,x105202))
% 28.73/28.52 [10521]E(x105211,f2(a1))+E(x105212,f2(a1))+E(f319(f250(a1,a1,a1,a1,f25(a1),f319(f75(a1),f76(a1,x105212))),f319(f319(f319(f86(f931(a1,a1)),f319(f319(a318,f319(f319(a317,f319(f319(f227(a1),f2(a1)),x105212)),f319(f319(f226(a1),f2(a1)),x105211))),f319(f319(a317,f319(f319(f227(a1),x105212),f2(a1))),f319(f319(f227(a1),x105211),f2(a1))))),f47(x105211,x105212)),f319(f319(f249(a1,a1,f931(a1,a1)),f319(f319(f18(a1,f932(a1,f931(a1,a1)),f932(a1,f931(a1,a1))),f319(f319(f8(f932(a1,f932(f931(a1,a1),f931(a1,a1))),f932(f932(a1,f931(a1,a1)),f932(a1,f931(a1,a1))),a1),f18(a1,f931(a1,a1),f931(a1,a1))),f319(f319(f8(f931(a1,a1),f932(a1,f932(f931(a1,a1),f931(a1,a1))),a1),f319(f7(a1,f931(a1,a1),f932(f931(a1,a1),f931(a1,a1))),f319(f319(f8(a923,f932(f931(a1,a1),f932(f931(a1,a1),f931(a1,a1))),a1),f86(f931(a1,a1))),f319(f319(f7(a1,a1,a923),a316),f2(a1))))),f319(f319(f7(a1,a1,f931(a1,a1)),f319(f319(f8(a1,f932(a1,f931(a1,a1)),a1),f244(a1,a1)),f73(a1))),f2(a1))))),f319(f319(f7(a1,f932(a1,a1),f932(a1,f931(a1,a1))),f319(f319(f8(f932(a1,f931(a1,a1)),f932(f932(a1,a1),f932(a1,f931(a1,a1))),a1),f8(a1,f931(a1,a1),a1)),f319(f319(f8(a1,f932(a1,f931(a1,a1)),a1),f244(a1,a1)),f319(f319(f7(a1,a1,a1),f319(f319(f8(a1,f932(a1,a1),a1),f23(a1)),f73(a1))),f72(a1))))),f319(f23(a1),f319(f69(a1),x105212))))),f47(x105211,x105212)))),f40(x105211,x105212))
% 28.73/28.52 [5921]~P126(x59211)+~P99(x59211)+E(f319(f69(x59211),f319(f319(f236(x59211),f319(f95(x59211),a89)),x59212)),f72(x59211))
% 28.73/28.52 [6422]~P145(x64221)+~P1(f319(f319(f227(a1),x64222),f2(a1)))+E(f319(f73(x64221),f319(f92(x64221),f319(a96,f319(f73(a1),x64222)))),f319(f94(x64221),x64222))
% 28.73/28.52 [6626]P1(f319(f319(f226(a91),x66261),f72(a91)))+E(f319(f319(f74(a91),f72(a91)),f264(x66261,f319(f319(f30(a91),x66262),x66261))),f264(x66261,x66262))+P1(f319(f319(f227(a91),x66262),x66261))
% 28.73/28.52 [7237]~P98(x72371)+~P1(f319(f319(f321(x72371),x72372),f101(x72371)))+~E(f319(f319(f74(x72371),f319(f319(f74(x72371),f72(x72371)),x72372)),x72372),f2(x72371))
% 28.73/28.52 [7352]~P1(f319(f319(f226(a1),x73522),f2(a1)))+~P1(f319(f319(f227(a1),x73521),f2(a1)))+E(f319(f243(a1,a1),f319(a45,f41(f319(f73(a1),x73521),f319(f73(a1),x73522)))),f319(f319(f30(a1),x73521),x73522))
% 28.73/28.52 [7369]~P1(f319(f319(f226(a1),x73692),f2(a1)))+~P1(f319(f319(f227(a1),x73691),f2(a1)))+E(f319(f248(a1,a1),f319(a45,f41(f319(f73(a1),x73691),f319(f73(a1),x73692)))),f39(a1,x73691,x73692))
% 28.73/28.52 [7377]~P1(f319(f319(f227(a1),x73772),f2(a1)))+E(f319(f243(a1,a1),f319(a45,f44(f319(f73(a1),x73771),f319(f73(a1),x73772)))),f319(f319(f30(a1),x73771),x73772))+~P1(f319(f319(f227(a1),f2(a1)),x73771))
% 28.73/28.52 [7395]~P1(f319(f319(f227(a1),x73952),f2(a1)))+E(f319(f248(a1,a1),f319(a45,f44(f319(f73(a1),x73951),f319(f73(a1),x73952)))),f39(a1,x73951,x73952))+~P1(f319(f319(f227(a1),f2(a1)),x73951))
% 28.73/28.52 [7448]E(f319(f319(f30(a1),f319(f319(f236(a1),x74481),x74482)),x74481),f319(f319(f236(a1),x74481),f319(f319(f23(a925),x74482),f319(a104,f2(a925)))))+~P1(f319(f319(f227(a925),f2(a925)),x74482))+~P1(f319(f319(f227(a1),f2(a1)),x74481))
% 28.73/28.52 [7550]~P1(f319(f319(f227(a925),f2(a925)),x75501))+~P1(f319(f319(f227(a925),f2(a925)),x75502))+P1(f319(f319(f227(a925),f319(f319(f23(a925),x75501),x75502)),x75501))
% 28.73/28.52 [7551]~P1(f319(f319(f227(a925),f2(a925)),x75511))+~P1(f319(f319(f227(a925),f72(a925)),x75512))+P1(f319(f319(f227(a925),f319(f319(f30(a925),x75511),x75512)),x75511))
% 28.73/28.52 [7552]~P1(f319(f319(f227(a1),f2(a1)),x75521))+~P1(f319(f319(f227(a1),f72(a1)),x75522))+P1(f319(f319(f227(a1),f319(f319(f30(a1),x75521),x75522)),x75521))
% 28.73/28.52 [7687]E(x76871,f2(a925))+~E(x76872,f2(a1))+~P1(f319(f319(f227(a1),f2(a1)),f319(f319(f236(a1),f319(f69(a1),x76872)),x76871)))
% 28.73/28.52 [8056]~P1(f319(x80561,x80562))+P1(f319(x80561,f2(a925)))+E(f319(a104,f230(a925,f319(f319(f8(a925,a923,a925),x80561),a104))),f230(a925,x80561))
% 28.73/28.52 [8105]~E(x81052,f105(f926(x81051)))+E(f319(f181(f926(f926(x81051))),f171(x81051,x81052)),f2(a925))+~P14(a925,f319(f160(a925),f319(f319(f146(f926(x81051),a925),f181(f926(x81051))),x81052)))
% 28.73/28.52 [8359]P1(f319(x83591,x83592))+~P1(f319(x83591,f319(a99,f590(x83591,x83592))))+~P1(f319(f319(f321(f932(f931(a925,a925),a923)),x83592),a90))
% 28.73/28.52 [8376]E(x83761,f105(f926(x83762)))+E(f319(f181(f926(x83762)),f319(f319(f156(f926(x83762)),x83761),f2(a925))),f319(f181(f926(f926(x83762))),f171(x83762,x83761)))+~P14(a925,f319(f160(a925),f319(f319(f146(f926(x83762),a925),f181(f926(x83762))),x83761)))
% 28.73/28.52 [8519]~P39(x85191,x85192)+~P40(x85191,x85192)+P39(x85191,f319(f319(f23(f932(f931(x85191,x85191),a923)),x85192),f299(x85191,f180(f932(f931(x85191,x85191),a923)))))
% 28.73/28.52 [9099]~P1(f319(f55(x90991),f319(f254(x90991),x90992)))+~P1(f319(f55(x90991),f234(f932(x90991,a923))))+P1(f319(f55(x90991),f319(f254(x90991),f319(f319(f8(a923,a923,x90991),a314),x90992))))
% 28.73/28.52 [9165]E(f319(f319(f244(a925,a925),f319(a104,f319(f319(f30(a925),f319(f319(f23(a925),x91651),x91652)),x91652))),f39(a925,f319(f319(f23(a925),x91651),x91652),x91652)),f79(f931(a925,a925),f42(x91651,x91652)))+~P1(f319(f319(f227(a925),f2(a925)),x91652))+~P1(f319(f319(f226(a925),x91652),x91651))
% 28.73/28.52 [9454]~P1(f319(f55(x94541),f319(f254(x94541),x94542)))+P1(f319(f55(x94541),f234(f932(x94541,a923))))+~P1(f319(f55(x94541),f319(f254(x94541),f319(f319(f8(a923,a923,x94541),a314),x94542))))
% 28.73/28.52 [10199]P28(x101991,x101992)+~P38(x101991,f319(f243(f932(f931(x101991,x101991),a923),f932(f931(x101991,x101991),a923)),x101992))+~P1(f319(f319(f226(f932(f931(x101991,x101991),a923)),f319(f319(f281(x101991,x101991,x101991),f319(f243(f932(f931(x101991,x101991),a923),f932(f931(x101991,x101991),a923)),x101992)),f319(f248(f932(f931(x101991,x101991),a923),f932(f931(x101991,x101991),a923)),x101992))),f319(f243(f932(f931(x101991,x101991),a923),f932(f931(x101991,x101991),a923)),x101992)))
% 28.73/28.52 [10243]E(f319(f37(f319(f95(a1),x102431)),f41(f319(f95(a1),x102432),f319(f319(f75(a1),f319(f95(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),f319(f95(a1),x102431)))),f41(f319(f95(a1),x102432),f319(f95(a1),x102431)))+~P1(f319(f319(f227(a1),f2(a1)),f319(f95(a1),x102431)))+P1(f319(f319(f227(a1),f319(f95(a1),x102432)),f319(f95(a1),x102431)))
% 28.73/28.52 [10249]E(f319(f37(f319(f95(a1),x102491)),f44(f319(f95(a1),x102492),f319(f319(f75(a1),f319(f95(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),f319(f95(a1),x102491)))),f44(f319(f95(a1),x102492),f319(f95(a1),x102491)))+~P1(f319(f319(f227(a1),f2(a1)),f319(f95(a1),x102491)))+P1(f319(f319(f226(a1),f2(a1)),f319(f319(f74(a1),f319(f95(a1),x102492)),f319(f95(a1),x102491))))
% 28.73/28.52 [10296]~E(f292(a925,f279(a925),f319(f319(f18(a925,f932(a925,a923),f932(a925,a923)),f319(f319(f8(f932(a925,f932(a923,a923)),f932(f932(a925,a923),f932(a925,a923)),a925),f18(a925,a923,a923)),f319(f319(f8(f932(a925,a923),f932(a925,f932(a923,a923)),a925),f319(f8(a923,f932(a923,a923),a925),a317)),f279(a925)))),f319(f319(f8(f932(a925,a923),f932(a925,a923),a925),f319(f8(a923,a923,a925),a314)),f319(f7(a925,a925,a923),f279(a925)))),x102962,x102961),f180(f932(a925,a923)))+~P1(f319(f319(f279(a925),x102962),x102961))+P1(f319(f319(f279(a925),x102961),x102962))
% 28.73/28.52 [10297]~E(f292(a925,f279(a925),f319(f319(f18(a925,f932(a925,a923),f932(a925,a923)),f319(f319(f8(f932(a925,f932(a923,a923)),f932(f932(a925,a923),f932(a925,a923)),a925),f18(a925,a923,a923)),f319(f319(f8(f932(a925,a923),f932(a925,f932(a923,a923)),a925),f319(f8(a923,f932(a923,a923),a925),a317)),f279(a925)))),f319(f319(f8(f932(a925,a923),f932(a925,a923),a925),f319(f8(a923,a923,a925),a314)),f319(f7(a925,a925,a923),f279(a925)))),x102972,x102971),f180(f932(a925,a923)))+~P1(f319(f319(f279(a925),x102972),x102971))+P1(f319(f319(f279(a925),x102971),x102972))
% 28.73/28.52 [10298]~E(f289(a925,f279(a925),f319(f319(f18(a925,f932(a925,a923),f932(a925,a923)),f319(f319(f8(f932(a925,f932(a923,a923)),f932(f932(a925,a923),f932(a925,a923)),a925),f18(a925,a923,a923)),f319(f319(f8(f932(a925,a923),f932(a925,f932(a923,a923)),a925),f319(f8(a923,f932(a923,a923),a925),a317)),f279(a925)))),f319(f319(f8(f932(a925,a923),f932(a925,a923),a925),f319(f8(a923,a923,a925),a314)),f319(f7(a925,a925,a923),f279(a925)))),x102982,x102981),f180(f932(a925,a923)))+~P1(f319(f319(f279(a925),x102982),x102981))+P1(f319(f319(f279(a925),x102981),x102982))
% 28.73/28.52 [7477]~P1(f319(f319(f227(a925),f2(a925)),x74772))+P1(f319(f319(f227(a925),x74771),x74772))+E(f319(a104,f319(f319(f30(a925),f319(f319(f23(a925),x74771),x74772)),x74772)),f319(f319(f30(a925),x74771),x74772))
% 28.73/28.52 [7478]~P1(f319(f319(f227(a925),f2(a925)),x74782))+P1(f319(f319(f227(a925),x74781),x74782))+E(f319(a104,f319(f319(f30(a925),f319(f319(f23(a925),x74781),x74782)),x74782)),f319(f319(f30(a925),x74781),x74782))
% 28.73/28.52 [7614]~P1(f319(f319(f227(a925),f2(a925)),x76142))+~P1(f319(f319(f226(a925),x76142),x76141))+E(f319(a104,f319(f319(f30(a925),f319(f319(f23(a925),x76141),x76142)),x76142)),f319(f319(f30(a925),x76141),x76142))
% 28.73/28.52 [8583]~P99(x85831)+~P98(x85831)+~P29(x85831,f319(f95(x85831),f319(f319(f23(a1),f319(f319(f74(a1),x85832),x85832)),a89)))
% 28.73/28.52 [9359]E(x93591,f2(a925))+E(f319(f319(f249(a925,a925,f931(a925,a925)),f319(f319(f8(a925,f932(a925,f931(a925,a925)),a925),f244(a925,a925)),a104)),f79(f931(a925,a925),f42(f319(f319(f23(a925),x93592),x93591),x93591))),f79(f931(a925,a925),f42(x93592,x93591)))+P1(f319(f319(f227(a925),x93592),x93591))
% 28.73/28.52 [9542]~P39(x95421,x95422)+~P56(x95421,x95422)+P1(f319(f319(f226(f932(f931(x95421,x95421),a923)),f319(f319(f281(x95421,x95421,x95421),f319(f278(x95421,x95421),x95422)),x95422)),x95422))
% 28.73/28.52 [9800]P1(f319(x98002,f663(x98002,x98001)))+P1(f319(x98001,f663(x98002,x98001)))+E(f319(f254(a1),f319(f319(f18(a1,a923,a923),f319(f319(f8(a923,f932(a923,a923),a1),a317),f319(f226(a1),f2(a1)))),x98001)),f319(f254(a1),f319(f319(f18(a1,a923,a923),f319(f319(f8(a923,f932(a923,a923),a1),a317),f319(f226(a1),f2(a1)))),x98002)))
% 28.73/28.52 [9804]~P1(f319(x98042,f663(x98042,x98041)))+~P1(f319(x98041,f663(x98042,x98041)))+E(f319(f254(a1),f319(f319(f18(a1,a923,a923),f319(f319(f8(a923,f932(a923,a923),a1),a317),f319(f226(a1),f2(a1)))),x98041)),f319(f254(a1),f319(f319(f18(a1,a923,a923),f319(f319(f8(a923,f932(a923,a923),a1),a317),f319(f226(a1),f2(a1)))),x98042)))
% 28.73/28.52 [7821]~P73(x78211)+~P99(x78211)+E(f319(f319(f283(x78211),x78212),f319(f95(x78211),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))),x78212)
% 28.73/28.52 [7822]~P73(x78221)+~P99(x78221)+E(f319(f319(f283(x78221),x78222),f319(f95(x78221),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))),x78222)
% 28.73/28.52 [9487]~P99(x94871)+~E(f319(f95(x94871),x94872),f72(x94871))+P29(x94871,f319(f95(x94871),f319(f319(f74(a1),x94872),f319(f73(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))))
% 28.73/28.52 [9675]~P144(x96751)+~E(x96752,f72(x96751))+E(f319(f319(f236(x96751),x96752),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),f72(x96751))
% 28.73/28.52 [9676]~P144(x96761)+~E(x96762,f2(x96761))+E(f319(f319(f236(x96761),x96762),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),f2(x96761))
% 28.73/28.52 [9691]~P144(x96911)+~E(x96912,f319(f73(x96911),f72(x96911)))+E(f319(f319(f236(x96911),x96912),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),f72(x96911))
% 28.73/28.52 [9711]~P87(x97111)+~P100(x97111)+E(f319(f319(f236(x97111),f319(f95(x97111),x97112)),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),f319(f319(f75(x97111),f319(f95(x97111),x97112)),f319(f95(x97111),x97112)))
% 28.73/28.52 [9735]~P99(x97351)+E(f319(f95(x97351),x97352),f72(x97351))+~P29(x97351,f319(f95(x97351),f319(f319(f74(a1),x97352),f319(f73(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))))
% 28.73/28.52 [9856]~P144(x98562)+E(x98561,f2(x98562))+~E(f319(f319(f236(x98562),x98561),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),f2(x98562))
% 28.73/28.52 [10140]~P126(x101402)+E(x101401,f2(x101402))+P1(f319(f319(f227(x101402),f2(x101402)),f319(f319(f236(x101402),x101401),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))))))
% 28.73/28.52 [10198]~P126(x101982)+~E(x101981,f2(x101982))+~P1(f319(f319(f227(x101982),f2(x101982)),f319(f319(f236(x101982),x101981),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))))))
% 28.73/28.52 [10234]P1(f319(f319(f226(a1),x102341),f2(a1)))+P1(f319(f319(f227(a1),x102342),x102341))+E(f319(f37(x102341),f41(x102342,f319(f319(f75(a1),f319(f95(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),x102341))),f41(x102342,x102341))
% 28.73/28.52 [10235]~P1(f319(f319(f227(a1),f2(a1)),x102351))+P1(f319(f319(f227(a1),x102352),x102351))+E(f319(f37(x102351),f41(x102352,f319(f319(f75(a1),f319(f95(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),x102351))),f41(x102352,x102351))
% 28.73/28.52 [10236]P1(f319(f319(f226(a1),x102361),f2(a1)))+P1(f319(f319(f226(a1),f2(a1)),f319(f319(f74(a1),x102362),x102361)))+E(f319(f37(x102361),f44(x102362,f319(f319(f75(a1),f319(f95(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),x102361))),f44(x102362,x102361))
% 28.73/28.52 [10237]~P1(f319(f319(f227(a1),f2(a1)),x102371))+P1(f319(f319(f226(a1),f2(a1)),f319(f319(f74(a1),x102372),x102371)))+E(f319(f37(x102371),f44(x102372,f319(f319(f75(a1),f319(f95(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),x102371))),f44(x102372,x102371))
% 28.73/28.52 [10238]~P149(x102381)+~P1(f319(f319(f226(a1),f2(a1)),x102382))+E(f319(f92(x102381),f319(a96,f319(f319(f75(a1),f319(f95(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),x102382))),f319(f319(f74(x102381),f319(f92(x102381),f319(a96,x102382))),f319(f92(x102381),f319(a96,x102382))))
% 28.73/28.52 [5255]~P151(x52551,x52553,x52552)+~E(x52553,f2(a1))+P1(f319(x52551,x52552))
% 28.73/28.52 [5385]~P4(x53851)+~P14(x53851,x53853)+P14(x53851,f162(x53851,x53852,x53853))
% 28.73/28.52 [5386]~P4(x53861)+~P14(x53861,x53863)+P14(x53861,f169(x53861,x53862,x53863))
% 28.73/28.52 [4947]~P69(x49472)+~E(x49473,f319(f73(x49472),x49471))+E(x49471,f319(f73(x49472),x49473))
% 28.73/28.52 [4948]~P69(x49482)+~E(x49483,f319(f73(x49482),x49481))+E(x49481,f319(f73(x49482),x49483))
% 28.73/28.52 [4949]~P69(x49491)+~E(f319(f73(x49491),x49493),x49492)+E(f319(f73(x49491),x49492),x49493)
% 28.73/28.52 [4950]~P69(x49501)+~E(f319(f73(x49501),x49503),x49502)+E(f319(f73(x49501),x49502),x49503)
% 28.73/28.52 [5029]~P4(x50293)+E(x50291,x50292)+~E(f319(f296(x50293),x50291),f319(f296(x50293),x50292))
% 28.73/28.52 [5030]~P4(x50303)+E(x50301,x50302)+~E(f319(f274(x50303),x50301),f319(f274(x50303),x50302))
% 28.73/28.52 [5031]~P4(x50313)+E(x50311,x50312)+~E(f319(f275(x50313),x50311),f319(f275(x50313),x50312))
% 28.73/28.52 [5032]~P4(x50323)+E(x50321,x50322)+~E(f319(f293(x50323),x50321),f319(f293(x50323),x50322))
% 28.73/28.52 [5033]~P96(x50333)+E(x50331,x50332)+~E(f319(f73(x50333),x50331),f319(f73(x50333),x50332))
% 28.73/28.52 [5034]~P69(x50343)+E(x50341,x50342)+~E(f319(f73(x50343),x50341),f319(f73(x50343),x50342))
% 28.73/28.52 [5035]~P110(x50353)+E(x50351,x50352)+~E(f319(f92(x50353),x50351),f319(f92(x50353),x50352))
% 28.73/28.52 [5036]~P98(x50363)+E(x50361,x50362)+~E(f319(f94(x50363),x50361),f319(f94(x50363),x50362))
% 28.73/28.52 [5137]~P5(x51371)+~P1(f319(x51372,x51373))+P1(f319(f50(x51371),x51372))
% 28.73/28.52 [5138]~P5(x51381)+~P1(f319(x51382,x51383))+P1(f319(f50(x51381),x51382))
% 28.73/28.52 [5174]~P5(x51743)+P1(f319(x51741,x51742))+~P1(f319(f51(x51743),x51741))
% 28.73/28.52 [5175]~P5(x51753)+P1(f319(x51751,x51752))+~P1(f319(f51(x51753),x51751))
% 28.73/28.52 [5275]~P152(x52751,x52752,x52753)+~E(x52752,f2(a1))+P1(f319(x52751,f2(a1)))
% 28.73/28.52 [5310]~P114(x53102)+~P1(f319(x53101,x53103))+P1(f319(x53101,f230(x53102,x53101)))
% 28.73/28.52 [5311]~P114(x53112)+~P1(f319(x53111,x53113))+P1(f319(x53111,f230(x53112,x53111)))
% 28.73/28.52 [5318]~E(x53181,f2(a925))+E(f328(x53181,x53182,x53183),f180(f932(x53183,a923)))+~E(f319(f29(x53183),x53182),f319(a104,x53181))
% 28.73/28.53 [5469]~E(x54692,f2(a925))+E(f319(f243(a925,a925),x54691),f2(a925))+~P1(f319(f42(x54693,x54692),x54691))
% 28.73/28.53 [5506]P1(f319(x55061,x55062))+~E(x55063,f319(f92(a1),x55062))+~P1(f319(x55061,f319(a96,x55063)))
% 28.73/28.53 [5985]~E(x59853,f2(a925))+~P1(f319(x59851,x59852))+P1(f319(x59851,f39(a925,x59852,x59853)))
% 28.73/28.53 [6042]~P114(x60421)+~P1(f319(x60422,x60423))+~P1(f319(f319(f227(x60421),x60423),f230(x60421,x60422)))
% 28.73/28.53 [6225]~P111(x62252)+~P111(x62251)+E(f123(x62251,x62252,f124(x62251,x62253),f124(x62252,x62253)),f124(f931(x62251,x62252),x62253))
% 28.73/28.53 [6403]~E(x64033,f2(a925))+P1(f319(x64031,x64032))+~P1(f319(x64031,f39(a925,x64032,x64033)))
% 28.73/28.53 [6415]~P6(x64151)+~P1(f319(f319(f226(x64151),x64152),f319(x64153,x64152)))+P1(f319(f319(f226(x64151),x64152),f88(x64151,x64153)))
% 28.73/28.53 [6900]E(x69001,f180(f932(x69002,a923)))+~P1(f319(f55(x69002),x69001))+P1(f319(f56(x69002,x69003,x69001),f870(x69003,x69001,x69002)))
% 28.73/28.53 [7094]E(x70941,f2(a925))+~P1(f319(x70942,f518(x70941,x70943,x70942)))+P1(f319(x70942,f39(a925,x70943,x70941)))
% 28.73/28.53 [7202]~P6(x72021)+~P1(f319(f319(f226(x72021),x72022),f434(x72023,x72022,x72021)))+P1(f319(f319(f226(x72021),x72022),f32(x72021,x72023)))
% 28.73/28.53 [7203]~P6(x72031)+~P1(f319(f319(f226(x72031),x72032),f710(x72032,x72033,x72031)))+P1(f319(f319(f226(x72031),x72032),f32(x72031,x72033)))
% 28.73/28.53 [7205]~P1(f319(x72051,x72052))+~P1(f319(x72051,f518(x72053,x72052,x72051)))+P1(f319(x72051,f39(a925,x72052,x72053)))
% 28.73/28.53 [7307]E(x73071,f105(x73072))+E(f319(f319(f143(x73072),f711(x73073,x73071,x73072)),f714(x73073,x73071,x73072)),x73071)+~P1(f319(f319(f321(f926(x73072)),x73071),f153(x73072,x73073)))
% 28.73/28.53 [7339]~P145(x73391)+~P1(f319(f319(f321(x73391),x73392),f101(x73391)))+P1(f319(f319(f321(x73391),f319(f319(f236(x73391),x73392),x73393)),f101(x73391)))
% 28.73/28.53 [7659]P38(x76591,x76592)+~P1(f319(f319(f321(x76591),x76593),f629(x76592,x76591)))+P1(f319(f319(f321(x76591),f660(x76592,x76591,x76593)),f629(x76592,x76591)))
% 28.73/28.53 [7926]E(x79261,f105(x79262))+~P1(f319(f319(f321(f926(x79262)),x79261),f153(x79262,x79263)))+P1(f319(f319(f321(f926(x79262)),f714(x79263,x79261,x79262)),f153(x79262,x79263)))
% 28.73/28.53 [7978]E(x79781,f2(a925))+E(f319(f319(f74(a925),f319(f319(f75(a925),x79781),f519(x79781,x79782,x79783))),f518(x79781,x79782,x79783)),x79782)+P1(f319(x79783,f39(a925,x79782,x79781)))
% 28.73/28.53 [8019]~P1(f319(x80193,x80192))+E(f319(f319(f74(a925),f319(f319(f75(a925),x80191),f519(x80191,x80192,x80193))),f518(x80191,x80192,x80193)),x80192)+P1(f319(x80193,f39(a925,x80192,x80191)))
% 28.73/28.53 [8162]P1(f319(f319(f227(a1),x81621),f508(x81622,x81623,x81621)))+P1(f319(f319(x81623,f319(f319(f30(a1),x81622),x81621)),f39(a1,x81622,x81621)))+~P1(f319(f319(f227(a1),x81621),f2(a1)))
% 28.73/28.53 [8432]P1(f319(f319(x84322,f319(f319(f30(a1),x84321),x84323)),f39(a1,x84321,x84323)))+~P1(f319(f319(f227(a1),x84323),f2(a1)))+P1(f319(f319(f226(a1),f508(x84321,x84322,x84323)),f2(a1)))
% 28.73/28.53 [8618]E(f319(f319(f74(a1),f319(f319(f75(a1),x86181),f509(x86182,x86183,x86181))),f508(x86182,x86183,x86181)),x86182)+P1(f319(f319(x86183,f319(f319(f30(a1),x86182),x86181)),f39(a1,x86182,x86181)))+~P1(f319(f319(f227(a1),x86181),f2(a1)))
% 28.73/28.53 [8860]~P1(f319(f319(x88601,f509(x88602,x88601,x88603)),f508(x88602,x88601,x88603)))+P1(f319(f319(x88601,f319(f319(f30(a1),x88602),x88603)),f39(a1,x88602,x88603)))+~P1(f319(f319(f227(a1),x88603),f2(a1)))
% 28.73/28.53 [9112]~P4(x91121)+~P14(x91121,x91123)+P14(x91121,f141(x91121,x91121,f5(x91121),x91122,x91123))
% 28.73/28.53 [9620]~P130(x96202)+E(x96201,f2(x96202))+~P1(f319(f319(f226(x96202),f319(f319(f74(x96202),f319(f319(f75(x96202),x96203),x96203)),f319(f319(f75(x96202),x96201),x96201))),f2(x96202)))
% 28.73/28.53 [9621]~P130(x96212)+E(x96211,f2(x96212))+~P1(f319(f319(f226(x96212),f319(f319(f74(x96212),f319(f319(f75(x96212),x96211),x96211)),f319(f319(f75(x96212),x96213),x96213))),f2(x96212)))
% 28.73/28.53 [10452]~P126(x104521)+~P1(f319(f319(f227(x104521),x104522),f2(x104521)))+P1(f319(f319(f227(x104521),f319(f319(f236(x104521),x104522),f319(a104,f319(f319(f75(a925),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),x104523)))),f2(x104521)))
% 28.73/28.53 [10461]~P126(x104612)+E(x104611,f2(x104612))+~P1(f319(f319(f226(x104612),f319(f319(f74(x104612),f319(f319(f236(x104612),x104613),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))))),f319(f319(f236(x104612),x104611),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))))),f2(x104612)))
% 28.73/28.53 [10462]~P126(x104622)+E(x104621,f2(x104622))+~P1(f319(f319(f226(x104622),f319(f319(f74(x104622),f319(f319(f236(x104622),x104621),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))))),f319(f319(f236(x104622),x104623),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))))),f2(x104622)))
% 28.73/28.53 [4984]~E(x49842,x49843)+~P69(x49841)+E(f319(f319(f23(x49841),x49842),x49843),f2(x49841))
% 28.73/28.53 [4985]~E(x49852,x49853)+~P70(x49851)+E(f319(f319(f23(x49851),x49852),x49853),f2(x49851))
% 28.73/28.53 [4998]~P148(x49981)+~E(x49983,f2(x49981))+E(f319(f319(f74(x49981),x49982),x49983),x49982)
% 28.73/28.53 [5015]~P147(x50151)+~E(x50153,f2(x50151))+E(f319(f319(f75(x50151),x50152),x50153),f2(x50151))
% 28.73/28.53 [5016]~P147(x50161)+~E(x50162,f2(x50161))+E(f319(f319(f75(x50161),x50162),x50163),f2(x50161))
% 28.73/28.53 [5037]~E(x50373,f105(x50371))+~E(x50372,f105(x50371))+E(f319(f319(f126(x50371),x50372),x50373),f105(x50371))
% 28.73/28.53 [5038]~E(x50383,f105(x50381))+~E(x50382,f105(x50381))+E(f319(f319(f126(x50381),x50382),x50383),f105(x50381))
% 28.73/28.53 [5128]~P148(x51282)+E(x51281,f2(x51282))+~E(f319(f319(f74(x51282),x51283),x51281),x51283)
% 28.73/28.53 [5129]~P69(x51291)+~E(x51292,f319(f73(x51291),x51293))+E(f319(f319(f74(x51291),x51292),x51293),f2(x51291))
% 28.73/28.53 [5136]E(x51361,f105(x51362))+E(x51363,f2(a925))+~E(f319(f319(f167(x51362),x51363),x51361),f105(x51362))
% 28.73/28.53 [5142]~P69(x51423)+E(x51421,x51422)+~E(f319(f319(f23(x51423),x51421),x51422),f2(x51423))
% 28.73/28.53 [5143]~P70(x51433)+E(x51431,x51432)+~E(f319(f319(f23(x51433),x51431),x51432),f2(x51433))
% 28.73/28.53 [5157]~P144(x51572)+E(x51571,f2(x51572))+~E(f319(f319(f236(x51572),x51571),x51573),f2(x51572))
% 28.73/28.53 [5158]~P103(x51582)+E(x51581,f234(x51582))+~E(f319(f319(f93(x51582),x51583),x51581),f234(x51582))
% 28.73/28.53 [5159]~P103(x51592)+E(x51591,f234(x51592))+~E(f319(f319(f93(x51592),x51591),x51593),f234(x51592))
% 28.73/28.53 [5160]~P104(x51602)+E(x51601,f180(x51602))+~E(f319(f319(f102(x51602),x51603),x51601),f180(x51602))
% 28.73/28.53 [5161]~P104(x51612)+E(x51611,f180(x51612))+~E(f319(f319(f102(x51612),x51611),x51613),f180(x51612))
% 28.73/28.53 [5229]~P69(x52292)+E(x52291,f319(f73(x52292),x52293))+~E(f319(f319(f74(x52292),x52291),x52293),f2(x52292))
% 28.73/28.53 [5230]~P69(x52301)+E(f319(f73(x52301),x52302),x52303)+~E(f319(f319(f74(x52301),x52302),x52303),f2(x52301))
% 28.73/28.53 [5231]~E(x52312,x52313)+~P113(x52311)+P1(f319(f319(f226(x52311),x52312),x52313))
% 28.73/28.53 [5232]~E(x52322,x52323)+~P2(x52321)+P1(f319(f319(f226(x52321),x52322),x52323))
% 28.73/28.53 [5233]~E(x52332,x52333)+~P113(x52331)+P1(f319(f319(f226(x52331),x52332),x52333))
% 28.73/28.53 [5234]~E(x52342,x52343)+~P113(x52341)+P1(f319(f319(f226(x52341),x52342),x52343))
% 28.73/28.53 [5335]~P117(x53351)+~E(x53352,f319(f73(x53351),x53353))+E(f319(f319(f75(x53351),x53352),x53352),f319(f319(f75(x53351),x53353),x53353))
% 28.73/28.53 [5343]~P4(x53431)+~P14(x53431,x53433)+P14(x53431,f319(f319(f167(x53431),x53432),x53433))
% 28.73/28.53 [5344]~P4(x53441)+~P14(x53441,x53443)+P14(x53441,f319(f319(f130(x53441),x53442),x53443))
% 28.73/28.53 [5382]E(x53821,x53822)+E(x53823,f2(a925))+~E(f319(f319(f75(a925),x53823),x53821),f319(f319(f75(a925),x53823),x53822))
% 28.73/28.53 [5383]E(x53831,x53832)+E(x53833,f2(a925))+~E(f319(f319(f75(a925),x53833),x53831),f319(f319(f75(a925),x53833),x53832))
% 28.73/28.53 [5384]E(x53841,x53842)+E(x53843,f2(a925))+~E(f319(f319(f75(a925),x53841),x53843),f319(f319(f75(a925),x53842),x53843))
% 28.73/28.53 [5462]~E(x54622,x54623)+~P113(x54621)+E(f295(x54621,x54622,x54623),f319(f319(f301(x54621),x54622),f180(f932(x54621,a923))))
% 28.73/28.53 [5499]~E(x54991,x54992)+~P4(x54993)+~P1(f319(f319(f227(x54993),x54991),x54992))
% 28.73/28.53 [5500]~E(x55001,x55002)+~P4(x55003)+~P1(f319(f319(f227(x55003),x55001),x55002))
% 28.73/28.53 [5501]~E(x55011,x55012)+~P113(x55013)+~P1(f319(f319(f227(x55013),x55011),x55012))
% 28.73/28.53 [5502]~E(x55021,x55022)+~P113(x55023)+~P1(f319(f319(f227(x55023),x55021),x55022))
% 28.73/28.53 [5503]~E(x55031,x55032)+~P113(x55033)+~P1(f319(f319(f227(x55033),x55031),x55032))
% 28.73/28.53 [5504]~E(x55041,x55042)+~P4(x55043)+~P1(f319(f319(f227(x55043),x55041),x55042))
% 28.73/28.53 [5505]~E(x55051,x55052)+~P113(x55053)+~P1(f319(f319(f227(x55053),x55051),x55052))
% 28.73/28.53 [5516]~P113(x55161)+E(f319(f294(x55161,x55162),x55163),f180(f932(x55161,a923)))+P1(f319(f319(f227(x55161),x55162),x55163))
% 28.73/28.53 [5517]~P113(x55171)+E(f319(f294(x55171,x55172),x55173),f180(f932(x55171,a923)))+P1(f319(f319(f227(x55171),x55172),x55173))
% 28.73/28.53 [5565]~P113(x55651)+E(f295(x55651,x55652,x55653),f180(f932(x55651,a923)))+P1(f319(f319(f226(x55651),x55652),x55653))
% 28.73/28.53 [5566]~P113(x55661)+E(f297(x55661,x55662,x55663),f180(f932(x55661,a923)))+P1(f319(f319(f227(x55661),x55662),x55663))
% 28.73/28.53 [5567]~P113(x55671)+E(f180(f932(x55671,a923)),f295(x55671,x55672,x55673))+P1(f319(f319(f226(x55671),x55672),x55673))
% 28.73/28.53 [5568]~P113(x55681)+E(f180(f932(x55681,a923)),f297(x55681,x55682,x55683))+P1(f319(f319(f227(x55681),x55682),x55683))
% 28.73/28.53 [5576]~P107(x55761)+~E(f319(f319(f102(x55761),x55762),x55763),x55763)+P1(f319(f319(f226(x55761),x55762),x55763))
% 28.73/28.53 [5577]~P108(x55771)+~E(f319(f319(f93(x55771),x55772),x55773),x55772)+P1(f319(f319(f226(x55771),x55772),x55773))
% 28.73/28.53 [5578]~P4(x55781)+~E(f319(f319(f224(x55781),x55782),x55783),x55782)+P1(f319(f319(f226(x55781),x55782),x55783))
% 28.73/28.53 [5579]~P4(x55791)+~E(f319(f319(f225(x55791),x55792),x55793),x55793)+P1(f319(f319(f226(x55791),x55792),x55793))
% 28.73/28.53 [5597]~P4(x55971)+P14(x55971,x55972)+~P14(x55971,f319(f319(f143(x55971),x55973),x55972))
% 28.73/28.53 [5598]~P4(x55981)+P14(x55981,x55982)+~P14(x55981,f319(f319(f143(x55981),x55983),x55982))
% 28.73/28.53 [5599]~P4(x55991)+P14(x55991,x55992)+~P14(x55991,f319(f319(f126(x55991),x55993),x55992))
% 28.73/28.53 [5600]~P4(x56001)+P14(x56001,x56002)+~P14(x56001,f319(f319(f126(x56001),x56002),x56003))
% 28.73/28.53 [5664]~P4(x56641)+P1(f319(f319(f226(x56641),x56643),x56642))+P1(f319(f319(f226(x56641),x56642),x56643))
% 28.73/28.53 [5665]~P4(x56651)+P1(f319(f319(f226(x56651),x56653),x56652))+P1(f319(f319(f226(x56651),x56652),x56653))
% 28.73/28.53 [5666]~P4(x56661)+P1(f319(f319(f227(x56661),x56663),x56662))+P1(f319(f319(f226(x56661),x56662),x56663))
% 28.73/28.53 [5667]~P4(x56671)+P1(f319(f319(f227(x56671),x56673),x56672))+P1(f319(f319(f226(x56671),x56672),x56673))
% 28.73/28.53 [5668]~P4(x56681)+P1(f319(f319(f227(x56681),x56683),x56682))+P1(f319(f319(f226(x56681),x56682),x56683))
% 28.73/28.53 [5669]~P4(x56691)+P1(f319(f319(f227(x56691),x56693),x56692))+P1(f319(f319(f226(x56691),x56692),x56693))
% 28.73/28.53 [5670]~P4(x56701)+P1(f319(f319(f227(x56701),x56703),x56702))+P1(f319(f319(f226(x56701),x56702),x56703))
% 28.73/28.53 [5708]~P107(x57081)+E(f319(f319(f102(x57081),x57082),x57083),x57082)+~P1(f319(f319(f226(x57081),x57083),x57082))
% 28.73/28.53 [5709]~P107(x57091)+E(f319(f319(f102(x57091),x57092),x57093),x57093)+~P1(f319(f319(f226(x57091),x57092),x57093))
% 28.73/28.53 [5710]~P107(x57101)+E(f319(f319(f102(x57101),x57102),x57103),x57103)+~P1(f319(f319(f226(x57101),x57102),x57103))
% 28.73/28.53 [5711]~P108(x57111)+E(f319(f319(f93(x57111),x57112),x57113),x57113)+~P1(f319(f319(f226(x57111),x57113),x57112))
% 28.73/28.53 [5712]~P108(x57121)+E(f319(f319(f93(x57121),x57122),x57123),x57122)+~P1(f319(f319(f226(x57121),x57122),x57123))
% 28.73/28.53 [5713]~P108(x57131)+E(f319(f319(f93(x57131),x57132),x57133),x57132)+~P1(f319(f319(f226(x57131),x57132),x57133))
% 28.73/28.53 [5714]~P4(x57141)+E(f319(f319(f224(x57141),x57142),x57143),x57143)+~P1(f319(f319(f226(x57141),x57143),x57142))
% 28.73/28.53 [5715]~P4(x57151)+E(f319(f319(f224(x57151),x57152),x57153),x57152)+~P1(f319(f319(f226(x57151),x57152),x57153))
% 28.73/28.53 [5716]~P4(x57161)+E(f319(f319(f224(x57161),x57162),x57163),x57162)+~P1(f319(f319(f226(x57161),x57162),x57163))
% 28.73/28.53 [5717]~P4(x57171)+E(f319(f319(f225(x57171),x57172),x57173),x57172)+~P1(f319(f319(f226(x57171),x57173),x57172))
% 28.73/28.53 [5718]~P4(x57181)+E(f319(f319(f225(x57181),x57182),x57183),x57183)+~P1(f319(f319(f226(x57181),x57182),x57183))
% 28.73/28.53 [5719]~P4(x57191)+E(f319(f319(f225(x57191),x57192),x57193),x57193)+~P1(f319(f319(f226(x57191),x57192),x57193))
% 28.73/28.53 [5726]~P124(x57262)+E(x57261,f2(x57262))+E(f319(f319(f283(x57262),f319(f73(x57262),x57263)),f319(f73(x57262),x57261)),f319(f319(f283(x57262),x57263),x57261))
% 28.73/28.53 [5777]~P113(x57771)+E(f319(f294(x57771,x57772),x57773),f180(f932(x57771,a923)))+~P1(f319(f319(f226(x57771),x57773),x57772))
% 28.73/28.53 [5809]~P113(x58091)+E(f295(x58091,x58092,x58093),f180(f932(x58091,a923)))+~P1(f319(f319(f227(x58091),x58093),x58092))
% 28.73/28.53 [5810]~P113(x58101)+E(f297(x58101,x58102,x58103),f180(f932(x58101,a923)))+~P1(f319(f319(f226(x58101),x58103),x58102))
% 28.73/28.53 [5811]~P113(x58111)+E(f298(x58111,x58112,x58113),f180(f932(x58111,a923)))+~P1(f319(f319(f226(x58111),x58113),x58112))
% 28.73/28.53 [5854]~P114(x58541)+~P1(f319(x58542,x58543))+P1(f319(f319(f226(x58541),f230(x58541,x58542)),x58543))
% 28.73/28.53 [5864]~E(f319(f319(f23(a925),x58641),x58643),x58642)+E(x58641,f319(f319(f74(a925),x58642),x58643))+~P1(f319(f319(f226(a925),x58643),x58641))
% 28.73/28.53 [5865]~E(x58651,f319(f319(f74(a925),x58653),x58652))+E(f319(f319(f23(a925),x58651),x58652),x58653)+~P1(f319(f319(f226(a925),x58652),x58651))
% 28.73/28.53 [5910]~P1(f319(x59101,x59103))+P1(f319(x59101,f354(x59101,x59102)))+~P1(f319(f319(f226(a925),x59103),x59102))
% 28.73/28.53 [5911]~P1(f319(x59111,x59113))+P1(f319(x59111,f360(x59111,x59112)))+~P1(f319(f319(f227(a925),x59113),x59112))
% 28.73/28.53 [5918]~P113(x59181)+~E(f319(f294(x59181,x59182),x59183),f180(f932(x59181,a923)))+~P1(f319(f319(f227(x59181),x59182),x59183))
% 28.73/28.53 [5919]~P113(x59191)+~E(f319(f294(x59191,x59192),x59193),f180(f932(x59191,a923)))+~P1(f319(f319(f227(x59191),x59192),x59193))
% 28.73/28.53 [5923]~P2(x59231)+~P1(f319(f319(f227(x59231),x59232),x59233))+P1(f319(f319(f226(x59231),x59232),x59233))
% 28.73/28.53 [5924]~P2(x59241)+~P1(f319(f319(f227(x59241),x59242),x59243))+P1(f319(f319(f226(x59241),x59242),x59243))
% 28.73/28.53 [5925]~P113(x59251)+~P1(f319(f319(f227(x59251),x59252),x59253))+P1(f319(f319(f226(x59251),x59252),x59253))
% 28.73/28.53 [5926]~P113(x59261)+~P1(f319(f319(f227(x59261),x59262),x59263))+P1(f319(f319(f226(x59261),x59262),x59263))
% 28.73/28.53 [6035]~P113(x60351)+~E(f295(x60351,x60352,x60353),f180(f932(x60351,a923)))+~P1(f319(f319(f226(x60351),x60352),x60353))
% 28.73/28.53 [6036]~P113(x60361)+~E(f297(x60361,x60362,x60363),f180(f932(x60361,a923)))+~P1(f319(f319(f227(x60361),x60362),x60363))
% 28.73/28.53 [6037]~P113(x60371)+~E(f180(f932(x60371,a923)),f295(x60371,x60372,x60373))+~P1(f319(f319(f226(x60371),x60372),x60373))
% 28.73/28.53 [6038]~P113(x60381)+~E(f180(f932(x60381,a923)),f297(x60381,x60382,x60383))+~P1(f319(f319(f227(x60381),x60382),x60383))
% 28.73/28.53 [6049]P1(f319(x60491,x60492))+~P1(f319(x60491,f361(x60491,x60493)))+~P1(f319(f319(f226(a925),x60492),x60493))
% 28.73/28.53 [6050]P1(f319(x60501,x60502))+~P1(f319(x60501,f366(x60501,x60503)))+~P1(f319(f319(f227(a925),x60502),x60503))
% 28.73/28.53 [6058]~E(x60581,f319(a104,x60583))+P1(f319(f319(f227(a925),x60581),f319(a104,x60582)))+~P1(f319(f319(f227(a925),x60583),x60582))
% 28.73/28.53 [6078]E(x60781,x60782)+~E(f319(f319(f75(a925),x60783),x60781),f319(f319(f75(a925),x60783),x60782))+~P1(f319(f319(f227(a925),f2(a925)),x60783))
% 28.73/28.53 [6138]E(f319(x61381,f355(x61381,x61382,x61383)),f72(a925))+~E(f319(f319(f6(x61383,a925),x61381),x61382),f72(a925))+~P1(f319(f55(x61383),x61382))
% 28.73/28.53 [6155]~P6(x61551)+P1(f319(f319(f226(x61551),x61552),f31(x61551,x61553)))+~P1(f319(f319(f321(x61551),x61552),x61553))
% 28.73/28.53 [6178]~P2(x61781)+~P1(f319(f319(f227(x61781),x61783),x61782))+~P1(f319(f319(f226(x61781),x61782),x61783))
% 28.73/28.53 [6179]~P2(x61791)+~P1(f319(f319(f227(x61791),x61793),x61792))+~P1(f319(f319(f227(x61791),x61792),x61793))
% 28.73/28.53 [6180]~P2(x61801)+~P1(f319(f319(f227(x61801),x61803),x61802))+~P1(f319(f319(f227(x61801),x61802),x61803))
% 28.73/28.53 [6181]~P2(x61811)+~P1(f319(f319(f227(x61811),x61813),x61812))+~P1(f319(f319(f227(x61811),x61812),x61813))
% 28.73/28.53 [6182]~P2(x61821)+~P1(f319(f319(f227(x61821),x61823),x61822))+~P1(f319(f319(f227(x61821),x61822),x61823))
% 28.73/28.53 [6183]~P4(x61831)+~P1(f319(f319(f227(x61831),x61833),x61832))+~P1(f319(f319(f226(x61831),x61832),x61833))
% 28.73/28.53 [6184]~P4(x61841)+~P1(f319(f319(f227(x61841),x61843),x61842))+~P1(f319(f319(f226(x61841),x61842),x61843))
% 28.73/28.53 [6185]~P4(x61851)+~P1(f319(f319(f227(x61851),x61853),x61852))+~P1(f319(f319(f226(x61851),x61852),x61853))
% 28.73/28.53 [6186]~P4(x61861)+~P1(f319(f319(f227(x61861),x61863),x61862))+~P1(f319(f319(f227(x61861),x61862),x61863))
% 28.73/28.53 [6187]~P113(x61871)+~P1(f319(f319(f227(x61871),x61873),x61872))+~P1(f319(f319(f227(x61871),x61872),x61873))
% 28.73/28.53 [6209]~E(x62092,x62093)+~E(x62091,x62092)+E(f282(a925,f279(a925),x62091,x62092),f319(f319(f301(a925),x62093),f180(f932(a925,a923))))
% 28.73/28.53 [6217]~E(f319(x62172,f356(x62172,x62173,x62171)),f2(a925))+E(f319(f319(f6(x62171,a925),x62172),x62173),f2(a925))+~P1(f319(f55(x62171),x62173))
% 28.73/28.53 [6218]~E(f319(x62182,f454(x62182,x62183,x62181)),f72(a925))+E(f319(f319(f9(x62181,a925),x62182),x62183),f72(a925))+~P1(f319(f55(x62181),x62183))
% 28.73/28.53 [6234]~P3(x62341)+~P1(f319(f319(f227(x62341),x62343),x62342))+P1(f319(f319(f321(x62341),x62342),f319(f296(x62341),x62343)))
% 28.73/28.53 [6235]~P3(x62351)+~P1(f319(f319(f226(x62351),x62353),x62352))+P1(f319(f319(f321(x62351),x62352),f319(f275(x62351),x62353)))
% 28.73/28.53 [6236]~P3(x62361)+~P1(f319(f319(f227(x62361),x62362),x62363))+P1(f319(f319(f321(x62361),x62362),f319(f274(x62361),x62363)))
% 28.73/28.53 [6237]~P3(x62371)+~P1(f319(f319(f226(x62371),x62372),x62373))+P1(f319(f319(f321(x62371),x62372),f319(f293(x62371),x62373)))
% 28.73/28.53 [6249]E(f319(x62491,f418(x62491,x62492,x62493)),f319(a104,f2(a925)))+~E(f319(f319(f6(x62493,a925),x62491),x62492),f319(a104,f2(a925)))+~P1(f319(f55(x62493),x62492))
% 28.73/28.53 [6330]~P6(x63301)+~P1(f319(f319(f321(x63301),x63303),x63302))+P1(f319(f319(f226(x63301),f32(x63301,x63302)),x63303))
% 28.73/28.53 [6349]~P1(f319(f319(f226(a925),x63491),x63493))+P1(f319(f319(f226(a925),x63491),x63492))+~P1(f319(f319(f226(a925),x63493),x63492))
% 28.73/28.53 [6350]~P1(f319(f319(f226(a1),x63501),x63503))+P1(f319(f319(f226(a1),x63501),x63502))+~P1(f319(f319(f226(a1),x63503),x63502))
% 28.73/28.53 [6370]~P3(x63701)+~P1(f319(f319(f321(x63701),x63703),f319(f275(x63701),x63702)))+P1(f319(f319(f226(x63701),x63702),x63703))
% 28.73/28.53 [6371]~P3(x63711)+~P1(f319(f319(f321(x63711),x63712),f319(f293(x63711),x63713)))+P1(f319(f319(f226(x63711),x63712),x63713))
% 28.73/28.53 [6372]~P3(x63721)+~P1(f319(f319(f321(x63721),x63723),f319(f296(x63721),x63722)))+P1(f319(f319(f227(x63721),x63722),x63723))
% 28.73/28.53 [6373]~P3(x63731)+~P1(f319(f319(f321(x63731),x63732),f319(f274(x63731),x63733)))+P1(f319(f319(f227(x63731),x63732),x63733))
% 28.73/28.53 [6447]~P1(f319(x64471,x64472))+P1(f319(x64471,f800(x64471)))+~P1(f319(f319(f321(x64473),x64472),f234(f932(x64473,a923))))
% 28.73/28.53 [6555]~P113(x65551)+~P41(a925,x65551,x65552)+P1(f319(f319(f226(x65551),f319(x65552,x65553)),f319(x65552,f319(a104,x65553))))
% 28.73/28.53 [6589]~P74(x65891)+P1(f319(f319(f227(x65891),f2(x65891)),f469(x65893,x65892,x65891)))+P1(f319(f319(f226(x65891),x65892),x65893))
% 28.73/28.53 [6590]~P75(x65901)+P1(f319(f319(f227(x65901),f2(x65901)),f788(x65903,x65902,x65901)))+P1(f319(f319(f226(x65901),x65902),x65903))
% 28.73/28.53 [6659]~P68(x66591)+~P1(f319(f319(f226(x66591),x66593),f319(f73(x66591),x66592)))+P1(f319(f319(f226(x66591),x66592),f319(f73(x66591),x66593)))
% 28.73/28.53 [6660]~P68(x66601)+~P1(f319(f319(f226(x66601),x66603),f319(f73(x66601),x66602)))+P1(f319(f319(f226(x66601),x66602),f319(f73(x66601),x66603)))
% 28.73/28.53 [6661]~P68(x66611)+~P1(f319(f319(f227(x66611),x66613),f319(f73(x66611),x66612)))+P1(f319(f319(f227(x66611),x66612),f319(f73(x66611),x66613)))
% 28.73/28.53 [6662]~P68(x66621)+~P1(f319(f319(f227(x66621),x66623),f319(f73(x66621),x66622)))+P1(f319(f319(f227(x66621),x66622),f319(f73(x66621),x66623)))
% 28.73/28.53 [6674]~P1(f319(f319(f227(a925),x66741),x66743))+~P1(f319(f319(f227(a925),x66743),x66742))+P1(f319(f319(f227(a925),f319(a104,x66741)),x66742))
% 28.73/28.53 [6702]~P129(x67021)+P1(f319(f319(f226(x67021),f319(f92(x67021),x67022)),f319(f92(x67021),x67023)))+~P1(f319(f319(f226(a925),x67022),x67023))
% 28.73/28.53 [6703]~P126(x67031)+P1(f319(f319(f226(x67031),f319(f94(x67031),x67032)),f319(f94(x67031),x67033)))+~P1(f319(f319(f226(a1),x67032),x67033))
% 28.73/28.53 [6704]~P129(x67041)+P1(f319(f319(f227(x67041),f319(f92(x67041),x67042)),f319(f92(x67041),x67043)))+~P1(f319(f319(f227(a925),x67042),x67043))
% 28.73/28.53 [6705]~P126(x67051)+P1(f319(f319(f227(x67051),f319(f94(x67051),x67052)),f319(f94(x67051),x67053)))+~P1(f319(f319(f227(a1),x67052),x67053))
% 28.73/28.53 [6706]~P129(x67061)+P1(f319(f319(f227(x67061),f319(f92(x67061),x67062)),f319(f92(x67061),x67063)))+~P1(f319(f319(f227(a925),x67062),x67063))
% 28.73/28.53 [6712]~P4(x67121)+E(f319(f319(f102(f932(x67121,a923)),f319(f274(x67121),x67122)),f319(f294(x67121,x67122),x67123)),f319(f274(x67121),x67123))+~P1(f319(f319(f226(x67121),x67122),x67123))
% 28.73/28.53 [6741]~P96(x67411)+~P1(f319(f319(f226(x67411),x67413),x67412))+P1(f319(f319(f226(x67411),f319(f73(x67411),x67412)),f319(f73(x67411),x67413)))
% 28.73/28.53 [6742]~P96(x67421)+~P1(f319(f319(f226(x67421),x67423),x67422))+P1(f319(f319(f226(x67421),f319(f73(x67421),x67422)),f319(f73(x67421),x67423)))
% 28.73/28.53 [6743]~P68(x67431)+~P1(f319(f319(f226(x67431),x67433),x67432))+P1(f319(f319(f226(x67431),f319(f73(x67431),x67432)),f319(f73(x67431),x67433)))
% 28.73/28.53 [6744]~P68(x67441)+~P1(f319(f319(f226(x67441),x67443),x67442))+P1(f319(f319(f226(x67441),f319(f73(x67441),x67442)),f319(f73(x67441),x67443)))
% 28.73/28.53 [6745]~P68(x67451)+~P1(f319(f319(f227(x67451),x67453),x67452))+P1(f319(f319(f227(x67451),f319(f73(x67451),x67452)),f319(f73(x67451),x67453)))
% 28.73/28.53 [6779]~P4(x67791)+E(f319(f319(f102(f932(x67791,a923)),f319(f274(x67791),x67792)),f295(x67791,x67792,x67793)),f319(f293(x67791),x67793))+~P1(f319(f319(f226(x67791),x67792),x67793))
% 28.73/28.53 [6780]~P4(x67801)+E(f319(f319(f102(f932(x67801,a923)),f319(f293(x67801),x67802)),f297(x67801,x67802,x67803)),f319(f293(x67801),x67803))+~P1(f319(f319(f226(x67801),x67802),x67803))
% 28.73/28.53 [6781]~P4(x67811)+E(f319(f319(f102(f932(x67811,a923)),f319(f293(x67811),x67812)),f298(x67811,x67812,x67813)),f319(f274(x67811),x67813))+~P1(f319(f319(f227(x67811),x67812),x67813))
% 28.73/28.53 [6818]~P4(x68181)+E(f319(f319(f102(f932(x68181,a923)),f319(f294(x68181,x68182),x68183)),f319(f275(x68181),x68183)),f319(f275(x68181),x68182))+~P1(f319(f319(f226(x68181),x68182),x68183))
% 28.73/28.53 [6886]~P6(x68861)+~P1(f319(f319(f226(x68861),f319(x68862,x68863)),x68863))+P1(f319(f319(f226(x68861),f87(x68861,x68862)),x68863))
% 28.73/28.53 [6975]~P4(x69751)+E(f319(f319(f102(f932(x69751,a923)),f295(x69751,x69752,x69753)),f319(f296(x69751),x69753)),f319(f275(x69751),x69752))+~P1(f319(f319(f226(x69751),x69752),x69753))
% 28.73/28.53 [6976]~P4(x69761)+E(f319(f319(f102(f932(x69761,a923)),f297(x69761,x69762,x69763)),f319(f296(x69761),x69763)),f319(f296(x69761),x69762))+~P1(f319(f319(f226(x69761),x69762),x69763))
% 28.73/28.53 [6977]~P4(x69771)+E(f319(f319(f102(f932(x69771,a923)),f298(x69771,x69772,x69773)),f319(f275(x69771),x69773)),f319(f296(x69771),x69772))+~P1(f319(f319(f227(x69771),x69772),x69773))
% 28.73/28.53 [6996]P1(f319(x69961,x69962))+~P1(f319(f319(f226(a925),x69962),x69963))+P1(f319(f319(f321(a925),f361(x69961,x69963)),f295(a925,f2(a925),x69963)))
% 28.73/28.53 [7030]E(x70301,x70302)+~E(f319(f319(f156(x70303),x70301),f659(x70303,x70302,x70301)),f319(f319(f156(x70303),x70302),f659(x70303,x70302,x70301)))+~E(f319(f181(f926(x70303)),x70301),f319(f181(f926(x70303)),x70302))
% 28.73/28.53 [7035]~E(x70353,f319(f319(f30(a925),x70351),x70352))+~P1(f319(f319(f227(a925),f2(a925)),x70352))+P1(f319(f319(f227(a925),x70351),f319(f319(f75(a925),x70352),f319(a104,x70353))))
% 28.73/28.53 [7051]~P1(f319(x70511,x70513))+~P1(f319(f319(f226(a925),x70513),x70512))+P1(f319(f319(f321(a925),f354(x70511,x70512)),f295(a925,f2(a925),x70512)))
% 28.73/28.53 [7092]~P1(f319(x70921,x70923))+P1(f319(x70921,f362(x70921,x70922)))+~P1(f319(f319(f321(a925),x70923),f295(a925,f2(a925),x70922)))
% 28.73/28.53 [7111]~P129(x71113)+~P1(f319(f319(f226(x71113),f319(f92(x71113),x71111)),f319(f92(x71113),x71112)))+P1(f319(f319(f226(a925),x71111),x71112))
% 28.73/28.53 [7112]~P126(x71123)+~P1(f319(f319(f226(x71123),f319(f94(x71123),x71121)),f319(f94(x71123),x71122)))+P1(f319(f319(f226(a1),x71121),x71122))
% 28.73/28.53 [7113]~P129(x71133)+~P1(f319(f319(f227(x71133),f319(f92(x71133),x71131)),f319(f92(x71133),x71132)))+P1(f319(f319(f227(a925),x71131),x71132))
% 28.73/28.53 [7114]~P129(x71143)+~P1(f319(f319(f227(x71143),f319(f92(x71143),x71141)),f319(f92(x71143),x71142)))+P1(f319(f319(f227(a925),x71141),x71142))
% 28.73/28.53 [7115]~P126(x71153)+~P1(f319(f319(f227(x71153),f319(f94(x71153),x71151)),f319(f94(x71153),x71152)))+P1(f319(f319(f227(a1),x71151),x71152))
% 28.73/28.53 [7131]~P129(x71311)+~P1(f319(f319(f227(x71311),f72(x71311)),x71312))+P1(f319(f319(f227(x71311),f72(x71311)),f319(f319(f236(x71311),x71312),f319(a104,x71313))))
% 28.73/28.53 [7134]~P96(x71341)+~P1(f319(f319(f226(x71341),f319(f73(x71341),x71343)),f319(f73(x71341),x71342)))+P1(f319(f319(f226(x71341),x71342),x71343))
% 28.73/28.53 [7135]~P68(x71351)+~P1(f319(f319(f226(x71351),f319(f73(x71351),x71353)),f319(f73(x71351),x71352)))+P1(f319(f319(f226(x71351),x71352),x71353))
% 28.73/28.53 [7136]~P68(x71361)+~P1(f319(f319(f227(x71361),f319(f73(x71361),x71363)),f319(f73(x71361),x71362)))+P1(f319(f319(f227(x71361),x71362),x71363))
% 28.73/28.53 [7160]P1(f319(x71601,x71602))+~P1(f319(x71601,f363(x71601,x71603)))+~P1(f319(f319(f321(a925),x71602),f295(a925,f2(a925),x71603)))
% 28.73/28.53 [7180]~P74(x71801)+P1(f319(f319(f227(x71801),f469(x71803,x71802,x71801)),f72(x71801)))+P1(f319(f319(f226(x71801),x71802),x71803))
% 28.73/28.53 [7199]~E(f39(a925,x71993,x71992),f39(a925,x71991,x71992))+E(f319(f319(f74(a925),x71991),f319(f319(f75(a925),x71992),f520(x71991,x71992,x71993))),x71993)+~P1(f319(f319(f226(a925),x71991),x71993))
% 28.73/28.53 [7254]E(f319(f319(f6(x72541,a925),x72542),x72543),f2(a925))+~P1(f319(f55(x72541),x72543))+P1(f319(f319(f321(x72541),f356(x72542,x72543,x72541)),x72543))
% 28.73/28.53 [7255]E(f319(f319(f9(x72551,a925),x72552),x72553),f72(a925))+~P1(f319(f55(x72551),x72553))+P1(f319(f319(f321(x72551),f454(x72552,x72553,x72551)),x72553))
% 28.73/28.53 [7277]~P4(x72771)+~P1(f319(f319(f226(x72771),x72773),x72772))+P1(f319(f319(f226(f932(x72771,a923)),f319(f296(x72771),x72772)),f319(f296(x72771),x72773)))
% 28.73/28.53 [7278]~P4(x72781)+~P1(f319(f319(f226(x72781),x72782),x72783))+P1(f319(f319(f226(f932(x72781,a923)),f319(f274(x72781),x72782)),f319(f274(x72781),x72783)))
% 28.73/28.53 [7279]~P113(x72791)+~P1(f319(f319(f226(x72791),x72793),x72792))+P1(f319(f319(f226(f932(x72791,a923)),f319(f275(x72791),x72792)),f319(f275(x72791),x72793)))
% 28.73/28.53 [7280]~P113(x72801)+~P1(f319(f319(f226(x72801),x72802),x72803))+P1(f319(f319(f226(f932(x72801,a923)),f319(f293(x72801),x72802)),f319(f293(x72801),x72803)))
% 28.73/28.53 [7281]~P4(x72811)+~P1(f319(f319(f227(x72811),x72812),x72813))+P1(f319(f319(f227(f932(x72811,a923)),f319(f274(x72811),x72812)),f319(f274(x72811),x72813)))
% 28.73/28.53 [7292]~P6(x72921)+P1(f319(f319(f226(x72921),x72922),f32(x72921,x72923)))+P1(f319(f319(f321(x72921),f434(x72923,x72922,x72921)),x72923))
% 28.73/28.53 [7293]~P6(x72931)+P1(f319(f319(f226(x72931),x72932),f32(x72931,x72933)))+P1(f319(f319(f321(x72931),f710(x72932,x72933,x72931)),x72933))
% 28.73/28.53 [7299]~P68(x72991)+P1(f319(f319(f226(x72991),f319(f319(f23(x72991),x72992),x72993)),f2(x72991)))+~P1(f319(f319(f226(x72991),x72992),x72993))
% 28.73/28.53 [7300]~P68(x73001)+P1(f319(f319(f227(x73001),f319(f319(f23(x73001),x73002),x73003)),f2(x73001)))+~P1(f319(f319(f227(x73001),x73002),x73003))
% 28.73/28.53 [7342]P1(f319(x73421,x73422))+P1(f319(f319(f226(a925),f363(x73421,x73423)),x73423))+~P1(f319(f319(f321(a925),x73422),f295(a925,f2(a925),x73423)))
% 28.73/28.53 [7384]~E(f319(f319(f6(x73841,a925),x73842),x73843),f72(a925))+~P1(f319(f55(x73841),x73843))+P1(f319(f319(f321(x73841),f355(x73842,x73843,x73841)),x73843))
% 28.73/28.53 [7385]~P1(f319(x73851,x73853))+P1(f319(f319(f226(a925),f362(x73851,x73852)),x73852))+~P1(f319(f319(f321(a925),x73853),f295(a925,f2(a925),x73852)))
% 28.73/28.53 [7424]~P6(x74241)+P1(f319(f319(f321(x74241),f428(x74243,x74242,x74241)),x74242))+P1(f319(f319(f226(x74241),f31(x74241,x74242)),x74243))
% 28.73/28.53 [7425]~P6(x74251)+P1(f319(f319(f321(x74251),f723(x74253,x74252,x74251)),x74252))+P1(f319(f319(f226(x74251),f31(x74251,x74252)),x74253))
% 28.73/28.53 [7459]~E(f319(f319(f6(x74591,a925),x74592),x74593),f319(a104,f2(a925)))+~P1(f319(f55(x74591),x74593))+P1(f319(f319(f321(x74591),f418(x74592,x74593,x74591)),x74593))
% 28.73/28.53 [7470]E(x74701,f2(a925))+P1(f319(x74702,f39(a925,x74703,x74701)))+P1(f319(f319(f227(a925),f518(x74701,x74703,x74702)),x74701))
% 28.73/28.53 [7579]~P1(f319(x75791,x75792))+P1(f319(x75791,f39(a925,x75792,x75793)))+P1(f319(f319(f227(a925),f518(x75793,x75792,x75791)),x75793))
% 28.73/28.53 [7691]E(x76911,f105(x76912))+~P1(f319(f319(f321(f926(x76912)),x76911),f153(x76912,x76913)))+P1(f319(f319(f321(x76912),f711(x76913,x76911,x76912)),x76913))
% 28.73/28.53 [7713]~P4(x77131)+E(f319(f319(f102(f932(x77131,a923)),f319(f319(f301(x77131),x77132),f180(f932(x77131,a923)))),f298(x77131,x77132,x77133)),f319(f294(x77131,x77132),x77133))+~P1(f319(f319(f227(x77131),x77132),x77133))
% 28.73/28.53 [7734]~P4(x77341)+E(f319(f319(f102(f932(x77341,a923)),f319(f319(f301(x77341),x77342),f180(f932(x77341,a923)))),f297(x77341,x77342,x77343)),f295(x77341,x77342,x77343))+~P1(f319(f319(f226(x77341),x77342),x77343))
% 28.73/28.53 [7844]~P4(x78441)+P1(f319(f319(f226(x78441),x78442),x78443))+~P1(f319(f319(f226(f932(x78441,a923)),f319(f296(x78441),x78443)),f319(f296(x78441),x78442)))
% 28.73/28.53 [7845]~P113(x78451)+P1(f319(f319(f226(x78451),x78452),x78453))+~P1(f319(f319(f226(f932(x78451,a923)),f319(f275(x78451),x78453)),f319(f275(x78451),x78452)))
% 28.73/28.53 [7846]~P4(x78461)+P1(f319(f319(f226(x78461),x78462),x78463))+~P1(f319(f319(f226(f932(x78461,a923)),f319(f274(x78461),x78462)),f319(f274(x78461),x78463)))
% 28.73/28.53 [7847]~P113(x78471)+P1(f319(f319(f226(x78471),x78472),x78473))+~P1(f319(f319(f226(f932(x78471,a923)),f319(f293(x78471),x78472)),f319(f293(x78471),x78473)))
% 28.73/28.53 [7848]~P4(x78481)+P1(f319(f319(f227(x78481),x78482),x78483))+~P1(f319(f319(f227(f932(x78481,a923)),f319(f274(x78481),x78482)),f319(f274(x78481),x78483)))
% 28.73/28.53 [7871]~P68(x78711)+~P1(f319(f319(f226(x78711),f319(f319(f23(x78711),x78712),x78713)),f2(x78711)))+P1(f319(f319(f226(x78711),x78712),x78713))
% 28.73/28.53 [7872]~P68(x78721)+~P1(f319(f319(f227(x78721),f319(f319(f23(x78721),x78722),x78723)),f2(x78721)))+P1(f319(f319(f227(x78721),x78722),x78723))
% 28.73/28.53 [8026]E(x80261,f2(a925))+~E(f319(f134(a925,a925,f74(a925),x80262),x80263),f2(a925))+~P1(f319(f319(f321(a925),x80261),f319(f164(a925),x80263)))
% 28.73/28.53 [8030]~P6(x80301)+~P1(f319(f319(f226(x80301),f428(x80303,x80302,x80301)),x80303))+P1(f319(f319(f226(x80301),f31(x80301,x80302)),x80303))
% 28.73/28.53 [8031]~P6(x80311)+~P1(f319(f319(f226(x80311),f723(x80313,x80312,x80311)),x80313))+P1(f319(f319(f226(x80311),f31(x80311,x80312)),x80313))
% 28.73/28.53 [8188]P1(f319(f319(f226(a1),f2(a1)),f512(x81881,x81882,x81883)))+P1(f319(f319(x81882,f319(f319(f30(a1),x81881),x81883)),f39(a1,x81881,x81883)))+~P1(f319(f319(f227(a1),f2(a1)),x81883))
% 28.73/28.53 [8277]E(x82771,x82772)+~E(f319(f181(f926(x82773)),x82771),f319(f181(f926(x82773)),x82772))+~P1(f319(f319(f249(x82773,x82773,a923),a316),f685(x82773,x82771,x82772)))
% 28.73/28.53 [8348]~P38(x83482,x83483)+E(x83481,f180(f932(x83482,a923)))+~P1(f319(f319(f226(f932(x83482,a923)),x83481),f319(f277(x83482,x83482,x83483),x83481)))
% 28.73/28.53 [8378]~P75(x83781)+~P1(f319(f319(f226(x83781),x83782),f319(f319(f74(x83781),x83783),f788(x83783,x83782,x83781))))+P1(f319(f319(f226(x83781),x83782),x83783))
% 28.73/28.53 [8414]P57(x84141,x84142,x84143)+P1(f319(f319(f321(x84141),f593(x84143,x84142,x84141)),x84142))+P1(f319(f319(f321(f931(x84141,x84141)),f594(x84143,x84142,x84141)),x84143))
% 28.73/28.53 [8435]P1(f319(f319(x84352,f319(f319(f30(a1),x84351),x84353)),f39(a1,x84351,x84353)))+~P1(f319(f319(f227(a1),f2(a1)),x84353))+P1(f319(f319(f227(a1),f512(x84351,x84352,x84353)),x84353))
% 28.73/28.53 [8459]E(f319(f302(a925,a925,f319(f319(f7(a925,a925,a925),f23(a925)),x84591)),f319(f294(a925,x84592),x84593)),f180(f932(a925,a923)))+P1(f319(f319(f227(a925),x84591),x84593))+P1(f319(f319(f227(a925),x84592),x84593))
% 28.73/28.53 [8572]E(f319(f302(a925,a925,f319(f319(f7(a925,a925,a925),f23(a925)),x85721)),f319(f294(a925,x85722),x85723)),f319(f319(f301(a925),f2(a925)),f180(f932(a925,a923))))+P1(f319(f319(f227(a925),x85721),x85723))+~P1(f319(f319(f227(a925),x85722),x85723))
% 28.73/28.53 [8586]~P4(x85861)+E(f141(x85861,x85861,f5(x85861),x85862,x85863),x85863)+~P1(f319(f319(f321(x85861),x85862),f319(f164(x85861),x85863)))
% 28.73/28.53 [8599]P26(x85991,x85991,x85992,x85993)+~P1(f319(f55(x85991),x85993))+~P1(f319(f319(f226(f932(x85991,a923)),x85993),f319(f302(x85991,x85991,x85992),x85993)))
% 28.73/28.53 [8626]E(f319(f319(f74(a1),f319(f319(f75(a1),x86261),f513(x86262,x86263,x86261))),f512(x86262,x86263,x86261)),x86262)+P1(f319(f319(x86263,f319(f319(f30(a1),x86262),x86261)),f39(a1,x86262,x86261)))+~P1(f319(f319(f227(a1),f2(a1)),x86261))
% 28.73/28.53 [8867]~P1(f319(f319(x88671,f513(x88672,x88671,x88673)),f512(x88672,x88671,x88673)))+P1(f319(f319(x88671,f319(f319(f30(a1),x88672),x88673)),f39(a1,x88672,x88673)))+~P1(f319(f319(f227(a1),f2(a1)),x88673))
% 28.73/28.53 [8949]P27(x89491,x89492,x89493,f234(f932(x89491,a923)),f234(f932(x89492,a923)))+~P26(x89491,x89492,x89493,f234(f932(x89491,a923)))+~E(f319(f302(x89491,x89492,x89493),f234(f932(x89491,a923))),f234(f932(x89492,a923)))
% 28.73/28.53 [8950]P27(x89501,x89502,x89503,f234(f932(x89501,a923)),f234(f932(x89502,a923)))+~P26(x89501,x89502,x89503,f234(f932(x89501,a923)))+~E(f319(f302(x89501,x89502,x89503),f234(f932(x89501,a923))),f234(f932(x89502,a923)))
% 28.73/28.53 [9766]~P1(f319(f55(x97661),x97662))+~P1(f319(f319(f321(x97661),x97663),x97662))+P1(f319(f319(f227(a925),f319(f29(x97661),f319(f319(f23(f932(x97661,a923)),x97662),f319(f319(f301(x97661),x97663),f180(f932(x97661,a923)))))),f319(f29(x97661),x97662)))
% 28.73/28.53 [10394]P57(x103941,x103942,x103943)+~P1(f319(f319(f249(x103941,x103941,a923),f319(f319(f7(x103941,f932(x103941,a923),f932(x103941,a923)),f319(f319(f8(f932(a923,a923),f932(f932(x103941,a923),f932(x103941,a923)),x103941),f8(a923,a923,x103941)),f319(f319(f8(a923,f932(a923,a923),x103941),a317),f319(f319(f7(x103941,f932(x103941,a923),a923),f321(x103941)),x103942)))),f319(f319(f7(x103941,f932(x103941,a923),a923),f321(x103941)),x103942))),f594(x103943,x103942,x103941)))+P1(f319(f319(f321(x103941),f593(x103943,x103942,x103941)),x103942))
% 28.73/28.53 [5687]~P124(x56872)+E(x56871,f2(x56872))+E(f319(f319(f283(x56872),x56873),f319(f73(x56872),x56871)),f319(f73(x56872),f319(f319(f283(x56872),x56873),x56871)))
% 28.73/28.53 [5825]~E(x58253,f180(f932(x58251,a923)))+~E(x58252,f180(f932(x58251,a923)))+E(f319(f319(f102(f932(x58251,a923)),x58252),x58253),f180(f932(x58251,a923)))
% 28.73/28.53 [5883]~E(x58833,f2(a925))+~P1(f319(x58831,f2(a925)))+P1(f319(x58831,f319(f319(f30(a925),x58832),x58833)))
% 28.73/28.53 [5884]~E(x58843,f2(a925))+~P1(f319(x58841,f2(a925)))+P1(f319(x58841,f319(f319(f30(a925),x58842),x58843)))
% 28.73/28.53 [6027]~P75(x60272)+E(x60271,f2(x60272))+E(f319(f319(f283(x60272),f319(f69(x60272),x60273)),f319(f69(x60272),x60271)),f319(f69(x60272),f319(f319(f283(x60272),x60273),x60271)))
% 28.73/28.53 [6148]~P65(x61481)+E(f319(f319(f75(x61481),x61482),f319(f319(f30(x61481),x61483),x61482)),x61483)+~P1(f319(f319(f279(x61481),x61482),x61483))
% 28.73/28.53 [6202]~P1(f319(f55(x62021),x62023))+E(f319(f29(x62021),f319(f319(f301(x62021),x62022),x62023)),f319(a104,f319(f29(x62021),x62023)))+P1(f319(f319(f321(x62021),x62022),x62023))
% 28.73/28.53 [6203]~P1(f319(f55(x62031),x62033))+E(f319(f29(x62031),f319(f319(f301(x62031),x62032),x62033)),f319(a104,f319(f29(x62031),x62033)))+P1(f319(f319(f321(x62031),x62032),x62033))
% 28.73/28.53 [6279]~E(x62792,f2(a925))+P1(f319(x62791,f2(a925)))+~P1(f319(x62791,f319(f319(f30(a925),x62793),x62792)))
% 28.73/28.53 [6296]~P1(f319(f55(x62961),x62963))+E(f319(f29(x62961),f319(f319(f301(x62961),x62962),x62963)),f319(f29(x62961),x62963))+~P1(f319(f319(f321(x62961),x62962),x62963))
% 28.73/28.53 [6332]~P1(f319(f55(x63321),x63323))+E(f319(f29(x63321),f319(f319(f301(x63321),x63322),x63323)),f319(f319(f74(a925),f72(a925)),f319(f29(x63321),x63323)))+P1(f319(f319(f321(x63321),x63322),x63323))
% 28.73/28.53 [6448]E(f319(f319(f74(a925),x64481),f357(x64481,x64482,x64483)),x64482)+~P1(f319(x64483,f2(a925)))+P1(f319(x64483,f319(f319(f23(a925),x64482),x64481)))
% 28.73/28.53 [6449]E(f319(f319(f74(a925),x64491),f358(x64491,x64492,x64493)),x64492)+~P1(f319(x64493,f2(a925)))+P1(f319(x64493,f319(f319(f23(a925),x64492),x64491)))
% 28.73/28.53 [6495]~P6(x64951)+~P1(f319(f55(x64951),x64953))+E(f319(f319(f58(x64951,x64951,f102(x64951)),x64952),x64953),f319(f319(f102(x64951),x64952),f31(x64951,x64953)))
% 28.73/28.53 [6496]~P6(x64961)+~P1(f319(f55(x64961),x64963))+E(f319(f319(f58(x64961,x64961,f93(x64961)),x64962),x64963),f319(f319(f93(x64961),x64962),f32(x64961,x64963)))
% 28.73/28.53 [6502]~P99(x65021)+~E(f319(f95(x65021),x65022),f319(f95(x65021),x65023))+P29(x65021,f319(f95(x65021),f319(f319(f74(a1),x65022),f319(f73(a1),x65023))))
% 28.73/28.53 [6511]~P145(x65111)+E(f319(f319(f23(x65111),f319(f92(x65111),x65112)),f319(f92(x65111),x65113)),f319(f92(x65111),f319(f319(f23(a925),x65112),x65113)))+~P1(f319(f319(f226(a925),x65113),x65112))
% 28.73/28.53 [6600]E(f319(f319(f74(a925),x66001),f357(x66001,x66002,x66003)),x66002)+P1(f319(f319(f227(a925),x66002),x66001))+P1(f319(x66003,f319(f319(f23(a925),x66002),x66001)))
% 28.73/28.53 [6601]E(f319(f319(f74(a925),x66011),f358(x66011,x66012,x66013)),x66012)+P1(f319(f319(f227(a925),x66012),x66011))+P1(f319(x66013,f319(f319(f23(a925),x66012),x66011)))
% 28.73/28.53 [6618]~P126(x66181)+E(f319(f319(f75(x66181),f319(f69(x66181),x66182)),x66183),f319(f69(x66181),f319(f319(f75(x66181),x66182),x66183)))+~P1(f319(f319(f226(x66181),f2(x66181)),x66183))
% 28.73/28.53 [6619]~P74(x66191)+E(f319(f319(f283(x66191),f319(f69(x66191),x66192)),x66193),f319(f69(x66191),f319(f319(f283(x66191),x66192),x66193)))+~P1(f319(f319(f227(x66191),f2(x66191)),x66193))
% 28.73/28.53 [6627]~P102(x66271)+~P1(f319(f55(x66271),x66273))+E(f319(f319(f58(x66271,x66271,f93(x66271)),x66272),x66273),f10(x66271,f319(f319(f301(x66271),x66272),x66273)))
% 28.73/28.53 [6628]~P102(x66281)+~P1(f319(f55(x66281),x66283))+E(f319(f319(f58(x66281,x66281,f102(x66281)),x66282),x66283),f13(x66281,f319(f319(f301(x66281),x66282),x66283)))
% 28.73/28.53 [6629]~P4(x66291)+~P1(f319(f55(x66291),x66293))+E(f319(f319(f58(x66291,x66291,f224(x66291)),x66292),x66293),f14(x66291,f319(f319(f301(x66291),x66292),x66293)))
% 28.73/28.53 [6630]~P4(x66301)+~P1(f319(f55(x66301),x66303))+E(f319(f319(f58(x66301,x66301,f225(x66301)),x66302),x66303),f15(x66301,f319(f319(f301(x66301),x66302),x66303)))
% 28.73/28.53 [6676]E(x66761,f105(x66762))+~E(f171(x66762,x66763),f105(f926(x66762)))+~P1(f319(f319(f321(f926(x66762)),x66761),f319(f164(f926(x66762)),x66763)))
% 28.73/28.53 [6720]~P1(f319(f129(x67201),x67203))+P1(f319(f319(f321(x67201),x67202),f319(f164(x67201),x67203)))+P1(f319(f129(x67201),f319(f319(f143(x67201),x67202),x67203)))
% 28.73/28.53 [6731]~P101(x67311)+~P1(f319(f55(x67311),x67313))+E(f319(f57(x67311,f75(x67311)),f319(f319(f301(x67311),x67312),x67313)),f319(f319(f58(x67311,x67311,f75(x67311)),x67312),x67313))
% 28.73/28.53 [6753]~P4(x67531)+~P1(f319(f55(x67531),x67533))+E(f11(x67531,f224(x67531),f319(f319(f301(x67531),x67532),x67533)),f319(f319(f58(x67531,x67531,f224(x67531)),x67532),x67533))
% 28.73/28.53 [6754]~P4(x67541)+~P1(f319(f55(x67541),x67543))+E(f12(x67541,f225(x67541),f319(f319(f301(x67541),x67542),x67543)),f319(f319(f58(x67541,x67541,f225(x67541)),x67542),x67543))
% 28.73/28.53 [6755]P1(f319(x67551,f2(a925)))+~P1(f319(f319(f227(a925),x67552),x67553))+~P1(f319(x67551,f319(f319(f23(a925),x67552),x67553)))
% 28.73/28.53 [6756]P1(f319(x67561,f2(a925)))+~P1(f319(f319(f227(a925),x67562),x67563))+~P1(f319(x67561,f319(f319(f23(a925),x67562),x67563)))
% 28.73/28.53 [6776]~P92(x67761)+P1(f319(f319(f226(x67761),x67762),x67763))+~P1(f319(f319(f226(x67761),f319(f69(x67761),x67762)),x67763))
% 28.73/28.53 [6777]~P92(x67771)+P1(f319(f319(f226(x67771),x67772),x67773))+~P1(f319(f319(f226(x67771),f319(f69(x67771),x67772)),x67773))
% 28.73/28.53 [6778]~P126(x67781)+P1(f319(f319(f227(x67781),x67782),x67783))+~P1(f319(f319(f227(x67781),f319(f69(x67781),x67782)),x67783))
% 28.73/28.53 [6795]E(x67951,f105(x67952))+E(f319(f133(x67952),f319(f319(f130(x67952),x67953),x67951)),f319(f319(f156(x67952),x67951),x67953))+~P1(f319(f319(f227(a925),x67953),f319(f181(f926(x67952)),x67951)))
% 28.73/28.53 [6851]~P1(f319(x68511,x68513))+P1(f319(x68511,f367(x68511,x68512)))+~P1(f319(f319(f321(a925),x68513),f319(f294(a925,f2(a925)),x68512)))
% 28.73/28.53 [6871]P1(f319(x68711,x68712))+~P1(f319(f319(f227(a925),x68712),x68713))+P1(f319(f319(f321(a925),f366(x68711,x68713)),f319(f294(a925,f2(a925)),x68713)))
% 28.73/28.53 [6887]~P129(x68871)+~P1(f319(f319(f226(x68871),f72(x68871)),x68872))+P1(f319(f319(f226(x68871),f72(x68871)),f319(f319(f236(x68871),x68872),x68873)))
% 28.73/28.53 [6889]~P129(x68891)+~P1(f319(f319(f226(x68891),f2(x68891)),x68892))+P1(f319(f319(f226(x68891),f2(x68891)),f319(f319(f236(x68891),x68892),x68893)))
% 28.73/28.53 [6891]~P129(x68911)+~P1(f319(f319(f227(x68911),f2(x68911)),x68912))+P1(f319(f319(f227(x68911),f2(x68911)),f319(f319(f236(x68911),x68912),x68913)))
% 28.73/28.53 [6916]~P1(f319(x69161,x69163))+~P1(f319(f319(f227(a925),x69163),x69162))+P1(f319(f319(f321(a925),f360(x69161,x69162)),f319(f294(a925,f2(a925)),x69162)))
% 28.73/28.53 [6925]P1(f319(f55(x69251),x69252))+~P1(f319(f55(x69251),x69253))+~P1(f319(f319(f226(f932(x69251,a923)),x69252),x69253))
% 28.73/28.53 [6926]P1(f319(f55(x69261),x69262))+~P1(f319(f55(x69261),x69263))+~P1(f319(f319(f226(f932(x69261,a923)),x69262),x69263))
% 28.73/28.53 [6933]P1(f319(x69331,x69332))+~P1(f319(x69331,f368(x69331,x69333)))+~P1(f319(f319(f321(a925),x69332),f319(f294(a925,f2(a925)),x69333)))
% 28.73/28.53 [6945]E(x69451,f2(a925))+P1(f319(x69452,f470(x69451,x69453,x69452)))+~P1(f319(x69452,f319(f319(f30(a925),x69453),x69451)))
% 28.73/28.53 [6952]~P130(x69522)+E(x69521,f2(x69522))+~E(f319(f319(f74(x69522),f319(f319(f75(x69522),x69523),x69523)),f319(f319(f75(x69522),x69521),x69521)),f2(x69522))
% 28.73/28.53 [6953]~P130(x69532)+E(x69531,f2(x69532))+~E(f319(f319(f74(x69532),f319(f319(f75(x69532),x69531),x69531)),f319(f319(f75(x69532),x69533),x69533)),f2(x69532))
% 28.73/28.53 [6997]E(x69971,f2(a925))+~P1(f319(x69972,f471(x69971,x69973,x69972)))+P1(f319(x69972,f319(f319(f30(a925),x69973),x69971)))
% 28.73/28.53 [7002]~P4(x70021)+~P14(x70021,x70023)+P14(x70021,f319(f319(f140(x70021,x70021,f5(x70021)),x70022),x70023))
% 28.73/28.53 [7044]P1(f319(x70441,f470(x70442,x70443,x70441)))+P1(f319(x70441,f2(a925)))+~P1(f319(x70441,f319(f319(f30(a925),x70443),x70442)))
% 28.73/28.53 [7050]~P99(x70501)+E(f319(f95(x70501),x70502),f319(f95(x70501),x70503))+~P29(x70501,f319(f95(x70501),f319(f319(f74(a1),x70502),f319(f73(a1),x70503))))
% 28.73/28.53 [7118]E(x71181,f2(a1))+E(x71182,f2(a1))+~P1(f319(f43(x71182,x71182),f319(f319(f244(a1,a1),x71183),x71181)))
% 28.73/28.53 [7119]E(x71191,f72(a1))+E(x71192,f2(a1))+~P1(f319(f43(x71192,x71192),f319(f319(f244(a1,a1),x71191),x71193)))
% 28.73/28.53 [7133]P1(f319(x71331,x71332))+P1(f319(f319(f227(a925),f368(x71331,x71333)),x71333))+~P1(f319(f319(f321(a925),x71332),f319(f294(a925,f2(a925)),x71333)))
% 28.73/28.53 [7156]~P1(f319(x71561,f357(x71563,x71562,x71561)))+~P1(f319(x71561,f2(a925)))+P1(f319(x71561,f319(f319(f23(a925),x71562),x71563)))
% 28.73/28.53 [7157]~P1(f319(x71571,f358(x71573,x71572,x71571)))+~P1(f319(x71571,f2(a925)))+P1(f319(x71571,f319(f319(f23(a925),x71572),x71573)))
% 28.73/28.53 [7158]~P1(f319(x71581,f471(x71583,x71582,x71581)))+~P1(f319(x71581,f2(a925)))+P1(f319(x71581,f319(f319(f30(a925),x71582),x71583)))
% 28.73/28.53 [7176]~P1(f319(x71761,x71763))+P1(f319(f319(f227(a925),f367(x71761,x71762)),x71762))+~P1(f319(f319(f321(a925),x71763),f319(f294(a925,f2(a925)),x71762)))
% 28.73/28.53 [7177]E(f319(f319(f23(a925),f319(f319(f23(a925),x71771),x71772)),f319(f319(f23(a925),x71773),x71772)),f319(f319(f23(a925),x71771),x71773))+~P1(f319(f319(f226(a925),x71772),x71771))+~P1(f319(f319(f226(a925),x71772),x71773))
% 28.73/28.53 [7212]~P68(x72121)+~P1(f319(f319(f226(x72121),f319(f73(x72121),x72123)),x72122))+P1(f319(f319(f226(x72121),f319(f73(x72121),x72122)),x72123))
% 28.73/28.53 [7213]~P68(x72131)+~P1(f319(f319(f226(x72131),f319(f73(x72131),x72133)),x72132))+P1(f319(f319(f226(x72131),f319(f73(x72131),x72132)),x72133))
% 28.73/28.53 [7214]~P92(x72141)+~P1(f319(f319(f226(x72141),f319(f69(x72141),x72142)),x72143))+P1(f319(f319(f226(x72141),f319(f73(x72141),x72142)),x72143))
% 28.73/28.53 [7215]~P92(x72151)+~P1(f319(f319(f226(x72151),f319(f69(x72151),x72152)),x72153))+P1(f319(f319(f226(x72151),f319(f73(x72151),x72152)),x72153))
% 28.73/28.53 [7216]~P68(x72161)+~P1(f319(f319(f227(x72161),f319(f73(x72161),x72163)),x72162))+P1(f319(f319(f227(x72161),f319(f73(x72161),x72162)),x72163))
% 28.73/28.53 [7217]~P68(x72171)+~P1(f319(f319(f227(x72171),f319(f73(x72171),x72173)),x72172))+P1(f319(f319(f227(x72171),f319(f73(x72171),x72172)),x72173))
% 28.73/28.53 [7218]~P126(x72181)+~P1(f319(f319(f227(x72181),f319(f69(x72181),x72182)),x72183))+P1(f319(f319(f227(x72181),f319(f73(x72181),x72182)),x72183))
% 28.73/28.53 [7249]~P1(f319(x72493,f357(x72492,x72491,x72493)))+P1(f319(f319(f227(a925),x72491),x72492))+P1(f319(x72493,f319(f319(f23(a925),x72491),x72492)))
% 28.73/28.53 [7250]~P1(f319(x72503,f358(x72502,x72501,x72503)))+P1(f319(f319(f227(a925),x72501),x72502))+P1(f319(x72503,f319(f319(f23(a925),x72501),x72502)))
% 28.73/28.53 [7303]~E(f883(x73033,x73032,x73031),f884(x73033,x73032,x73031))+E(f319(f319(f93(f932(x73031,a923)),x73032),f31(f932(x73031,a923),x73033)),f180(f932(x73031,a923)))+P1(f319(f319(f321(f932(x73031,a923)),x73032),x73033))
% 28.73/28.53 [7311]~P1(f319(f55(x73111),x73113))+P1(f319(f55(x73111),f32(f932(x73111,a923),x73112)))+~P1(f319(f319(f321(f932(x73111,a923)),x73113),x73112))
% 28.73/28.53 [7371]~P4(x73711)+E(f319(f319(f102(f932(x73711,a923)),f319(f294(x73711,x73712),x73713)),f319(f319(f301(x73711),x73713),f180(f932(x73711,a923)))),f295(x73711,x73712,x73713))+~P1(f319(f319(f226(x73711),x73712),x73713))
% 28.73/28.53 [7374]E(x73741,f2(a925))+P1(f319(f319(f227(a925),f501(x73741,x73743,x73742)),x73741))+P1(f319(x73742,f319(f319(f30(a925),x73743),x73741)))
% 28.73/28.53 [7403]P1(f319(f319(f227(a925),f319(f181(f926(x74031)),x74032)),f802(x74033,x74031)))+~P1(f319(f55(f926(x74031)),x74033))+~P1(f319(f319(f321(f926(x74031)),x74032),x74033))
% 28.73/28.53 [7408]E(x74081,x74082)+~P1(f319(f319(f226(f932(x74083,a923)),x74081),x74082))+P1(f319(f319(f227(f932(x74083,a923)),x74081),x74082))
% 28.73/28.53 [7409]E(x74091,x74092)+~P1(f319(f319(f226(f932(x74093,a923)),x74091),x74092))+P1(f319(f319(f227(f932(x74093,a923)),x74091),x74092))
% 28.73/28.53 [7421]E(x74211,x74212)+~E(f319(f181(f926(x74213)),x74211),f319(f181(f926(x74213)),x74212))+P1(f319(f319(f227(a925),f659(x74213,x74211,x74212)),f319(f181(f926(x74213)),x74212)))
% 28.73/28.53 [7471]P9(x74711,x74712,x74713)+~E(f319(f256(x74711,x74711),x74713),x74712)+~E(f319(f319(f281(x74711,x74711,x74711),f319(f278(x74711,x74711),x74713)),x74713),x74713)
% 28.73/28.53 [7549]~P1(f319(x75491,f2(a925)))+P1(f319(f319(f227(a925),f501(x75493,x75492,x75491)),x75493))+P1(f319(x75491,f319(f319(f30(a925),x75492),x75493)))
% 28.73/28.53 [7558]~P4(x75581)+E(f319(f319(f102(f932(x75581,a923)),f298(x75581,x75582,x75583)),f319(f319(f301(x75581),x75583),f180(f932(x75581,a923)))),f297(x75581,x75582,x75583))+~P1(f319(f319(f227(x75581),x75582),x75583))
% 28.73/28.53 [7648]~P1(f319(f55(x76481),x76483))+P1(f319(f319(f226(a925),f319(f29(x76481),x76482)),f319(f29(x76481),x76483)))+~P1(f319(f319(f226(f932(x76481,a923)),x76482),x76483))
% 28.73/28.53 [7649]~P1(f319(f55(x76491),x76493))+P1(f319(f319(f227(a925),f319(f29(x76491),x76492)),f319(f29(x76491),x76493)))+~P1(f319(f319(f227(f932(x76491,a923)),x76492),x76493))
% 28.73/28.53 [7778]E(x77781,x77782)+~P1(f319(f319(f226(f932(x77783,a923)),x77782),x77781))+~P1(f319(f319(f226(f932(x77783,a923)),x77781),x77782))
% 28.73/28.53 [7779]E(x77791,x77792)+~P1(f319(f319(f226(f932(x77793,a923)),x77792),x77791))+~P1(f319(f319(f226(f932(x77793,a923)),x77791),x77792))
% 28.73/28.53 [7782]~P4(x77821)+P14(x77821,x77822)+~P14(x77821,f319(f319(f140(x77821,x77821,f5(x77821)),x77823),x77822))
% 28.73/28.53 [7853]~P1(f319(f319(f227(a925),x78533),x78532))+~P1(f319(f319(f227(a925),x78533),x78531))+P1(f319(f319(f227(a925),f319(f319(f23(a925),x78531),x78532)),f319(f319(f23(a925),x78531),x78533)))
% 28.73/28.53 [7854]~P1(f319(f319(f226(a925),x78542),x78541))+~P1(f319(f319(f227(a925),x78541),x78543))+P1(f319(f319(f227(a925),f319(f319(f23(a925),x78541),x78542)),f319(f319(f23(a925),x78543),x78542)))
% 28.73/28.53 [7869]~P1(f319(f319(f227(a1),x78692),f2(a1)))+~P1(f319(f319(f226(a1),x78693),x78691))+P1(f319(f319(f226(a1),f319(f319(f30(a1),x78691),x78692)),f319(f319(f30(a1),x78693),x78692)))
% 28.73/28.53 [7885]~P1(f319(f319(f227(a925),f2(a925)),x78851))+~P1(f319(f319(f226(a925),x78852),x78853))+P1(f319(f319(f226(a925),f319(f319(f75(a925),x78851),x78852)),f319(f319(f75(a925),x78851),x78853)))
% 28.73/28.53 [7886]~P1(f319(f319(f227(a925),f2(a925)),x78863))+~P1(f319(f319(f226(a925),x78863),x78862))+P1(f319(f319(f226(a925),f319(f319(f30(a925),x78861),x78862)),f319(f319(f30(a925),x78861),x78863)))
% 28.73/28.53 [7887]~P1(f319(f319(f227(a1),f2(a1)),x78872))+~P1(f319(f319(f226(a1),x78871),x78873))+P1(f319(f319(f226(a1),f319(f319(f30(a1),x78871),x78872)),f319(f319(f30(a1),x78873),x78872)))
% 28.73/28.53 [7888]~P1(f319(f319(f227(a925),f2(a925)),x78881))+~P1(f319(f319(f227(a925),x78882),x78883))+P1(f319(f319(f227(a925),f319(f319(f75(a925),x78881),x78882)),f319(f319(f75(a925),x78881),x78883)))
% 28.73/28.53 [7889]~P1(f319(f319(f227(a925),f2(a925)),x78891))+~P1(f319(f319(f227(a925),x78892),x78893))+P1(f319(f319(f227(a925),f319(f319(f75(a925),x78891),x78892)),f319(f319(f75(a925),x78891),x78893)))
% 28.73/28.53 [7890]~P1(f319(f319(f227(a925),f2(a925)),x78902))+~P1(f319(f319(f227(a925),x78901),x78903))+P1(f319(f319(f227(a925),f319(f319(f75(a925),x78901),x78902)),f319(f319(f75(a925),x78903),x78902)))
% 28.73/28.53 [7891]~P1(f319(f319(f227(a925),f2(a925)),x78912))+~P1(f319(f319(f227(a925),x78911),x78913))+P1(f319(f319(f227(a925),f319(f319(f75(a925),x78911),x78912)),f319(f319(f75(a925),x78913),x78912)))
% 28.73/28.53 [7892]~P1(f319(f319(f227(a925),f2(a925)),x78921))+~P1(f319(f319(f227(a925),x78922),x78923))+P1(f319(f319(f227(a925),f319(f319(f75(a925),x78921),x78922)),f319(f319(f75(a925),x78921),x78923)))
% 28.73/28.53 [7893]~P1(f319(f319(f227(a1),f2(a1)),x78931))+~P1(f319(f319(f227(a1),x78932),x78933))+P1(f319(f319(f227(a1),f319(f319(f75(a1),x78931),x78932)),f319(f319(f75(a1),x78931),x78933)))
% 28.73/28.53 [7941]E(x79411,f2(a925))+E(f319(f319(f74(a925),f319(f319(f75(a925),x79411),f471(x79411,x79412,x79413))),f501(x79411,x79412,x79413)),x79412)+P1(f319(x79413,f319(f319(f30(a925),x79412),x79411)))
% 28.73/28.53 [8000]E(f319(f319(f74(a925),f319(f319(f75(a925),x80001),f471(x80001,x80002,x80003))),f501(x80001,x80002,x80003)),x80002)+~P1(f319(x80003,f2(a925)))+P1(f319(x80003,f319(f319(f30(a925),x80002),x80001)))
% 28.73/28.53 [8017]~P1(f319(f55(x80171),x80173))+P1(f319(f319(f321(x80171),f474(x80172,x80173,x80171)),x80173))+P1(f319(f319(f227(a925),f2(a925)),f319(f319(f9(x80171,a925),x80172),x80173)))
% 28.73/28.53 [8018]~P1(f319(f55(x80181),x80183))+P1(f319(f319(f321(x80181),f511(x80182,x80183,x80181)),x80183))+P1(f319(f319(f227(a925),f2(a925)),f319(f319(f9(x80181,a925),x80182),x80183)))
% 28.73/28.53 [8120]E(x81201,f2(a925))+P1(f319(f319(f279(a925),x81202),x81203))+~P1(f319(f319(f279(a925),f319(f319(f75(a925),x81201),x81202)),f319(f319(f75(a925),x81201),x81203)))
% 28.73/28.53 [8313]E(x83131,f180(f932(x83132,a923)))+E(x83131,f319(f319(f301(x83132),x83133),f180(f932(x83132,a923))))+~P1(f319(f319(f226(f932(x83132,a923)),x83131),f319(f319(f301(x83132),x83133),f180(f932(x83132,a923)))))
% 28.73/28.53 [8337]~P4(x83371)+~P14(x83371,x83373)+P14(x83371,f319(f319(f130(x83371),f319(f181(f926(x83371)),f169(x83371,x83372,x83373))),x83373))
% 28.73/28.53 [8349]~P1(f319(f319(f227(a925),f72(a925)),x83493))+P1(f319(f319(f226(a925),x83491),x83492))+~P1(f319(f319(f279(a925),f319(f319(f236(a925),x83493),x83491)),f319(f319(f236(a925),x83493),x83492)))
% 28.73/28.53 [8350]~P1(f319(f319(f227(a925),f2(a925)),x83503))+P1(f319(f319(f226(a925),x83501),x83502))+~P1(f319(f319(f226(a925),f319(f319(f75(a925),x83503),x83501)),f319(f319(f75(a925),x83503),x83502)))
% 28.73/28.53 [8351]~P1(f319(f319(f227(a925),f2(a925)),x83513))+P1(f319(f319(f226(a925),x83511),x83512))+~P1(f319(f319(f226(a925),f319(f319(f75(a925),x83513),x83511)),f319(f319(f75(a925),x83513),x83512)))
% 28.73/28.53 [8352]~P1(f319(f319(f227(a925),f2(a925)),x83523))+P1(f319(f319(f226(a925),x83521),x83522))+~P1(f319(f319(f226(a925),f319(f319(f75(a925),x83521),x83523)),f319(f319(f75(a925),x83522),x83523)))
% 28.73/28.53 [8353]~P1(f319(f319(f227(a925),f2(a925)),x83533))+P1(f319(f319(f227(a925),x83531),x83532))+~P1(f319(f319(f227(a925),f319(f319(f75(a925),x83533),x83531)),f319(f319(f75(a925),x83533),x83532)))
% 28.73/28.53 [8354]~P1(f319(f319(f227(a925),f2(a925)),x83543))+P1(f319(f319(f227(a925),x83541),x83542))+~P1(f319(f319(f227(a925),f319(f319(f236(a925),x83543),x83541)),f319(f319(f236(a925),x83543),x83542)))
% 28.73/28.53 [8395]~E(f319(f319(f93(f932(x83951,a923)),f884(x83953,x83952,x83951)),f883(x83953,x83952,x83951)),f180(f932(x83951,a923)))+E(f319(f319(f93(f932(x83951,a923)),x83952),f31(f932(x83951,a923),x83953)),f180(f932(x83951,a923)))+P1(f319(f319(f321(f932(x83951,a923)),x83952),x83953))
% 28.73/28.53 [8408]E(x84081,f105(x84082))+~E(f319(f134(f926(x84082),f926(x84082),f126(x84082),f105(x84082)),x84083),f105(x84082))+~P1(f319(f319(f321(f926(x84082)),x84081),f319(f164(f926(x84082)),x84083)))
% 28.73/28.53 [8409]E(x84091,f105(x84092))+~E(f319(f134(f926(x84092),f926(x84092),f126(x84092),f105(x84092)),x84093),f105(x84092))+~P1(f319(f319(f321(f926(x84092)),x84091),f319(f164(f926(x84092)),x84093)))
% 28.73/28.53 [8464]E(x84641,f180(f932(f932(x84642,a923),a923)))+P1(f319(f319(f321(f932(x84642,a923)),f882(x84643,x84641,x84642)),x84641))+P1(f319(f319(f226(f932(x84642,a923)),f32(f932(x84642,a923),x84641)),x84643))
% 28.73/28.53 [8471]~P78(x84711)+~P79(x84711)+E(f319(f319(f6(a1,x84711),f319(f319(f8(a925,x84711,a1),x84712),a96)),f319(f302(a925,a1,f92(a1)),x84713)),f319(f319(f6(a925,x84711),x84712),x84713))
% 28.73/28.53 [8472]~P78(x84721)+~P79(x84721)+E(f319(f319(f9(a1,x84721),f319(f319(f8(a925,x84721,a1),x84722),a96)),f319(f302(a925,a1,f92(a1)),x84723)),f319(f319(f9(a925,x84721),x84722),x84723))
% 28.73/28.53 [8515]~P1(f319(f55(x85151),x85153))+~P1(f319(f319(f227(a925),f2(a925)),f319(x85152,f474(x85152,x85153,x85151))))+P1(f319(f319(f227(a925),f2(a925)),f319(f319(f9(x85151,a925),x85152),x85153)))
% 28.73/28.53 [8516]~P1(f319(f55(x85161),x85163))+~P1(f319(f319(f227(a925),f2(a925)),f319(x85162,f511(x85162,x85163,x85161))))+P1(f319(f319(f227(a925),f2(a925)),f319(f319(f9(x85161,a925),x85162),x85163)))
% 28.73/28.53 [8553]~P73(x85532)+E(x85531,f72(x85532))+E(f319(f319(f283(x85532),f319(f319(f23(x85532),f319(f319(f236(x85532),x85531),x85533)),f72(x85532))),f319(f319(f23(x85532),x85531),f72(x85532))),f319(f319(f6(a925,x85532),f319(f236(x85532),x85531)),f319(f294(a925,f2(a925)),x85533)))
% 28.73/28.53 [8610]E(x86101,f2(a925))+~P1(f319(x86103,f319(f319(f30(a925),x86102),x86101)))+P1(f319(f319(f227(a925),x86102),f319(f319(f75(a925),x86101),f319(a104,f470(x86101,x86102,x86103)))))
% 28.73/28.53 [8629]P1(f319(x86291,f2(a925)))+~P1(f319(x86291,f319(f319(f30(a925),x86292),x86293)))+P1(f319(f319(f227(a925),x86292),f319(f319(f75(a925),x86293),f319(a104,f470(x86293,x86292,x86291)))))
% 28.73/28.53 [8667]E(x86671,f2(a925))+~P1(f319(x86673,f319(f319(f30(a925),x86672),x86671)))+P1(f319(f319(f226(a925),f319(f319(f75(a925),x86671),f470(x86671,x86672,x86673))),x86672))
% 28.73/28.53 [8700]P1(f319(x87001,f2(a925)))+~P1(f319(x87001,f319(f319(f30(a925),x87003),x87002)))+P1(f319(f319(f226(a925),f319(f319(f75(a925),x87002),f470(x87002,x87003,x87001))),x87003))
% 28.73/28.53 [8708]~P4(x87081)+E(f319(f319(f140(x87081,x87081,f5(x87081)),x87082),x87083),f141(x87081,x87081,f5(x87081),x87082,x87083))+P1(f319(f319(f321(x87081),x87082),f319(f164(x87081),x87083)))
% 28.73/28.53 [8745]~E(f319(x87453,f599(x87452,x87453,x87451)),f319(x87453,f603(x87452,x87453,x87451)))+~P64(x87451,f319(x87453,f600(x87452,x87453,x87451)))+P64(x87451,f319(f319(f33(x87452,f932(x87451,f932(x87451,a923))),f234(f932(x87452,a923))),x87453))
% 28.73/28.53 [8754]E(x87541,f180(f932(f932(x87542,a923),a923)))+~P1(f319(f319(f226(f932(x87542,a923)),f882(x87543,x87541,x87542)),x87543))+P1(f319(f319(f226(f932(x87542,a923)),f32(f932(x87542,a923),x87541)),x87543))
% 28.73/28.53 [8815]~P75(x88151)+~P1(f319(f319(f227(x88151),x88152),x88153))+P1(f319(f319(f227(x88151),x88152),f319(f319(f283(x88151),f319(f319(f74(x88151),x88152),x88153)),f319(f319(f74(x88151),f72(x88151)),f72(x88151)))))
% 28.73/28.53 [8873]~P1(f319(f319(x88731,f531(x88731,x88733,x88732)),f535(x88731,x88733,x88732)))+P1(f319(f319(x88731,x88732),x88733))+~P1(f319(f307(f931(a1,a1),a46),f319(f319(f244(a1,a1),x88732),x88733)))
% 28.73/28.53 [8874]~P1(f319(f319(x88741,f536(x88741,x88743,x88742)),f538(x88741,x88743,x88742)))+P1(f319(f319(x88741,x88742),x88743))+~P1(f319(f307(f931(a1,a1),a52),f319(f319(f244(a1,a1),x88742),x88743)))
% 28.73/28.53 [8875]~P1(f319(f319(x88751,f541(x88751,x88753,x88752)),f542(x88751,x88753,x88752)))+P1(f319(f319(x88751,x88752),x88753))+~P1(f319(f307(f931(a1,a1),a213),f319(f319(f244(a1,a1),x88752),x88753)))
% 28.73/28.53 [8876]~P1(f319(f319(x88761,f543(x88761,x88763,x88762)),f544(x88761,x88763,x88762)))+P1(f319(f319(x88761,x88762),x88763))+~P1(f319(f307(f931(a925,a925),a211),f319(f319(f244(a925,a925),x88762),x88763)))
% 28.73/28.53 [8877]~P1(f319(f319(x88771,f698(x88771,x88773,x88772)),f699(x88771,x88773,x88772)))+P1(f319(f319(x88771,x88772),x88773))+~P1(f319(f307(f931(a1,a1),a174),f319(f319(f244(a1,a1),x88772),x88773)))
% 28.73/28.53 [8878]~P1(f319(f319(x88781,f795(x88781,x88783,x88782)),f796(x88781,x88783,x88782)))+P1(f319(f319(x88781,x88782),x88783))+~P1(f319(f307(f931(a1,a1),a125),f319(f319(f244(a1,a1),x88782),x88783)))
% 28.73/28.53 [9155]P1(f319(f319(x91551,x91552),x91553))+P1(f319(f307(f931(a925,a925),a211),f319(f319(f244(a925,a925),f543(x91551,x91553,x91552)),f544(x91551,x91553,x91552))))+~P1(f319(f307(f931(a925,a925),a211),f319(f319(f244(a925,a925),x91552),x91553)))
% 28.73/28.53 [9156]P1(f319(f319(x91561,x91562),x91563))+P1(f319(f307(f931(a1,a1),a46),f319(f319(f244(a1,a1),f531(x91561,x91563,x91562)),f535(x91561,x91563,x91562))))+~P1(f319(f307(f931(a1,a1),a46),f319(f319(f244(a1,a1),x91562),x91563)))
% 28.73/28.53 [9157]P1(f319(f319(x91571,x91572),x91573))+P1(f319(f307(f931(a1,a1),a52),f319(f319(f244(a1,a1),f536(x91571,x91573,x91572)),f538(x91571,x91573,x91572))))+~P1(f319(f307(f931(a1,a1),a52),f319(f319(f244(a1,a1),x91572),x91573)))
% 28.73/28.53 [9158]P1(f319(f319(x91581,x91582),x91583))+P1(f319(f307(f931(a1,a1),a213),f319(f319(f244(a1,a1),f541(x91581,x91583,x91582)),f542(x91581,x91583,x91582))))+~P1(f319(f307(f931(a1,a1),a213),f319(f319(f244(a1,a1),x91582),x91583)))
% 28.73/28.53 [9159]P1(f319(f319(x91591,x91592),x91593))+P1(f319(f307(f931(a1,a1),a174),f319(f319(f244(a1,a1),f698(x91591,x91593,x91592)),f699(x91591,x91593,x91592))))+~P1(f319(f307(f931(a1,a1),a174),f319(f319(f244(a1,a1),x91592),x91593)))
% 28.73/28.53 [9160]P1(f319(f319(x91601,x91602),x91603))+P1(f319(f307(f931(a1,a1),a125),f319(f319(f244(a1,a1),f795(x91601,x91603,x91602)),f796(x91601,x91603,x91602))))+~P1(f319(f307(f931(a1,a1),a125),f319(f319(f244(a1,a1),x91602),x91603)))
% 28.73/28.53 [9501]~P1(f319(f55(x95011),x95013))+P1(f319(f319(f321(f931(f932(x95011,a923),f932(x95011,a923))),f319(f319(f244(f932(x95011,a923),f932(x95011,a923)),x95012),x95013)),f306(x95011)))+~P1(f319(f319(f227(f932(x95011,a923)),x95012),x95013))
% 28.73/28.53 [9576]~P64(x95761,f319(x95763,f600(x95762,x95763,x95761)))+P64(x95761,f319(f319(f33(x95762,f932(x95761,f932(x95761,a923))),f234(f932(x95762,a923))),x95763))+~E(f319(f319(f93(f932(x95761,a923)),f241(x95761,x95761,f319(x95763,f599(x95762,x95763,x95761)))),f242(x95761,x95761,f319(x95763,f603(x95762,x95763,x95761)))),f180(f932(x95761,a923)))
% 28.73/28.53 [9781]P57(x97811,x97812,x97813)+P1(f319(f319(f321(f931(x97811,x97811)),f594(x97813,x97812,x97811)),x97813))+~P1(f319(f319(f321(f931(x97811,x97811)),f319(f319(f244(x97811,x97811),f593(x97813,x97812,x97811)),f593(x97813,x97812,x97811))),x97813))
% 28.73/28.53 [10397]P57(x103971,x103972,x103973)+~P1(f319(f319(f249(x103971,x103971,a923),f319(f319(f7(x103971,f932(x103971,a923),f932(x103971,a923)),f319(f319(f8(f932(a923,a923),f932(f932(x103971,a923),f932(x103971,a923)),x103971),f8(a923,a923,x103971)),f319(f319(f8(a923,f932(a923,a923),x103971),a317),f319(f319(f7(x103971,f932(x103971,a923),a923),f321(x103971)),x103972)))),f319(f319(f7(x103971,f932(x103971,a923),a923),f321(x103971)),x103972))),f594(x103973,x103972,x103971)))+~P1(f319(f319(f321(f931(x103971,x103971)),f319(f319(f244(x103971,x103971),f593(x103973,x103972,x103971)),f593(x103973,x103972,x103971))),x103973))
% 28.73/28.53 [5866]~P65(x58662)+E(x58661,f2(x58662))+E(f319(f319(f30(x58662),f319(f319(f75(x58662),x58663),x58661)),x58661),x58663)
% 28.73/28.53 [5867]~P65(x58672)+E(x58671,f2(x58672))+E(f319(f319(f30(x58672),f319(f319(f75(x58672),x58671),x58673)),x58671),x58673)
% 28.73/28.53 [6512]~P65(x65121)+E(f319(f319(f75(x65121),f319(f319(f30(x65121),x65122),x65123)),x65123),x65122)+~P1(f319(f319(f279(x65121),x65123),x65122))
% 28.73/28.53 [6675]~P79(x66751)+~E(f319(x66752,f2(a925)),f2(x66751))+E(f319(f319(f6(a925,x66751),x66752),f319(f294(a925,f319(a104,f2(a925))),x66753)),f319(f319(f6(a925,x66751),x66752),f319(f294(a925,f2(a925)),x66753)))
% 28.73/28.53 [6811]~P65(x68112)+E(x68111,f2(x68112))+E(f319(f319(f30(x68112),f319(f319(f74(x68112),x68113),x68111)),x68111),f319(f319(f74(x68112),f319(f319(f30(x68112),x68113),x68111)),f72(x68112)))
% 28.73/28.53 [6812]~P65(x68122)+E(x68121,f2(x68122))+E(f319(f319(f30(x68122),f319(f319(f74(x68122),x68121),x68123)),x68121),f319(f319(f74(x68122),f319(f319(f30(x68122),x68123),x68121)),f72(x68122)))
% 28.73/28.53 [7033]~P1(f319(x70333,f2(a1)))+P1(f319(f319(f226(a925),x70331),x70332))+P1(f319(x70333,f319(f92(a1),f319(f319(f23(a925),x70332),x70331))))
% 28.73/28.53 [7139]P1(f319(f319(f227(a925),x71392),x71391))+P1(f319(f319(f226(a925),x71391),x71392))+P1(f319(x71393,f319(f92(a1),f319(f319(f23(a925),x71392),x71391))))
% 28.73/28.53 [7211]E(f319(f319(f74(a925),f319(f95(a925),x72111)),f319(f319(f74(a925),f319(f95(a925),x72112)),x72113)),f319(f319(f74(a925),f319(f95(a925),x72111)),x72113))+P1(f319(a185,f319(f95(a1),x72111)))+~P1(f319(a185,f319(f95(a1),x72112)))
% 28.73/28.53 [7289]~E(x72892,f319(f319(f30(a925),x72893),x72891))+~P1(f319(f319(f227(a925),f2(a925)),x72891))+P1(f319(f319(f226(a925),f319(f319(f75(a925),x72891),x72892)),x72893))
% 28.73/28.53 [7405]~P1(f319(f55(x74051),x74053))+~P1(f319(f55(x74051),x74052))+P1(f319(f55(x74051),f319(f319(f102(f932(x74051,a923)),x74052),x74053)))
% 28.73/28.53 [7406]~P1(f319(f55(x74061),x74063))+~P1(f319(f55(x74061),x74062))+P1(f319(f55(x74061),f319(f319(f102(f932(x74061,a923)),x74062),x74063)))
% 28.73/28.53 [7407]~P1(f319(f55(x74071),x74073))+~P1(f319(f55(x74071),x74072))+P1(f319(f55(x74071),f319(f319(f23(f932(x74071,a923)),x74072),x74073)))
% 28.73/28.53 [7456]~P39(x74561,x74563)+~P39(x74561,x74562)+P39(x74561,f319(f319(f93(f932(f931(x74561,x74561),a923)),x74562),x74563))
% 28.73/28.53 [7457]~P56(x74571,x74573)+~P56(x74571,x74572)+P56(x74571,f319(f319(f102(f932(f931(x74571,x74571),a923)),x74572),x74573))
% 28.73/28.53 [7458]~P56(x74581,x74583)+~P56(x74581,x74582)+P56(x74581,f319(f319(f93(f932(f931(x74581,x74581),a923)),x74582),x74583))
% 28.73/28.53 [7697]~P4(x76971)+~P1(f319(f55(x76971),x76972))+E(f131(x76971,f319(f319(f23(f932(x76971,a923)),x76972),f319(f319(f301(x76971),x76973),f180(f932(x76971,a923))))),f162(x76971,x76973,f131(x76971,x76972)))
% 28.73/28.53 [7758]P1(f319(x77581,f2(a1)))+~P1(f319(f319(f227(a925),x77582),x77583))+~P1(f319(x77581,f319(f92(a1),f319(f319(f23(a925),x77582),x77583))))
% 28.73/28.53 [7776]~P1(f319(f55(x77761),x77762))+E(f319(f29(x77761),f319(f319(f23(f932(x77761,a923)),x77762),f319(f319(f301(x77761),x77763),f180(f932(x77761,a923))))),f319(f29(x77761),x77762))+P1(f319(f319(f321(x77761),x77763),x77762))
% 28.73/28.53 [7909]~P129(x79091)+~P1(f319(f319(f227(x79091),f72(x79091)),x79092))+P1(f319(f319(f227(x79091),f72(x79091)),f319(f319(f75(x79091),x79092),f319(f319(f236(x79091),x79092),x79093))))
% 28.73/28.53 [7951]~P1(f319(f55(x79511),x79513))+E(f319(f319(f23(a925),f319(f29(x79511),x79512)),f319(f29(x79511),x79513)),f319(f29(x79511),f319(f319(f23(f932(x79511,a923)),x79512),x79513)))+~P1(f319(f319(f226(f932(x79511,a923)),x79513),x79512))
% 28.73/28.53 [8008]~P1(f319(f319(f226(a925),x80082),x80083))+~P1(f319(f319(f226(a925),x80081),f319(f319(f23(a925),x80083),x80082)))+P1(f319(f319(f226(a925),f319(f319(f74(a925),x80081),x80082)),x80083))
% 28.73/28.53 [8063]P1(f319(f55(x80631),x80632))+~P1(f319(f55(x80631),x80633))+~P1(f319(f55(x80631),f319(f319(f23(f932(x80631,a923)),x80632),x80633)))
% 28.73/28.53 [8068]~P1(f319(f55(x80681),x80682))+E(f319(f29(x80681),f319(f319(f23(f932(x80681,a923)),x80682),f319(f319(f301(x80681),x80683),f180(f932(x80681,a923))))),f319(f319(f23(a925),f319(f29(x80681),x80682)),f72(a925)))+~P1(f319(f319(f321(x80681),x80683),x80682))
% 28.73/28.53 [8069]~P1(f319(f55(x80691),x80692))+E(f319(f29(x80691),f319(f319(f23(f932(x80691,a923)),x80692),f319(f319(f301(x80691),x80693),f180(f932(x80691,a923))))),f319(f319(f23(a925),f319(f29(x80691),x80692)),f72(a925)))+~P1(f319(f319(f321(x80691),x80693),x80692))
% 28.73/28.53 [8145]P64(x81451,x81452)+~P64(x81451,x81453)+~P1(f319(f319(f226(f932(x81451,f932(x81451,a923))),x81452),x81453))
% 28.73/28.53 [8187]~P1(f319(f319(f226(a925),x81873),x81872))+P1(f319(f319(f226(a925),x81871),f319(f319(f23(a925),x81872),x81873)))+~P1(f319(f319(f226(a925),f319(f319(f74(a925),x81871),x81873)),x81872))
% 28.73/28.53 [8205]P38(x82051,x82052)+~P38(x82051,x82053)+~P1(f319(f319(f226(f932(f931(x82051,x82051),a923)),x82052),x82053))
% 28.73/28.53 [8206]P62(x82061,x82062)+~P62(x82061,x82063)+~P1(f319(f319(f226(f932(f931(x82061,x82061),a923)),x82062),x82063))
% 28.73/28.53 [8207]P40(x82071,x82072)+~P40(x82071,x82073)+~P1(f319(f319(f226(f932(f931(x82071,x82071),a923)),x82072),x82073))
% 28.73/28.53 [8442]~P129(x84421)+~P1(f319(f319(f227(x84421),f72(x84421)),x84422))+P1(f319(f319(f227(x84421),f319(f319(f236(x84421),x84422),x84423)),f319(f319(f75(x84421),x84422),f319(f319(f236(x84421),x84422),x84423))))
% 28.73/28.53 [8534]~P1(f319(x85341,f2(a1)))+~P1(f319(x85341,f319(f319(f23(a1),f319(f92(a1),x85342)),f319(f92(a1),x85343))))+P1(f319(x85341,f319(f92(a1),f319(f319(f23(a925),x85342),x85343))))
% 28.73/28.53 [8549]~P1(f319(f319(f226(a925),x85493),x85492))+P1(f319(x85491,f319(f319(f23(a1),f319(f92(a1),x85492)),f319(f92(a1),x85493))))+~P1(f319(x85491,f319(f92(a1),f319(f319(f23(a925),x85492),x85493))))
% 28.73/28.53 [8569]P1(f319(f319(f227(a925),x85691),x85692))+~P1(f319(x85693,f319(f319(f23(a1),f319(f92(a1),x85691)),f319(f92(a1),x85692))))+P1(f319(x85693,f319(f92(a1),f319(f319(f23(a925),x85691),x85692))))
% 28.73/28.53 [8623]~P130(x86232)+E(x86231,f2(x86232))+P1(f319(f319(f227(x86232),f2(x86232)),f319(f319(f74(x86232),f319(f319(f75(x86232),x86233),x86233)),f319(f319(f75(x86232),x86231),x86231))))
% 28.73/28.53 [8624]~P130(x86242)+E(x86241,f2(x86242))+P1(f319(f319(f227(x86242),f2(x86242)),f319(f319(f74(x86242),f319(f319(f75(x86242),x86241),x86241)),f319(f319(f75(x86242),x86243),x86243))))
% 28.73/28.53 [8728]~P1(f319(f319(f227(a925),f2(a925)),x87281))+~P1(f319(f319(f227(a1),x87282),x87283))+P1(f319(f319(f227(a1),f319(f319(f75(a1),f319(f92(a1),x87281)),x87282)),f319(f319(f75(a1),f319(f92(a1),x87281)),x87283)))
% 28.73/28.53 [8783]E(f319(f319(f93(f932(x87831,a923)),x87832),f31(f932(x87831,a923),x87833)),f180(f932(x87831,a923)))+P1(f319(f319(f321(f932(x87831,a923)),x87832),x87833))+P1(f319(f319(f321(f932(x87831,a923)),f884(x87833,x87832,x87831)),f319(f319(f301(f932(x87831,a923)),x87832),x87833)))
% 28.73/28.53 [8784]E(f319(f319(f93(f932(x87841,a923)),x87842),f31(f932(x87841,a923),x87843)),f180(f932(x87841,a923)))+P1(f319(f319(f321(f932(x87841,a923)),x87842),x87843))+P1(f319(f319(f321(f932(x87841,a923)),f883(x87843,x87842,x87841)),f319(f319(f301(f932(x87841,a923)),x87842),x87843)))
% 28.73/28.53 [8814]E(x88141,x88142)+~E(f319(f181(f926(x88143)),x88141),f319(f181(f926(x88143)),x88142))+P1(f319(f319(f321(f931(x88143,x88143)),f685(x88143,x88141,x88142)),f319(f164(f931(x88143,x88143)),f319(f319(f173(x88143,x88143),x88142),x88141))))
% 28.73/28.53 [9065]E(f299(x90651,x90652),f299(x90651,x90653))+~P1(f319(f319(f226(f932(f931(x90651,x90651),a923)),x90653),f299(x90651,x90652)))+~P1(f319(f319(f226(f932(f931(x90651,x90651),a923)),x90652),x90653))
% 28.73/28.53 [9133]~P57(x91331,f234(f932(x91331,a923)),x91333)+P1(f319(f319(f226(f932(f931(f926(x91331),f926(x91331)),a923)),f149(x91331,x91332)),f150(x91331,x91333)))+~P1(f319(f319(f226(f932(f931(x91331,x91331),a923)),x91332),x91333))
% 28.73/28.53 [9335]P38(x93351,x93352)+~P1(f319(f319(f321(x93351),x93353),f629(x93352,x93351)))+P1(f319(f319(f321(f931(x93351,x93351)),f319(f319(f244(x93351,x93351),f660(x93352,x93351,x93353)),x93353)),x93352))
% 28.73/28.53 [9370]~P1(f319(f55(x93701),x93702))+P1(f319(f55(f932(x93701,a923)),f319(f319(f54(x93701),x93702),x93703)))+~P1(f319(f319(f226(f932(f931(x93701,x93701),a923)),x93703),f319(f319(f246(x93701,x93701),x93702),f319(f16(f932(x93701,a923),x93701),x93702))))
% 28.73/28.53 [9408]P57(x94081,x94082,x94083)+P1(f319(f319(f321(x94081),f583(x94083,x94082,x94081)),x94082))+~P1(f319(f319(f226(f932(f931(x94081,x94081),a923)),x94083),f319(f319(f246(x94081,x94081),x94082),f319(f16(f932(x94081,a923),x94081),x94082))))
% 28.73/28.53 [9409]P57(x94091,x94092,x94093)+P1(f319(f319(f321(x94091),f591(x94092,x94093,x94091)),x94092))+~P1(f319(f319(f226(f932(f931(x94091,x94091),a923)),x94093),f319(f319(f246(x94091,x94091),x94092),f319(f16(f932(x94091,a923),x94091),x94092))))
% 28.73/28.53 [9444]~P75(x94441)+~P1(f319(f319(f227(x94441),x94442),x94443))+P1(f319(f319(f227(x94441),f319(f319(f283(x94441),f319(f319(f74(x94441),x94442),x94443)),f319(f319(f74(x94441),f72(x94441)),f72(x94441)))),x94443))
% 28.73/28.53 [9473]~P74(x94731)+P1(f319(f319(f226(x94731),x94732),x94733))+~P1(f319(f319(f226(x94731),f319(f319(f75(x94731),f469(x94733,x94732,x94731)),x94732)),x94733))
% 28.73/28.53 [9611]E(f319(f181(f926(f926(x96111))),f319(f128(f926(x96111),f319(f319(f8(a925,a923,f926(x96111)),f319(f227(a925),x96112)),f181(f926(x96111)))),f171(x96111,x96113))),f319(f181(f926(x96111)),f319(f319(f156(f926(x96111)),x96113),x96112)))+~P14(a925,f319(f160(a925),f319(f319(f146(f926(x96111),a925),f181(f926(x96111))),x96113)))+~P1(f319(f319(f227(a925),x96112),f319(f181(f926(f926(x96111))),x96113)))
% 28.73/28.53 [9727]~P38(x97271,x97272)+P28(x97271,f319(f319(f244(f932(f931(x97271,x97271),a923),f932(f931(x97271,x97271),a923)),x97272),x97273))+~P1(f319(f319(f226(f932(f931(x97271,x97271),a923)),f319(f319(f281(x97271,x97271,x97271),x97272),x97273)),x97272))
% 28.73/28.53 [9732]E(f319(f319(f146(f926(x97321),x97321),f319(f319(f7(f926(x97321),a925,x97321),f156(x97321)),x97322)),f319(f128(f926(x97321),f319(f319(f8(a925,a923,f926(x97321)),f319(f227(a925),x97322)),f181(f926(x97321)))),f171(x97321,x97323))),f319(f319(f156(f926(x97321)),x97323),x97322))+~P14(a925,f319(f160(a925),f319(f319(f146(f926(x97321),a925),f181(f926(x97321))),x97323)))+~P1(f319(f319(f227(a925),x97322),f319(f181(f926(f926(x97321))),x97323)))
% 28.73/28.53 [9870]P57(x98701,x98702,x98703)+~P1(f319(f319(f321(f931(x98701,x98701)),f319(f319(f244(x98701,x98701),f583(x98703,x98702,x98701)),f583(x98703,x98702,x98701))),x98703))+~P1(f319(f319(f226(f932(f931(x98701,x98701),a923)),x98703),f319(f319(f246(x98701,x98701),x98702),f319(f16(f932(x98701,a923),x98701),x98702))))
% 28.73/28.53 [9871]P57(x98711,x98712,x98713)+~P1(f319(f319(f321(f931(x98711,x98711)),f319(f319(f244(x98711,x98711),f591(x98712,x98713,x98711)),f591(x98712,x98713,x98711))),x98713))+~P1(f319(f319(f226(f932(f931(x98711,x98711),a923)),x98713),f319(f319(f246(x98711,x98711),x98712),f319(f16(f932(x98711,a923),x98711),x98712))))
% 28.73/28.53 [10057]~P145(x100571)+~P128(x100571)+E(f319(f319(f283(x100571),f319(f94(x100571),f319(f319(f66(f931(a1,a1),a1,x100572,f243(a1,a1)),f204(x100572)),x100573))),f319(f94(x100571),f319(f319(f66(f931(a1,a1),a1,x100572,f248(a1,a1)),f204(x100572)),x100573))),f214(x100572,x100571,x100573))
% 28.73/28.53 [10266]~E(x102663,f2(a925))+~E(f319(f181(f926(x102661)),f319(f319(f156(f926(x102661)),x102662),f733(x102663,x102661,x102662))),x102663)+E(f319(f319(f146(a925,f926(x102661)),f319(f319(f7(a925,f926(a925),f926(x102661)),f319(f319(f8(f932(a925,x102661),f932(f926(a925),f926(x102661)),a925),f146(a925,x102661)),f319(f7(a925,a925,x102661),f319(f319(f8(f926(x102661),f932(a925,x102661),a925),f156(x102661)),f319(f156(f926(x102661)),x102662))))),f131(a925,f319(f294(a925,f2(a925)),f319(f181(f926(f926(x102661))),x102662))))),f131(a925,f319(f294(a925,f2(a925)),x102663))),f171(x102661,x102662))
% 28.73/28.53 [10267]E(x102671,f105(f926(x102672)))+~E(f319(f181(f926(x102672)),f319(f319(f156(f926(x102672)),x102671),f733(x102673,x102672,x102671))),x102673)+E(f319(f319(f146(a925,f926(x102672)),f319(f319(f7(a925,f926(a925),f926(x102672)),f319(f319(f8(f932(a925,x102672),f932(f926(a925),f926(x102672)),a925),f146(a925,x102672)),f319(f7(a925,a925,x102672),f319(f319(f8(f926(x102672),f932(a925,x102672),a925),f156(x102672)),f319(f156(f926(x102672)),x102671))))),f131(a925,f319(f294(a925,f2(a925)),f319(f181(f926(f926(x102672))),x102671))))),f131(a925,f319(f294(a925,f2(a925)),x102673))),f171(x102672,x102671))
% 28.73/28.53 [10268]~E(x102683,f2(a925))+E(f319(f319(f146(a925,f926(x102681)),f319(f319(f7(a925,f926(a925),f926(x102681)),f319(f319(f8(f932(a925,x102681),f932(f926(a925),f926(x102681)),a925),f146(a925,x102681)),f319(f7(a925,a925,x102681),f319(f319(f8(f926(x102681),f932(a925,x102681),a925),f156(x102681)),f319(f156(f926(x102681)),x102682))))),f131(a925,f319(f294(a925,f2(a925)),f319(f181(f926(f926(x102681))),x102682))))),f131(a925,f319(f294(a925,f2(a925)),x102683))),f171(x102681,x102682))+P1(f319(f319(f227(a925),f733(x102683,x102681,x102682)),f319(f181(f926(f926(x102681))),x102682)))
% 28.73/28.53 [10269]E(x102691,f105(f926(x102692)))+E(f319(f319(f146(a925,f926(x102692)),f319(f319(f7(a925,f926(a925),f926(x102692)),f319(f319(f8(f932(a925,x102692),f932(f926(a925),f926(x102692)),a925),f146(a925,x102692)),f319(f7(a925,a925,x102692),f319(f319(f8(f926(x102692),f932(a925,x102692),a925),f156(x102692)),f319(f156(f926(x102692)),x102691))))),f131(a925,f319(f294(a925,f2(a925)),f319(f181(f926(f926(x102692))),x102691))))),f131(a925,f319(f294(a925,f2(a925)),x102693))),f171(x102692,x102691))+P1(f319(f319(f227(a925),f733(x102693,x102692,x102691)),f319(f181(f926(f926(x102692))),x102691)))
% 28.73/28.53 [7948]E(f319(f319(f74(a925),f319(f95(a925),x79481)),f319(f319(f74(a925),f319(f95(a925),x79482)),x79483)),f319(f319(f74(a925),f319(f95(a925),f319(f319(f74(a1),x79481),x79482))),x79483))+P1(f319(a185,f319(f95(a1),x79481)))+P1(f319(a185,f319(f95(a1),x79482)))
% 28.73/28.53 [8719]~P1(f319(f55(x87191),x87192))+~P1(f319(f319(f321(x87191),x87193),x87192))+E(f319(a104,f319(f29(x87191),f319(f319(f23(f932(x87191,a923)),x87192),f319(f319(f301(x87191),x87193),f180(f932(x87191,a923)))))),f319(f29(x87191),x87192))
% 28.73/28.53 [8735]~P1(f319(f55(x87351),x87352))+~P1(f319(f319(f321(x87351),x87353),x87352))+E(f319(f319(f74(a925),f72(a925)),f319(f29(x87351),f319(f319(f23(f932(x87351,a923)),x87352),f319(f319(f301(x87351),x87353),f180(f932(x87351,a923)))))),f319(f29(x87351),x87352))
% 28.73/28.53 [8823]~P4(x88231)+~P1(f319(f55(x88231),x88233))+E(f319(f319(f140(x88231,x88231,f5(x88231)),x88232),f131(x88231,f319(f319(f23(f932(x88231,a923)),x88233),f319(f319(f301(x88231),x88232),f180(f932(x88231,a923)))))),f131(x88231,f319(f319(f301(x88231),x88232),x88233)))
% 28.73/28.53 [8988]~P1(f319(f55(x89881),x89883))+~P1(f319(f55(x89881),x89882))+E(f319(f319(f74(a925),f319(f29(x89881),f319(f319(f102(f932(x89881,a923)),x89882),x89883))),f319(f29(x89881),f319(f319(f93(f932(x89881,a923)),x89882),x89883))),f319(f319(f74(a925),f319(f29(x89881),x89882)),f319(f29(x89881),x89883)))
% 28.73/28.53 [8989]~P1(f319(f55(x89891),x89893))+~P1(f319(f55(x89891),x89892))+E(f319(f319(f74(a925),f319(f29(x89891),f319(f319(f102(f932(x89891,a923)),x89892),x89893))),f319(f29(x89891),f319(f319(f93(f932(x89891,a923)),x89892),x89893))),f319(f319(f74(a925),f319(f29(x89891),x89892)),f319(f29(x89891),x89893)))
% 28.73/28.53 [10213]~P26(x102131,f932(f932(x102131,a923),a923),f319(f319(f7(x102131,f932(f931(x102131,x102131),a923),f932(f932(x102131,a923),a923)),f319(f319(f8(f932(x102131,a923),f932(f932(f931(x102131,x102131),a923),f932(f932(x102131,a923),a923)),x102131),f54(x102131)),f319(f319(f7(x102131,f932(x102131,a923),f932(x102131,a923)),f301(x102131)),f180(f932(x102131,a923))))),x102133),x102132)+~P1(f319(f55(x102131),x102132))+E(f319(f29(f932(x102131,a923)),f319(f319(f54(x102131),x102132),x102133)),f319(f29(x102131),x102132))
% 28.73/28.53 [10508]~P41(f932(x105081,a923),f932(x105081,a923),x105082)+~P1(f319(f319(f226(f932(x105081,a923)),x105083),f319(x105082,f87(f932(x105081,a923),f319(f319(f7(f932(x105081,a923),f932(x105081,a923),f932(x105081,a923)),f319(f319(f8(f932(x105081,a923),f932(f932(x105081,a923),f932(x105081,a923)),f932(x105081,a923)),f102(f932(x105081,a923))),f319(f319(f7(f932(x105081,a923),f932(x105081,a923),f932(x105081,a923)),f319(f319(f8(f932(x105081,a923),f932(f932(x105081,a923),f932(x105081,a923)),f932(x105081,a923)),f102(f932(x105081,a923))),x105082)),x105083))),f88(f932(x105081,a923),x105082))))))+P1(f319(f319(f226(f932(x105081,a923)),f87(f932(x105081,a923),f319(f319(f7(f932(x105081,a923),f932(x105081,a923),f932(x105081,a923)),f319(f319(f8(f932(x105081,a923),f932(f932(x105081,a923),f932(x105081,a923)),f932(x105081,a923)),f102(f932(x105081,a923))),f319(f319(f7(f932(x105081,a923),f932(x105081,a923),f932(x105081,a923)),f319(f319(f8(f932(x105081,a923),f932(f932(x105081,a923),f932(x105081,a923)),f932(x105081,a923)),f102(f932(x105081,a923))),x105082)),x105083))),f88(f932(x105081,a923),x105082)))),f319(x105082,f87(f932(x105081,a923),f319(f319(f7(f932(x105081,a923),f932(x105081,a923),f932(x105081,a923)),f319(f319(f8(f932(x105081,a923),f932(f932(x105081,a923),f932(x105081,a923)),f932(x105081,a923)),f102(f932(x105081,a923))),f319(f319(f7(f932(x105081,a923),f932(x105081,a923),f932(x105081,a923)),f319(f319(f8(f932(x105081,a923),f932(f932(x105081,a923),f932(x105081,a923)),f932(x105081,a923)),f102(f932(x105081,a923))),x105082)),x105083))),f88(f932(x105081,a923),x105082))))))
% 28.73/28.53 [8220]~P99(x82201)+P1(f319(f319(f226(a1),f2(a1)),f319(f95(a1),x82203)))+E(f319(f319(f236(x82201),x82202),f319(f95(a925),f319(f319(f23(a1),f319(f319(f74(a1),x82203),x82203)),a89))),f72(x82201))
% 28.73/28.53 [8314]~P99(x83141)+P1(f319(f319(f226(a1),f2(a1)),f319(f95(a1),x83143)))+E(f319(f319(f236(x83141),f319(f95(x83141),x83142)),f319(f95(a925),f319(f319(f23(a1),f319(f319(f74(a1),x83143),x83143)),a89))),f72(x83141))
% 28.73/28.53 [9712]~P99(x97121)+~P1(f319(f319(f226(a1),f2(a1)),f319(f95(a1),x97123)))+E(f319(f319(f236(x97121),x97122),f319(f95(a925),f319(f319(f23(a1),f319(f319(f74(a1),x97123),x97123)),a89))),f319(f319(f80(x97121,x97121),f319(f319(f236(x97121),x97122),f319(f95(a925),x97123))),f319(f319(f18(x97121,x97121,x97121),f319(f319(f8(x97121,f932(x97121,x97121),x97121),f75(x97121)),f319(f75(x97121),x97122))),f5(x97121))))
% 28.73/28.53 [9780]~P99(x97801)+~P1(f319(f319(f226(a1),f2(a1)),f319(f95(a1),x97803)))+E(f319(f319(f236(x97801),f319(f95(x97801),x97802)),f319(f95(a925),f319(f319(f23(a1),f319(f319(f74(a1),x97803),x97803)),a89))),f319(f319(f80(x97801,x97801),f319(f319(f236(x97801),f319(f95(x97801),x97802)),f319(f95(a925),x97803))),f319(f319(f18(x97801,x97801,x97801),f319(f319(f8(x97801,f932(x97801,x97801),x97801),f75(x97801)),f319(f75(x97801),f319(f95(x97801),x97802)))),f5(x97801))))
% 28.73/28.53 [10122]~P1(f319(f129(x101221),x101223))+~P1(f319(f319(f321(x101221),x101222),f319(f164(x101221),x101223)))+E(f319(f319(f130(x101221),f319(f181(f926(x101221)),f169(x101221,f319(f319(f8(a923,a923,x101221),a314),f319(f319(f7(x101221,x101221,a923),a316),x101222)),f319(f160(x101221),x101223)))),f319(f160(x101221),x101223)),f319(f319(f143(x101221),x101222),f319(f160(x101221),f169(x101221,f319(f319(f8(a923,a923,x101221),a314),f319(f319(f7(x101221,x101221,a923),a316),x101222)),x101223))))
% 28.73/28.53 [10182]P1(f319(f319(f226(f932(f931(x101821,x101821),a923)),f299(x101821,x101822)),x101823))+~P1(f319(f319(f226(f932(f931(x101821,x101821),a923)),f299(x101821,f180(f932(f931(x101821,x101821),a923)))),x101823))+~P1(f319(f319(f226(f932(f931(x101821,x101821),a923)),f319(f319(f281(x101821,x101821,x101821),f319(f319(f93(f932(f931(x101821,x101821),a923)),f299(x101821,x101822)),x101823)),x101822)),x101823))
% 28.73/28.53 [10035]~P1(f319(f55(x100351),f319(f254(x100351),x100353)))+~P1(f319(f55(x100351),f319(f254(x100351),x100352)))+P1(f319(f55(x100351),f319(f254(x100351),f319(f319(f18(x100351,a923,a923),f319(f319(f8(a923,f932(a923,a923),x100351),a318),x100352)),x100353))))
% 28.73/28.53 [10333]P1(f319(f319(f226(f932(f931(x103331,x103331),a923)),f319(f319(f281(x103331,x103331,x103331),x103332),f299(x103331,x103332))),x103333))+~P1(f319(f319(f226(f932(f931(x103331,x103331),a923)),x103332),x103333))+~P1(f319(f319(f226(f932(f931(x103331,x103331),a923)),f319(f319(f281(x103331,x103331,x103331),f319(f319(f93(f932(f931(x103331,x103331),a923)),f319(f319(f281(x103331,x103331,x103331),x103332),f299(x103331,x103332))),x103333)),x103332)),x103333))
% 28.73/28.53 [10283]~P126(x102832)+E(x102831,f2(x102832))+~E(f319(f319(f74(x102832),f319(f319(f236(x102832),x102833),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))))),f319(f319(f236(x102832),x102831),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))))),f2(x102832))
% 28.73/28.53 [10284]~P126(x102842)+E(x102841,f2(x102842))+~E(f319(f319(f74(x102842),f319(f319(f236(x102842),x102841),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))))),f319(f319(f236(x102842),x102843),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))))),f2(x102842))
% 28.73/28.53 [10290]~P1(f319(f129(x102901),x102903))+~P1(f319(f319(f321(x102901),x102902),f319(f164(x102901),x102903)))+E(f319(f160(x102901),f319(f163(x102901),f319(f319(f130(x102901),f319(f181(f926(x102901)),f169(x102901,f319(f319(f8(a923,a923,x102901),a314),f319(f319(f7(x102901,x102901,a923),a316),x102902)),x102903))),x102903))),f169(x102901,f319(f319(f8(a923,a923,x102901),a314),f319(f319(f7(x102901,x102901,a923),a316),x102902)),f319(f160(x102901),x102903)))
% 28.73/28.53 [10379]~P126(x103792)+E(x103791,f2(x103792))+P1(f319(f319(f227(x103792),f2(x103792)),f319(f319(f74(x103792),f319(f319(f236(x103792),x103793),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))))),f319(f319(f236(x103792),x103791),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))))))
% 28.73/28.53 [10380]~P126(x103802)+E(x103801,f2(x103802))+P1(f319(f319(f227(x103802),f2(x103802)),f319(f319(f74(x103802),f319(f319(f236(x103802),x103801),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))))),f319(f319(f236(x103802),x103803),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))))))
% 28.73/28.53 [10436]~P126(x104361)+P1(f319(f319(f226(x104361),f2(x104361)),x104362))+~P1(f319(f319(f226(x104361),f2(x104361)),f319(f319(f236(x104361),x104362),f319(a104,f319(f319(f75(a925),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),x104363)))))
% 28.73/28.53 [5700]~P15(x57001,x57004,x57003)+P15(x57001,x57002,x57003)+~P15(x57001,x57002,x57004)
% 28.73/28.53 [5167]~E(x51672,f84(x51673,x51671))+P1(f319(x51671,x51672))+~P1(f319(x51671,x51674))
% 28.73/28.53 [5418]E(f62(x54183,x54182,x54184),x54182)+E(x54181,f757(x54182,x54183,x54184))+~P1(f319(x54184,x54181))
% 28.73/28.53 [6732]E(f62(x67321,x67322,x67323),f79(x67321,x67323))+~E(f798(x67322,x67321,x67323,x67324),x67324)+~P1(f319(x67323,x67324))
% 28.73/28.53 [6946]~P38(x69462,x69464)+~P38(x69461,x69463)+P38(f931(x69461,x69462),f312(x69461,x69462,x69463,x69464))
% 28.73/28.53 [6947]~P39(x69472,x69474)+~P39(x69471,x69473)+P39(f931(x69471,x69472),f312(x69471,x69472,x69473,x69474))
% 28.73/28.53 [5357]~P8(x53574,x53571)+~E(f319(x53571,x53572),f319(x53571,x53573))+P1(f319(f319(x53571,x53572),x53573))
% 28.73/28.53 [5514]~P8(x55144,x55141)+E(f319(x55141,x55142),f319(x55141,x55143))+~P1(f319(f319(x55141,x55142),x55143))
% 28.73/28.53 [5515]~P17(x55154,x55151)+E(f319(x55151,x55152),f319(x55151,x55153))+~P1(f319(f319(x55151,x55152),x55153))
% 28.73/28.53 [5607]~P20(x56073,x56074,x56071)+E(f319(x56071,x56072),f319(f57(x56073,x56074),x56072))+~P1(f319(f55(x56073),x56072))
% 28.73/28.53 [5608]~P10(x56083,x56084,x56081)+E(f319(x56081,x56082),f319(f57(x56083,x56084),x56082))+~P1(f319(f55(x56083),x56082))
% 28.73/28.53 [5733]~P8(x57334,x57331)+~P1(f319(f319(x57331,x57333),x57332))+P1(f319(f319(x57331,x57332),x57333))
% 28.73/28.53 [5734]~P55(x57344,x57341)+~P1(f319(f319(x57341,x57343),x57342))+P1(f319(f319(x57341,x57342),x57343))
% 28.73/28.53 [5735]~P17(x57354,x57351)+~P1(f319(f319(x57351,x57353),x57352))+P1(f319(f319(x57351,x57352),x57353))
% 28.73/28.53 [5736]~P17(x57363,x57361)+P1(f319(f319(x57361,x57362),x57362))+~P1(f319(f319(x57361,x57364),x57362))
% 28.73/28.53 [5737]~P17(x57373,x57371)+P1(f319(f319(x57371,x57372),x57372))+~P1(f319(f319(x57371,x57372),x57374))
% 28.73/28.53 [5806]E(x58061,x58062)+~E(f319(f243(x58063,x58064),x58061),f319(f243(x58063,x58064),x58062))+~E(f319(f248(x58063,x58064),x58061),f319(f248(x58063,x58064),x58062))
% 28.73/28.53 [5807]E(x58071,x58072)+~E(f319(f243(x58073,x58074),x58071),f319(f243(x58073,x58074),x58072))+~E(f319(f248(x58073,x58074),x58071),f319(f248(x58073,x58074),x58072))
% 28.73/28.53 [5834]E(x58341,x58342)+~P1(f319(f42(x58343,x58344),x58342))+~P1(f319(f42(x58343,x58344),x58341))
% 28.73/28.53 [6026]~P79(x60262)+E(f223(x60261,x60262,x60263,x60264),f2(x60262))+P1(f319(f55(x60261),x60264))
% 28.73/28.53 [6076]~P8(x60763,x60762)+~P1(f319(x60761,x60764))+P1(f319(x60761,f839(x60761,x60762,x60763)))
% 28.73/28.53 [6171]~P1(f319(f307(x61711,x61712),x61714))+P1(f319(f307(x61711,x61712),x61713))+~P1(f319(f319(x61712,x61713),x61714))
% 28.73/28.53 [6172]~P1(f319(f307(x61721,x61722),x61724))+P1(f319(f307(x61721,x61722),x61723))+~P1(f319(f319(x61722,x61723),x61724))
% 28.73/28.53 [6173]~P1(f319(f307(x61731,x61732),x61734))+P1(f319(f307(x61731,x61732),x61733))+~P1(f319(f319(x61732,x61733),x61734))
% 28.73/28.53 [6606]P52(x66061,x66062,x66063,x66064)+P1(f319(f319(x66062,x66064),x66063))+~P1(f319(f319(x66062,x66063),x66064))
% 28.73/28.53 [6980]~P30(x69801,x69803,x69804)+P1(f319(x69801,x69802))+~P1(f319(f319(f321(a1),x69802),f295(a1,x69803,x69804)))
% 28.73/28.53 [7173]~P8(x71731,x71733)+~P1(f319(x71732,x71734))+P1(f319(f319(f321(x71731),f839(x71732,x71733,x71731)),f262(x71731,x71733)))
% 28.73/28.53 [8058]E(x80581,f2(a925))+~P1(f319(x80582,x80583))+P1(f319(x80582,f791(x80582,x80583,x80581,x80584)))
% 28.73/28.53 [8140]~P4(x81402)+~P1(f319(f129(x81401),x81404))+P1(f319(f129(x81401),f142(x81401,x81402,x81403,x81404)))
% 28.73/28.53 [8186]E(f62(x81861,x81862,x81863),f79(x81861,x81863))+~P1(f319(x81863,x81864))+P1(f319(x81863,f798(x81862,x81861,x81863,x81864)))
% 28.73/28.53 [8366]~P1(f319(f55(x83662),x83664))+~P1(f319(f55(x83661),x83663))+P1(f319(f55(f933(x83661,x83662)),f305(x83661,x83662,x83663,x83664)))
% 28.73/28.53 [8367]~P1(f319(f55(x83672),x83674))+~P1(f319(f55(x83671),x83673))+P1(f319(f55(f933(x83671,x83672)),f305(x83671,x83672,x83673,x83674)))
% 28.73/28.53 [8368]~P1(f319(f129(x83682),x83684))+~P1(f319(f129(x83681),x83683))+P1(f319(f129(f931(x83681,x83682)),f53(x83681,x83682,x83683,x83684)))
% 28.73/28.53 [8371]P1(f319(f319(f321(f926(x83711)),f319(f319(f126(x83711),x83712),x83713)),f153(x83711,x83714)))+~P1(f319(f319(f321(f926(x83711)),x83713),f153(x83711,x83714)))+~P1(f319(f319(f321(f926(x83711)),x83712),f153(x83711,x83714)))
% 28.73/28.53 [8653]E(x86531,f2(a925))+P1(f319(x86532,x86533))+~P1(f319(x86532,f794(x86532,x86533,x86531,x86534)))
% 28.73/28.53 [8692]~P4(x86923)+~P1(f319(f129(x86921),f142(x86921,x86923,x86924,x86922)))+P1(f319(f129(x86921),x86922))
% 28.73/28.53 [8977]~P1(f319(f319(f321(f931(x89771,x89771)),f319(f319(f244(x89771,x89771),x89772),x89774)),f299(x89771,x89773)))+P1(f319(f319(f321(x89771),x89772),f308(x89771,x89773)))+~P1(f319(f319(f321(x89771),x89774),f308(x89771,x89773)))
% 28.73/28.53 [8978]~P1(f319(f319(f321(f931(x89781,x89781)),f319(f319(f244(x89781,x89781),x89782),x89784)),f299(x89781,x89783)))+P1(f319(f319(f321(x89781),x89782),f308(x89781,x89783)))+~P1(f319(f319(f321(x89781),x89784),f308(x89781,x89783)))
% 28.73/28.53 [5336]~P79(x53362)+E(f319(f319(f6(x53361,x53362),x53363),x53364),f2(x53362))+P1(f319(f55(x53361),x53364))
% 28.73/28.53 [5337]~P79(x53372)+E(f319(f319(f6(x53371,x53372),x53373),x53374),f2(x53372))+P1(f319(f55(x53371),x53374))
% 28.73/28.53 [5338]~P79(x53382)+E(f319(f319(f6(x53381,x53382),x53383),x53384),f2(x53382))+P1(f319(f55(x53381),x53384))
% 28.73/28.53 [5339]~P78(x53392)+E(f319(f319(f9(x53391,x53392),x53393),x53394),f72(x53392))+P1(f319(f55(x53391),x53394))
% 28.73/28.53 [5340]~P78(x53402)+E(f319(f319(f9(x53401,x53402),x53403),x53404),f72(x53402))+P1(f319(f55(x53401),x53404))
% 28.73/28.53 [5341]~P78(x53412)+E(f319(f319(f9(x53411,x53412),x53413),x53414),f72(x53412))+P1(f319(f55(x53411),x53414))
% 28.73/28.53 [5478]~P80(x54783)+E(x54781,x54782)+~E(f319(f319(f74(x54783),x54784),x54781),f319(f319(f74(x54783),x54784),x54782))
% 28.73/28.53 [5479]~P80(x54793)+E(x54791,x54792)+~E(f319(f319(f74(x54793),x54794),x54791),f319(f319(f74(x54793),x54794),x54792))
% 28.73/28.53 [5480]~P81(x54803)+E(x54801,x54802)+~E(f319(f319(f74(x54803),x54804),x54801),f319(f319(f74(x54803),x54804),x54802))
% 28.73/28.53 [5481]~P80(x54813)+E(x54811,x54812)+~E(f319(f319(f74(x54813),x54811),x54814),f319(f319(f74(x54813),x54812),x54814))
% 28.73/28.53 [5482]~P80(x54823)+E(x54821,x54822)+~E(f319(f319(f74(x54823),x54821),x54824),f319(f319(f74(x54823),x54822),x54824))
% 28.73/28.53 [5575]~P123(x55751)+~E(x55753,f319(f319(f75(x55751),x55752),x55754))+P1(f319(f319(f279(x55751),x55752),x55753))
% 28.73/28.53 [5603]~P6(x56033)+E(x56031,f180(f932(x56032,a923)))+E(f319(f319(f33(x56032,x56033),x56031),f319(f16(x56033,x56032),x56034)),x56034)
% 28.73/28.53 [5604]~P6(x56043)+E(x56041,f180(f932(x56042,a923)))+E(f319(f319(f34(x56042,x56043),x56041),f319(f16(x56043,x56042),x56044)),x56044)
% 28.73/28.53 [5820]~P113(x58203)+E(x58201,x58202)+~E(f295(x58203,x58204,x58201),f319(f319(f301(x58203),x58202),f180(f932(x58203,a923))))
% 28.73/28.53 [5821]~P113(x58213)+E(x58211,x58212)+~E(f295(x58213,x58211,x58212),f319(f319(f301(x58213),x58214),f180(f932(x58213,a923))))
% 28.73/28.53 [5882]~P36(x58823,x58821,x58824)+P36(x58823,x58821,f319(f319(f143(x58823),x58822),x58824))+P1(f319(x58821,x58822))
% 28.73/28.53 [5984]~P32(x59841,x59842,x59844)+~P1(f319(x59842,x59843))+P32(x59841,x59842,f319(f319(f143(x59841),x59843),x59844))
% 28.73/28.53 [6128]P1(f319(x61281,x61282))+~P1(f319(f240(x61283,x61281),x61284))+~P1(f319(f319(f321(x61283),x61282),x61284))
% 28.73/28.53 [6137]~P32(x61371,x61372,x61374)+~P32(x61371,x61372,x61373)+P32(x61371,x61372,f319(f319(f126(x61371),x61373),x61374))
% 28.73/28.53 [6152]P34(x61521,x61522,x61523)+~P34(x61521,x61522,f319(f319(f143(x61521),x61524),x61523))+P1(f319(x61522,x61524))
% 28.73/28.53 [6153]P36(x61531,x61532,x61533)+~P36(x61531,x61532,f319(f319(f143(x61531),x61534),x61533))+P1(f319(x61532,x61534))
% 28.73/28.53 [6231]P34(x62311,x62312,x62313)+P34(x62311,x62312,x62314)+~P34(x62311,x62312,f319(f319(f126(x62311),x62314),x62313))
% 28.73/28.53 [6250]~P79(x62501)+E(f319(f319(f6(a925,x62501),x62502),f319(f294(a925,x62503),f319(a104,x62504))),f2(x62501))+~P1(f319(f319(f227(a925),x62504),x62503))
% 28.73/28.53 [6255]~P66(x62551)+~E(f39(x62551,x62552,x62553),f39(x62551,x62554,x62553))+E(f39(x62551,f319(f73(x62551),x62552),x62553),f39(x62551,f319(f73(x62551),x62554),x62553))
% 28.73/28.53 [6321]P1(f319(x63211,x63212))+~E(f319(f128(x63213,x63211),x63214),x63214)+~P1(f319(f319(f321(x63213),x63212),f319(f164(x63213),x63214)))
% 28.73/28.53 [6340]~E(f319(f319(f74(a925),x63403),x63402),f319(f319(f74(a925),x63401),x63404))+~P1(f319(f319(f227(a925),x63403),x63404))+P1(f319(f319(f227(a925),x63401),x63402))
% 28.73/28.53 [6344]P34(x63441,x63442,x63443)+~P1(f319(x63442,x63444))+~P1(f319(f319(f321(x63441),x63444),f319(f164(x63441),x63443)))
% 28.73/28.53 [6345]P34(x63451,x63452,x63453)+~P1(f319(x63452,x63454))+~P1(f319(f319(f321(x63451),x63454),f319(f164(x63451),x63453)))
% 28.73/28.53 [6346]P34(x63461,x63462,x63463)+~P1(f319(x63462,x63464))+~P1(f319(f319(f321(x63461),x63464),f319(f164(x63461),x63463)))
% 28.73/28.53 [6383]~P32(x63833,x63831,x63834)+P1(f319(x63831,x63832))+~P1(f319(f319(f321(x63833),x63832),f319(f164(x63833),x63834)))
% 28.73/28.53 [6384]~P32(x63843,x63841,x63844)+P1(f319(x63841,x63842))+~P1(f319(f319(f321(x63843),x63842),f319(f164(x63843),x63844)))
% 28.73/28.53 [6385]~P32(x63853,x63851,x63854)+P1(f319(x63851,x63852))+~P1(f319(f319(f321(x63853),x63852),f319(f164(x63853),x63854)))
% 28.73/28.53 [6387]~E(f319(f128(x63871,x63872),x63873),f105(x63871))+~P1(f319(x63872,x63874))+~P1(f319(f319(f321(x63871),x63874),f319(f164(x63871),x63873)))
% 28.73/28.53 [6388]~E(f169(x63883,x63881,x63884),x63884)+P1(f319(x63881,x63882))+~P1(f319(f319(f321(x63883),x63882),f319(f164(x63883),x63884)))
% 28.73/28.53 [6414]~E(x64144,f180(f932(x64142,a923)))+~E(x64143,f180(f932(x64141,a923)))+E(f305(x64141,x64142,x64143,x64144),f180(f932(f933(x64141,x64142),a923)))
% 28.73/28.53 [6562]P1(f319(x65621,x65622))+~P1(f319(f152(x65623,x65621),x65624))+~P1(f319(f319(f321(x65623),x65622),f319(f164(x65623),x65624)))
% 28.73/28.53 [6701]~P31(x67011,x67013,x67014)+P1(f319(x67011,x67012))+~P1(f319(f319(f321(a925),x67012),f319(f294(a925,x67013),x67014)))
% 28.73/28.53 [6841]~P79(x68411)+E(f319(f319(f6(a925,x68411),x68412),f295(a925,x68413,f319(a104,x68414))),f2(x68411))+~P1(f319(f319(f227(a925),f319(a104,x68414)),x68413))
% 28.73/28.53 [6983]~P4(x69831)+E(f319(f319(f23(f932(x69831,a923)),f319(f294(x69831,x69832),x69833)),f319(f294(x69831,x69832),x69834)),f319(f294(x69831,x69834),x69833))+~P1(f319(f319(f226(x69831),x69832),x69834))
% 28.73/28.53 [7054]~E(x70543,x70544)+E(x70541,f2(a925))+P1(f319(f319(f321(x70542),x70543),f319(f164(x70542),f161(x70542,x70541,x70544))))
% 28.73/28.53 [7336]~P1(f319(f319(f321(f926(x73361)),x73364),f153(x73361,x73363)))+P1(f319(f319(f321(x73361),x73362),x73363))+~P1(f319(f319(f321(x73361),x73362),f319(f164(x73361),x73364)))
% 28.73/28.53 [7343]~P38(x73431,x73432)+P1(f319(f319(f321(x73431),f630(x73432,x73431,x73433)),x73433))+~P1(f319(f319(f321(x73431),x73434),x73433))
% 28.73/28.53 [7376]~P26(x73762,x73761,x73763,x73764)+E(f319(f29(x73761),f319(f302(x73762,x73761,x73763),x73764)),f319(f29(x73762),x73764))+~P1(f319(f55(x73762),x73764))
% 28.73/28.53 [7399]~P79(x73991)+E(f319(f319(f319(f59(x73991,x73992,f74(x73991)),x73993),f2(x73991)),x73994),f319(f319(f6(x73992,x73991),x73993),x73994))+~P1(f319(f55(x73992),x73994))
% 28.73/28.53 [7400]~P79(x74001)+E(f319(f319(f319(f59(x74001,x74002,f74(x74001)),x74003),f2(x74001)),x74004),f319(f319(f6(x74002,x74001),x74003),x74004))+~P1(f319(f55(x74002),x74004))
% 28.73/28.53 [7401]~P78(x74011)+E(f319(f319(f319(f59(x74011,x74012,f75(x74011)),x74013),f72(x74011)),x74014),f319(f319(f9(x74012,x74011),x74013),x74014))+~P1(f319(f55(x74012),x74014))
% 28.73/28.53 [7402]~P78(x74021)+E(f319(f319(f319(f59(x74021,x74022,f75(x74021)),x74023),f72(x74021)),x74024),f319(f319(f9(x74022,x74021),x74023),x74024))+~P1(f319(f55(x74022),x74024))
% 28.73/28.53 [7430]P26(x74301,x74302,x74303,x74304)+~E(f319(f29(x74302),f319(f302(x74301,x74302,x74303),x74304)),f319(f29(x74301),x74304))+~P1(f319(f55(x74301),x74304))
% 28.73/28.53 [7431]P26(x74311,x74312,x74313,x74314)+~E(f319(f29(x74312),f319(f302(x74311,x74312,x74313),x74314)),f319(f29(x74311),x74314))+~P1(f319(f55(x74311),x74314))
% 28.73/28.53 [7620]~P79(x76201)+E(f319(f319(f74(x76201),f319(x76202,x76203)),f319(f319(f6(a925,x76201),x76202),f297(a925,x76203,x76204))),f319(f319(f6(a925,x76201),x76202),f295(a925,x76203,x76204)))+~P1(f319(f319(f226(a925),x76203),x76204))
% 28.73/28.53 [7629]~P79(x76291)+~P26(x76292,x76291,x76293,x76294)+E(f319(f319(f6(x76291,x76291),f25(x76291)),f319(f302(x76292,x76291,x76293),x76294)),f319(f319(f6(x76292,x76291),x76293),x76294))
% 28.73/28.53 [7630]~P78(x76301)+~P26(x76302,x76301,x76303,x76304)+E(f319(f319(f9(x76301,x76301),f25(x76301)),f319(f302(x76302,x76301,x76303),x76304)),f319(f319(f9(x76302,x76301),x76303),x76304))
% 28.73/28.53 [7678]E(f319(f29(f933(x76781,x76782)),f305(x76781,x76782,x76783,x76784)),f319(f319(f74(a925),f319(f29(x76781),x76783)),f319(f29(x76782),x76784)))+~P1(f319(f55(x76782),x76784))+~P1(f319(f55(x76781),x76783))
% 28.73/28.53 [7679]E(f319(f29(f933(x76791,x76792)),f305(x76791,x76792,x76793,x76794)),f319(f319(f74(a925),f319(f29(x76791),x76793)),f319(f29(x76792),x76794)))+~P1(f319(f55(x76792),x76794))+~P1(f319(f55(x76791),x76793))
% 28.73/28.53 [7759]E(x77591,x77592)+P1(f319(f319(f321(x77593),x77591),f319(f164(x77593),f162(x77593,x77592,x77594))))+~P1(f319(f319(f321(x77593),x77591),f319(f164(x77593),x77594)))
% 28.73/28.53 [7902]~P1(f319(f319(f226(f932(x79021,a923)),x79024),f319(x79023,x79024)))+~P1(f319(f319(f321(x79021),x79022),x79024))+P1(f319(f319(f321(x79021),x79022),f88(f932(x79021,a923),x79023)))
% 28.73/28.53 [7987]~P79(x79871)+E(f319(f319(f74(x79871),f319(f319(f6(a925,x79871),x79872),f319(f294(a925,x79873),x79874))),f319(x79872,x79874)),f319(f319(f6(a925,x79871),x79872),f319(f294(a925,x79873),f319(a104,x79874))))+P1(f319(f319(f227(a925),x79874),x79873))
% 28.73/28.53 [8037]~P26(x80371,x80372,x80373,f234(f932(x80371,a923)))+~P1(f319(f55(x80372),x80374))+P1(f319(f55(x80371),f319(f303(x80371,x80372,x80373),x80374)))
% 28.73/28.53 [8155]P1(f319(f319(f321(f926(x81551)),f319(f319(f143(x81551),x81552),x81553)),f153(x81551,x81554)))+~P1(f319(f319(f321(f926(x81551)),x81553),f153(x81551,x81554)))+~P1(f319(f319(f321(x81551),x81552),x81554))
% 28.73/28.53 [8204]E(x82041,x82042)+~P1(f319(f319(f321(x82043),x82041),f319(f164(x82043),f162(x82043,x82042,x82044))))+P1(f319(f319(f321(x82043),x82041),f319(f164(x82043),x82044)))
% 28.73/28.53 [8244]~E(f319(f302(x82443,x82441,x82444),f234(f932(x82443,a923))),f234(f932(x82441,a923)))+P1(f319(f55(x82441),x82442))+~P1(f319(f55(x82443),f319(f303(x82443,x82441,x82444),x82442)))
% 28.73/28.53 [8339]~P26(x83391,x83393,x83394,x83392)+P1(f319(f55(x83391),x83392))+~P1(f319(f55(x83393),f319(f302(x83391,x83393,x83394),x83392)))
% 28.73/28.53 [8360]~E(x83602,x83603)+P1(f319(f319(f321(f931(x83601,x83601)),f319(f319(f244(x83601,x83601),x83602),x83603)),f255(x83601,x83604)))+~P1(f319(f319(f321(x83601),x83602),x83604))
% 28.73/28.53 [8361]~E(x83612,x83613)+P1(f319(f319(f321(f931(x83611,x83611)),f319(f319(f244(x83611,x83611),x83612),x83613)),f255(x83611,x83614)))+~P1(f319(f319(f321(x83611),x83612),x83614))
% 28.73/28.53 [8396]~P79(x83961)+E(f319(f319(f74(x83961),f319(f319(f6(a925,x83961),x83962),f295(a925,x83963,x83964))),f319(x83962,f319(a104,x83964))),f319(f319(f6(a925,x83961),x83962),f295(a925,x83963,f319(a104,x83964))))+P1(f319(f319(f227(a925),f319(a104,x83964)),x83963))
% 28.73/28.53 [8454]~E(x84542,x84544)+P1(f319(f319(f321(f931(x84541,x84541)),f319(f319(f244(x84541,x84541),x84542),x84544)),f299(x84541,x84543)))+P1(f319(f319(f321(x84541),x84542),f319(f256(x84541,x84541),x84543)))
% 28.73/28.53 [8456]P1(f319(x84561,x84562))+~P1(f319(x84561,f319(f319(f156(x84563),x84564),f684(x84561,x84564,x84563))))+~P1(f319(f319(f321(x84563),x84562),f319(f164(x84563),x84564)))
% 28.73/28.53 [8598]~P1(f319(f319(f321(x85981),x85982),f308(x85981,x85984)))+P1(f319(f319(f321(f926(x85981)),f319(f319(f143(x85981),x85982),x85983)),f308(f926(x85981),f149(x85981,x85984))))+~P1(f319(f319(f321(f926(x85981)),x85983),f308(f926(x85981),f149(x85981,x85984))))
% 28.73/28.53 [8613]~P26(x86132,x86133,x86134,f896(x86134,x86133,x86132,x86131))+P26(x86132,x86133,x86134,f32(f932(x86132,a923),x86131))+E(x86131,f180(f932(f932(x86132,a923),a923)))
% 28.73/28.53 [8887]E(x88871,x88872)+~P1(f319(f319(f321(f931(x88873,x88873)),f319(f319(f244(x88873,x88873),x88871),x88872)),f299(x88873,x88874)))+P1(f319(f319(f321(x88873),x88871),f319(f256(x88873,x88873),x88874)))
% 28.73/28.53 [9171]E(x91711,f2(a925))+P1(f319(x91712,x91713))+P1(f319(f319(f321(x91714),f794(x91712,x91713,x91711,x91714)),f319(f164(x91714),f161(x91714,x91711,x91713))))
% 28.73/28.53 [9183]E(x91831,f2(a925))+~P1(f319(x91833,x91834))+P1(f319(f319(f321(x91832),f791(x91833,x91834,x91831,x91832)),f319(f164(x91832),f161(x91832,x91831,x91834))))
% 28.73/28.53 [9185]~P27(x91851,x91852,x91853,f234(f932(x91851,a923)),f234(f932(x91852,a923)))+~P1(f319(f55(x91852),x91854))+P1(f319(f55(x91851),f319(f303(x91851,x91852,x91853),x91854)))
% 28.73/28.53 [9188]P26(x91882,x91883,x91884,f32(f932(x91882,a923),x91881))+E(x91881,f180(f932(f932(x91882,a923),a923)))+P1(f319(f319(f321(f932(x91882,a923)),f896(x91884,x91883,x91882,x91881)),x91881))
% 28.73/28.53 [9305]~P27(x93053,x93051,x93054,f234(f932(x93053,a923)),f234(f932(x93051,a923)))+P1(f319(f55(x93051),x93052))+~P1(f319(f55(x93053),f319(f303(x93053,x93051,x93054),x93052)))
% 28.73/28.53 [9322]P1(f319(f55(x93221),x93222))+~P1(f319(f55(x93224),f319(f302(x93221,x93224,x93223),x93222)))+P1(f319(f319(f321(x93221),f467(x93223,x93224,x93222,x93221)),x93222))
% 28.73/28.53 [9419]~P6(x94192)+E(f319(f319(f58(x94191,x94192,f319(f319(f8(x94192,f932(x94192,x94192),x94191),f102(x94192)),x94193)),f180(x94192)),x94194),f319(f319(f33(x94191,x94192),x94194),x94193))+~P1(f319(f55(x94191),x94194))
% 28.73/28.53 [9420]~P6(x94202)+E(f319(f319(f58(x94201,x94202,f319(f319(f8(x94202,f932(x94202,x94202),x94201),f93(x94202)),x94203)),f234(x94202)),x94204),f319(f319(f34(x94201,x94202),x94204),x94203))+~P1(f319(f55(x94201),x94204))
% 28.73/28.53 [9504]P1(f319(x95041,x95042))+~P1(f319(x95041,f319(f319(f156(x95043),x95044),f719(x95042,x95041,x95044,x95043))))+~P1(f319(f319(f321(x95043),x95042),f319(f164(x95043),x95044)))
% 28.73/28.53 [9525]E(x95251,x95252)+~P1(f319(f319(f321(f931(x95253,x95253)),f319(f319(f244(x95253,x95253),x95251),x95252)),f299(x95253,x95254)))+P1(f319(f319(f321(f931(x95253,x95253)),f319(f319(f244(x95253,x95253),x95251),x95252)),f319(f319(f281(x95253,x95253,x95253),x95254),f299(x95253,x95254))))
% 28.73/28.53 [9526]E(x95261,x95262)+~P1(f319(f319(f321(f931(x95263,x95263)),f319(f319(f244(x95263,x95263),x95261),x95262)),f299(x95263,x95264)))+P1(f319(f319(f321(f931(x95263,x95263)),f319(f319(f244(x95263,x95263),x95261),x95262)),f319(f319(f281(x95263,x95263,x95263),x95264),f299(x95263,x95264))))
% 28.73/28.53 [9577]~E(f319(f181(f926(x95771)),x95772),f319(f181(f926(x95771)),x95773))+~P1(f319(f319(f321(f931(f926(x95771),f926(x95771))),f319(f319(f244(f926(x95771),f926(x95771)),x95772),x95773)),f139(x95771,x95774)))+P1(f319(f319(f321(f931(f926(x95771),f926(x95771))),f319(f319(f244(f926(x95771),f926(x95771)),x95772),x95773)),f137(x95771,x95774)))
% 28.73/28.53 [9599]E(x95991,x95992)+P1(f319(f319(f321(f931(x95993,x95993)),f319(f319(f244(x95993,x95993),x95991),x95992)),f299(x95993,x95994)))+~P1(f319(f319(f321(f931(x95993,x95993)),f319(f319(f244(x95993,x95993),x95991),x95992)),f319(f319(f281(x95993,x95993,x95993),x95994),f299(x95993,x95994))))
% 28.73/28.53 [9817]P32(x98171,f319(f319(f18(x98171,a923,a923),f319(f319(f8(a923,f932(a923,a923),x98171),a318),f319(f319(f8(a923,a923,x98171),a314),x98172))),f319(a316,x98173)),x98174)+~P1(f319(x98172,x98173))+~P36(x98171,x98172,f319(f319(f143(x98171),x98173),x98174))
% 28.73/28.53 [9996]~P32(x99961,f319(f319(f18(x99961,a923,a923),f319(f319(f8(a923,f932(a923,a923),x99961),a318),f319(f319(f8(a923,a923,x99961),a314),x99962))),f319(a316,x99963)),x99964)+~P1(f319(x99962,x99963))+P36(x99961,x99962,f319(f319(f143(x99961),x99963),x99964))
% 28.73/28.53 [10000]~P36(x100001,x100002,x100004)+~P32(x100001,f319(f319(f18(x100001,a923,a923),f319(f319(f8(a923,f932(a923,a923),x100001),a318),f319(f319(f8(a923,a923,x100001),a314),x100002))),f319(a316,x100003)),x100004)+P36(x100001,x100002,f319(f319(f143(x100001),x100003),x100004))
% 28.73/28.53 [10036]~P70(x100361)+E(f319(f319(f6(a925,x100361),f319(f319(f18(a925,x100361,x100361),f319(f319(f8(x100361,f932(x100361,x100361),a925),f23(x100361)),x100362)),f319(f319(f8(a925,x100361,a925),x100362),f319(f319(f7(a925,a925,a925),f74(a925)),f72(a925))))),f295(a925,x100363,x100364)),f2(x100361))+P1(f319(f319(f226(a925),x100363),x100364))
% 28.73/28.53 [10282]~P38(x102822,x102824)+~P26(x102822,x102821,x102823,f234(f932(x102822,a923)))+P38(x102821,f319(f302(f931(x102822,x102822),f931(x102821,x102821),f250(x102822,x102821,x102822,x102821,x102823,x102823)),x102824))
% 28.73/28.53 [10472]~E(f319(f181(f926(x104721)),x104723),f319(f181(f926(x104721)),x104722))+P1(f319(f319(f321(f931(f926(x104721),f926(x104721))),f319(f319(f244(f926(x104721),f926(x104721)),x104722),x104723)),f150(x104721,x104724)))+~P1(f319(f319(f249(x104721,x104721,a923),f319(f319(f7(x104721,f932(f931(x104721,x104721),a923),f932(x104721,a923)),f319(f319(f8(f932(x104721,f932(f932(f931(x104721,x104721),a923),a923)),f932(f932(f931(x104721,x104721),a923),f932(x104721,a923)),x104721),f7(x104721,f932(f931(x104721,x104721),a923),a923)),f319(f319(f8(f932(x104721,f931(x104721,x104721)),f932(x104721,f932(f932(f931(x104721,x104721),a923),a923)),x104721),f319(f8(f931(x104721,x104721),f932(f932(f931(x104721,x104721),a923),a923),x104721),f321(f931(x104721,x104721)))),f244(x104721,x104721)))),x104724)),f686(x104724,x104723,x104722,x104721)))
% 28.73/28.53 [6302]~P65(x63021)+~E(x63022,f2(x63021))+E(f319(f319(f30(x63021),f319(f319(f75(x63021),x63022),x63023)),f319(f319(f75(x63021),x63022),x63024)),f2(x63021))
% 28.73/28.53 [6343]E(x63431,f105(x63432))+E(x63433,f319(f319(f23(a925),f319(f181(f926(x63432)),x63431)),f72(a925)))+E(f136(x63432,f319(f319(f151(x63432,x63431),x63433),x63434)),f136(x63432,x63431))
% 28.73/28.53 [6376]E(x63761,x63762)+P1(f319(x63763,x63762))+~P1(f319(f319(f319(f301(x63764),x63761),x63763),x63762))
% 28.73/28.53 [6392]~P79(x63921)+~P1(f319(f129(x63922),x63924))+E(f319(f157(x63921),f319(f319(f146(x63922,x63921),x63923),x63924)),f319(f319(f6(x63922,x63921),x63923),f319(f164(x63922),x63924)))
% 28.73/28.53 [6407]~P78(x64072)+~P1(f319(f55(x64071),x64074))+E(f319(f319(f9(x64071,x64072),f319(f16(x64072,x64071),x64073)),x64074),f319(f319(f236(x64072),x64073),f319(f29(x64071),x64074)))
% 28.73/28.53 [6461]~P72(x64612)+E(x64611,f2(x64612))+E(f319(f319(f283(x64612),f319(f319(f75(x64612),x64613),x64611)),f319(f319(f75(x64612),x64614),x64611)),f319(f319(f283(x64612),x64613),x64614))
% 28.73/28.53 [6462]~P72(x64622)+E(x64621,f2(x64622))+E(f319(f319(f283(x64622),f319(f319(f75(x64622),x64621),x64623)),f319(f319(f75(x64622),x64621),x64624)),f319(f319(f283(x64622),x64623),x64624))
% 28.73/28.53 [6463]~P65(x64632)+E(x64631,f2(x64632))+E(f319(f319(f30(x64632),f319(f319(f75(x64632),x64633),x64631)),f319(f319(f75(x64632),x64634),x64631)),f319(f319(f30(x64632),x64633),x64634))
% 28.73/28.53 [6464]~P65(x64642)+E(x64641,f2(x64642))+E(f319(f319(f30(x64642),f319(f319(f75(x64642),x64641),x64643)),f319(f319(f75(x64642),x64641),x64644)),f319(f319(f30(x64642),x64643),x64644))
% 28.73/28.53 [6465]~P65(x64652)+E(x64651,f2(x64652))+E(f319(f319(f30(x64652),f319(f319(f75(x64652),x64651),x64653)),f319(f319(f75(x64652),x64651),x64654)),f319(f319(f30(x64652),x64653),x64654))
% 28.73/28.53 [6529]P1(f319(x65291,x65292))+~E(x65293,f319(f319(f74(a925),x65294),x65292))+~P1(f319(x65291,f319(f319(f23(a925),x65293),x65294)))
% 28.73/28.53 [6530]P1(f319(x65301,x65302))+~E(x65303,f319(f319(f74(a925),x65304),x65302))+~P1(f319(x65301,f319(f319(f23(a925),x65303),x65304)))
% 28.73/28.53 [6617]~P1(f319(x66172,x66173))+~P1(f319(f152(x66171,x66172),x66174))+P1(f319(f152(x66171,x66172),f319(f319(f143(x66171),x66173),x66174)))
% 28.73/28.53 [6658]E(x66581,f105(x66582))+~E(x66583,f319(f319(f23(a925),f319(f181(f926(x66582)),x66581)),f72(a925)))+E(f136(x66582,f319(f319(f151(x66582,x66581),x66583),x66584)),x66584)
% 28.73/28.53 [6681]~P107(x66811)+~P1(f319(f319(f226(x66811),x66812),x66814))+P1(f319(f319(f226(x66811),x66812),f319(f319(f102(x66811),x66813),x66814)))
% 28.73/28.53 [6682]~P107(x66821)+~P1(f319(f319(f226(x66821),x66822),x66823))+P1(f319(f319(f226(x66821),x66822),f319(f319(f102(x66821),x66823),x66824)))
% 28.73/28.53 [6683]~P4(x66831)+~P1(f319(f319(f226(x66831),x66832),x66834))+P1(f319(f319(f226(x66831),x66832),f319(f319(f225(x66831),x66833),x66834)))
% 28.73/28.53 [6684]~P4(x66841)+~P1(f319(f319(f226(x66841),x66842),x66844))+P1(f319(f319(f226(x66841),x66842),f319(f319(f225(x66841),x66843),x66844)))
% 28.73/28.53 [6685]~P4(x66851)+~P1(f319(f319(f226(x66851),x66852),x66853))+P1(f319(f319(f226(x66851),x66852),f319(f319(f225(x66851),x66853),x66854)))
% 28.73/28.53 [6686]~P4(x66861)+~P1(f319(f319(f226(x66861),x66862),x66863))+P1(f319(f319(f226(x66861),x66862),f319(f319(f225(x66861),x66863),x66864)))
% 28.73/28.53 [6687]~P107(x66871)+~P1(f319(f319(f227(x66871),x66872),x66874))+P1(f319(f319(f227(x66871),x66872),f319(f319(f102(x66871),x66873),x66874)))
% 28.73/28.53 [6688]~P107(x66881)+~P1(f319(f319(f227(x66881),x66882),x66883))+P1(f319(f319(f227(x66881),x66882),f319(f319(f102(x66881),x66883),x66884)))
% 28.73/28.53 [6689]~P4(x66891)+~P1(f319(f319(f227(x66891),x66892),x66894))+P1(f319(f319(f227(x66891),x66892),f319(f319(f225(x66891),x66893),x66894)))
% 28.73/28.53 [6690]~P4(x66901)+~P1(f319(f319(f227(x66901),x66902),x66904))+P1(f319(f319(f227(x66901),x66902),f319(f319(f225(x66901),x66903),x66904)))
% 28.73/28.53 [6691]~P4(x66911)+~P1(f319(f319(f227(x66911),x66912),x66913))+P1(f319(f319(f227(x66911),x66912),f319(f319(f225(x66911),x66913),x66914)))
% 28.73/28.53 [6692]~P4(x66921)+~P1(f319(f319(f227(x66921),x66922),x66923))+P1(f319(f319(f227(x66921),x66922),f319(f319(f225(x66921),x66923),x66924)))
% 28.73/28.53 [6693]~P121(x66931)+~P1(f319(f319(f279(x66931),x66932),x66934))+P1(f319(f319(f279(x66931),x66932),f319(f319(f75(x66931),x66933),x66934)))
% 28.73/28.53 [6694]~P121(x66941)+~P1(f319(f319(f279(x66941),x66942),x66943))+P1(f319(f319(f279(x66941),x66942),f319(f319(f75(x66941),x66943),x66944)))
% 28.73/28.53 [6782]~E(f319(f319(f156(x67821),x67822),x67823),x67824)+E(f319(f319(f151(x67821,x67822),x67823),x67824),x67822)+~P1(f319(f319(f227(a925),x67823),f319(f181(f926(x67821)),x67822)))
% 28.73/28.53 [6824]P1(f319(x68241,x68242))+~P1(f319(x68243,x68242))+~P1(f319(f319(f226(f932(x68244,a923)),x68243),x68241))
% 28.73/28.53 [6825]P1(f319(x68251,x68252))+~P1(f319(x68253,x68252))+~P1(f319(f319(f226(f932(x68254,a923)),x68253),x68251))
% 28.73/28.53 [6858]~E(f319(f319(f151(x68581,x68582),x68583),x68584),x68582)+E(f319(f319(f156(x68581),x68582),x68583),x68584)+~P1(f319(f319(f227(a925),x68583),f319(f181(f926(x68581)),x68582)))
% 28.73/28.53 [6872]~P1(f319(f152(x68721,x68722),x68724))+~P1(f319(f152(x68721,x68722),x68723))+P1(f319(f152(x68721,x68722),f319(f319(f126(x68721),x68723),x68724)))
% 28.73/28.53 [6979]E(x69791,f180(f932(x69792,a923)))+E(x69793,f180(f932(x69794,a923)))+~E(f319(f319(f246(x69794,x69792),x69793),f319(f16(f932(x69792,a923),x69794),x69791)),f180(f932(f931(x69794,x69792),a923)))
% 28.73/28.53 [6998]E(x69981,x69982)+P1(f319(f319(f321(x69983),x69981),x69984))+~P1(f319(f319(f321(x69983),x69981),f319(f319(f301(x69983),x69982),x69984)))
% 28.73/28.53 [6999]E(x69991,x69992)+P1(f319(f319(f321(x69993),x69991),x69994))+~P1(f319(f319(f321(x69993),x69991),f319(f319(f301(x69993),x69992),x69994)))
% 28.73/28.53 [7015]~P4(x70151)+P1(f319(f319(f226(x70151),x70152),x70153))+~P1(f319(f319(f226(x70151),x70152),f319(f319(f224(x70151),x70154),x70153)))
% 28.73/28.53 [7016]~P4(x70161)+P1(f319(f319(f226(x70161),x70162),x70163))+~P1(f319(f319(f226(x70161),x70162),f319(f319(f224(x70161),x70164),x70163)))
% 28.73/28.53 [7017]~P4(x70171)+P1(f319(f319(f226(x70171),x70172),x70173))+~P1(f319(f319(f226(x70171),x70172),f319(f319(f224(x70171),x70173),x70174)))
% 28.73/28.53 [7018]~P4(x70181)+P1(f319(f319(f226(x70181),x70182),x70183))+~P1(f319(f319(f226(x70181),x70182),f319(f319(f224(x70181),x70183),x70184)))
% 28.73/28.53 [7019]~P108(x70191)+P1(f319(f319(f226(x70191),x70192),x70193))+~P1(f319(f319(f226(x70191),x70192),f319(f319(f93(x70191),x70194),x70193)))
% 28.73/28.53 [7020]~P108(x70201)+P1(f319(f319(f226(x70201),x70202),x70203))+~P1(f319(f319(f226(x70201),x70202),f319(f319(f93(x70201),x70204),x70203)))
% 28.73/28.53 [7021]~P108(x70211)+P1(f319(f319(f226(x70211),x70212),x70213))+~P1(f319(f319(f226(x70211),x70212),f319(f319(f93(x70211),x70213),x70214)))
% 28.73/28.53 [7022]~P108(x70221)+P1(f319(f319(f226(x70221),x70222),x70223))+~P1(f319(f319(f226(x70221),x70222),f319(f319(f93(x70221),x70223),x70224)))
% 28.73/28.53 [7023]~P4(x70231)+P1(f319(f319(f227(x70231),x70232),x70233))+~P1(f319(f319(f227(x70231),x70232),f319(f319(f224(x70231),x70234),x70233)))
% 28.73/28.53 [7024]~P4(x70241)+P1(f319(f319(f227(x70241),x70242),x70243))+~P1(f319(f319(f227(x70241),x70242),f319(f319(f224(x70241),x70243),x70244)))
% 28.73/28.53 [7045]~E(f319(f319(f156(x70451),x70453),x70454),x70452)+P1(f319(f319(f321(x70451),x70452),f319(f164(x70451),x70453)))+~P1(f319(f319(f227(a925),x70454),f319(f181(f926(x70451)),x70453)))
% 28.73/28.53 [7055]~P4(x70551)+~P14(x70551,f319(f319(f143(x70551),x70552),f319(f319(f143(x70551),x70553),x70554)))+P1(f319(f319(f226(x70551),x70552),x70553))
% 28.73/28.53 [7110]~P4(x71101)+P14(x71101,f319(f319(f143(x71101),x71102),x71103))+~P14(x71101,f319(f319(f143(x71101),x71104),f319(f319(f143(x71101),x71102),x71103)))
% 28.73/28.53 [7200]~P32(x72002,x72001,x72003)+P1(f319(x72001,f319(f319(f156(x72002),x72003),x72004)))+~P1(f319(f319(f227(a925),x72004),f319(f181(f926(x72002)),x72003)))
% 28.73/28.53 [7219]E(x72191,f2(a1))+E(f319(f319(f30(a1),x72192),x72191),x72193)+~P1(f319(f43(x72192,x72191),f319(f319(f244(a1,a1),x72193),x72194)))
% 28.73/28.53 [7240]E(f39(a1,x72402,x72401),x72403)+E(x72401,f2(a1))+~P1(f319(f43(x72402,x72401),f319(f319(f244(a1,a1),x72404),x72403)))
% 28.73/28.53 [7357]P1(f319(f319(f321(x73571),x73572),x73573))+~P1(f319(f319(f321(x73571),x73572),x73574))+~P1(f319(f319(f226(f932(x73571,a923)),x73574),x73573))
% 28.73/28.53 [7358]P1(f319(f319(f321(x73581),x73582),x73583))+~P1(f319(f319(f321(x73581),x73582),x73584))+~P1(f319(f319(f226(f932(x73581,a923)),x73584),x73583))
% 28.73/28.53 [7359]P1(f319(f319(f321(x73591),x73592),x73593))+~P1(f319(f319(f321(x73591),x73592),x73594))+~P1(f319(f319(f226(f932(x73591,a923)),x73594),x73593))
% 28.73/28.53 [7360]P1(f319(f319(f321(x73601),x73602),x73603))+~P1(f319(f319(f321(x73601),x73602),x73604))+~P1(f319(f319(f227(f932(x73601,a923)),x73604),x73603))
% 28.73/28.53 [7361]P1(f319(f319(f321(x73611),x73612),x73613))+~P1(f319(f319(f321(x73611),x73612),x73614))+~P1(f319(f319(f226(f932(x73611,a923)),x73614),x73613))
% 28.73/28.53 [7372]~P117(x73721)+~E(x73723,f2(x73721))+P1(f319(f319(f279(x73721),f319(f319(f75(x73721),x73722),x73723)),f319(f319(f75(x73721),x73724),x73723)))
% 28.73/28.53 [7373]~P117(x73731)+~E(x73732,f2(x73731))+P1(f319(f319(f279(x73731),f319(f319(f75(x73731),x73732),x73733)),f319(f319(f75(x73731),x73732),x73734)))
% 28.73/28.53 [7475]P34(x74751,x74752,x74753)+~P1(f319(x74752,f319(f319(f156(x74751),x74753),x74754)))+~P1(f319(f319(f227(a925),x74754),f319(f181(f926(x74751)),x74753)))
% 28.73/28.53 [7587]~P3(x75872)+~P1(f319(f319(f227(f932(x75871,x75872)),x75873),x75874))+P1(f319(f319(f226(f932(x75871,x75872)),x75873),x75874))
% 28.73/28.53 [7668]~P15(x76681,x76682,x76684)+P15(x76681,x76682,f319(f319(f301(f924(x76681)),x76683),x76684))+~P15(x76681,x76682,f319(f319(f301(f924(x76681)),x76683),f180(f932(f924(x76681),a923))))
% 28.73/28.53 [7710]~P1(f319(f319(f321(x77101),x77102),x77104))+P1(f319(f319(f321(x77101),x77102),f31(f932(x77101,a923),x77103)))+~P1(f319(f319(f321(f932(x77101,a923)),x77104),x77103))
% 28.73/28.53 [7737]~P90(x77371)+~P1(f319(f319(f226(x77371),x77373),x77374))+P1(f319(f319(f226(x77371),f319(f319(f74(x77371),x77372),x77373)),f319(f319(f74(x77371),x77372),x77374)))
% 28.73/28.53 [7738]~P91(x77381)+~P1(f319(f319(f226(x77381),x77383),x77384))+P1(f319(f319(f226(x77381),f319(f319(f74(x77381),x77382),x77383)),f319(f319(f74(x77381),x77382),x77384)))
% 28.73/28.53 [7739]~P90(x77391)+~P1(f319(f319(f226(x77391),x77392),x77394))+P1(f319(f319(f226(x77391),f319(f319(f74(x77391),x77392),x77393)),f319(f319(f74(x77391),x77394),x77393)))
% 28.73/28.53 [7740]~P91(x77401)+~P1(f319(f319(f226(x77401),x77402),x77404))+P1(f319(f319(f226(x77401),f319(f319(f74(x77401),x77402),x77403)),f319(f319(f74(x77401),x77404),x77403)))
% 28.73/28.53 [7741]~P89(x77411)+~P1(f319(f319(f227(x77411),x77413),x77414))+P1(f319(f319(f227(x77411),f319(f319(f74(x77411),x77412),x77413)),f319(f319(f74(x77411),x77412),x77414)))
% 28.73/28.53 [7742]~P90(x77421)+~P1(f319(f319(f227(x77421),x77423),x77424))+P1(f319(f319(f227(x77421),f319(f319(f74(x77421),x77422),x77423)),f319(f319(f74(x77421),x77422),x77424)))
% 28.73/28.53 [7743]~P89(x77431)+~P1(f319(f319(f227(x77431),x77432),x77434))+P1(f319(f319(f227(x77431),f319(f319(f74(x77431),x77432),x77433)),f319(f319(f74(x77431),x77434),x77433)))
% 28.73/28.53 [7744]~P90(x77441)+~P1(f319(f319(f227(x77441),x77442),x77444))+P1(f319(f319(f227(x77441),f319(f319(f74(x77441),x77442),x77443)),f319(f319(f74(x77441),x77444),x77443)))
% 28.73/28.53 [7745]~P117(x77451)+~P1(f319(f319(f279(x77451),x77453),x77454))+P1(f319(f319(f279(x77451),f319(f319(f75(x77451),x77452),x77453)),f319(f319(f75(x77451),x77452),x77454)))
% 28.73/28.53 [7746]~P117(x77461)+~P1(f319(f319(f279(x77461),x77462),x77464))+P1(f319(f319(f279(x77461),f319(f319(f75(x77461),x77462),x77463)),f319(f319(f75(x77461),x77464),x77463)))
% 28.73/28.53 [7753]~P116(x77531)+~P100(x77531)+E(f319(f319(f23(x77531),f319(f319(f75(x77531),x77532),f319(f95(x77531),x77533))),f319(f319(f75(x77531),x77534),f319(f95(x77531),x77533))),f319(f319(f75(x77531),f319(f319(f23(x77531),x77532),x77534)),f319(f95(x77531),x77533)))
% 28.73/28.53 [7754]~P146(x77541)+~P100(x77541)+E(f319(f319(f74(x77541),f319(f319(f75(x77541),x77542),f319(f95(x77541),x77543))),f319(f319(f75(x77541),x77544),f319(f95(x77541),x77543))),f319(f319(f75(x77541),f319(f319(f74(x77541),x77542),x77544)),f319(f95(x77541),x77543)))
% 28.73/28.53 [7790]~P79(x77901)+E(f319(f319(f74(x77901),f319(x77902,x77903)),f319(f319(f6(a925,x77901),x77902),f295(a925,f319(a104,x77903),x77904))),f319(f319(f6(a925,x77901),x77902),f295(a925,x77903,x77904)))+~P1(f319(f319(f226(a925),x77903),x77904))
% 28.73/28.53 [7802]~P26(x78022,x78021,x78023,f319(f164(x78022),x78024))+~P1(f319(f129(x78022),x78024))+P1(f319(f129(x78021),f319(f319(f146(x78022,x78021),x78023),x78024)))
% 28.73/28.53 [7851]~P1(f319(f319(f226(a925),x78512),x78514))+~P1(f319(f319(f226(a925),x78511),x78513))+P1(f319(f319(f226(a925),f319(f319(f75(a925),x78511),x78512)),f319(f319(f75(a925),x78513),x78514)))
% 28.73/28.53 [7852]~P1(f319(f319(f226(a925),x78522),x78524))+~P1(f319(f319(f226(a925),x78521),x78523))+P1(f319(f319(f226(a925),f319(f319(f74(a925),x78521),x78522)),f319(f319(f74(a925),x78523),x78524)))
% 28.73/28.53 [7855]~P1(f319(f319(f227(a925),x78552),x78554))+~P1(f319(f319(f227(a925),x78551),x78553))+P1(f319(f319(f227(a925),f319(f319(f74(a925),x78551),x78552)),f319(f319(f74(a925),x78553),x78554)))
% 28.73/28.53 [7856]~P1(f319(f319(f226(a1),x78562),x78564))+~P1(f319(f319(f227(a1),x78561),x78563))+P1(f319(f319(f227(a1),f319(f319(f74(a1),x78561),x78562)),f319(f319(f74(a1),x78563),x78564)))
% 28.73/28.53 [7903]P1(f319(f319(f321(x79031),x79032),x79033))+~P1(f319(f319(f321(x79031),x79032),f32(f932(x79031,a923),x79034)))+~P1(f319(f319(f321(f932(x79031,a923)),x79033),x79034))
% 28.73/28.53 [7904]P1(f319(f319(f321(x79041),x79042),x79043))+~P1(f319(f319(f321(x79041),x79042),f32(f932(x79041,a923),x79044)))+~P1(f319(f319(f321(f932(x79041,a923)),x79043),x79044))
% 28.73/28.53 [7920]~P1(f319(x79201,f679(x79201,x79203,x79202)))+P1(f319(x79201,f319(f319(f156(x79202),x79203),x79204)))+~P1(f319(f319(f227(a925),x79204),f319(f181(f926(x79202)),x79203)))
% 28.73/28.53 [7925]P1(f319(x79251,x79252))+~P1(f319(f319(f321(x79254),x79252),f319(f164(x79254),x79253)))+P1(f319(f319(f227(a925),f684(x79251,x79253,x79254)),f319(f181(f926(x79254)),x79253)))
% 28.73/28.53 [7972]~P3(x79721)+~P1(f319(f319(f227(f932(x79722,x79721)),x79724),x79723))+~P1(f319(f319(f226(f932(x79722,x79721)),x79723),x79724))
% 28.73/28.53 [8015]~P1(f319(x80154,x80152))+~P1(f319(f319(f321(x80151),x80152),x80153))+P1(f319(f319(f321(x80151),x80152),f319(f319(f93(f932(x80151,a923)),x80153),f319(f254(x80151),x80154))))
% 28.73/28.53 [8028]P1(f319(f319(f321(x80281),x80282),x80283))+~P1(f319(f319(f226(f932(x80281,a923)),x80283),x80284))+P1(f319(f319(f226(f932(x80281,a923)),x80283),f319(f319(f301(x80281),x80282),x80284)))
% 28.73/28.53 [8029]P1(f319(f319(f321(x80291),x80292),x80293))+~P1(f319(f319(f226(f932(x80291,a923)),x80293),x80294))+P1(f319(f319(f226(f932(x80291,a923)),x80293),f319(f319(f301(x80291),x80292),x80294)))
% 28.73/28.53 [8163]~P1(f319(f319(f321(x81631),x81633),x81634))+~P1(f319(f319(f227(f932(x81631,a923)),x81632),x81634))+P1(f319(f319(f227(f932(x81631,a923)),x81632),f319(f319(f301(x81631),x81633),x81634)))
% 28.73/28.53 [8165]E(f319(f319(f93(f932(x81651,a923)),x81652),x81653),f180(f932(x81651,a923)))+~E(f319(f319(f93(f932(x81651,a923)),f31(f932(x81651,a923),x81654)),x81653),f180(f932(x81651,a923)))+~P1(f319(f319(f321(f932(x81651,a923)),x81652),x81654))
% 28.73/28.53 [8239]P1(f319(f319(f321(x82391),x82392),x82393))+~P1(f319(f319(f226(f932(x82391,a923)),x82393),f319(f319(f301(x82391),x82392),x82394)))+P1(f319(f319(f226(f932(x82391,a923)),x82393),x82394))
% 28.73/28.53 [8240]P1(f319(f319(f321(x82401),x82402),x82403))+~P1(f319(f319(f226(f932(x82401,a923)),x82403),f319(f319(f301(x82401),x82402),x82404)))+P1(f319(f319(f226(f932(x82401,a923)),x82403),x82404))
% 28.73/28.53 [8257]P1(f319(f319(f321(x82572),f679(x82571,x82573,x82572)),f319(f164(x82572),x82573)))+P1(f319(x82571,f319(f319(f156(x82572),x82573),x82574)))+~P1(f319(f319(f227(a925),x82574),f319(f181(f926(x82572)),x82573)))
% 28.73/28.53 [8265]~P1(f319(f319(f226(f932(x82651,a923)),x82652),x82654))+P1(f319(f319(f226(f932(x82651,a923)),x82652),x82653))+~P1(f319(f319(f226(f932(x82651,a923)),x82654),x82653))
% 28.73/28.53 [8266]~P1(f319(f319(f227(f932(x82661,a923)),x82662),x82664))+~P1(f319(f319(f226(f932(x82661,a923)),x82664),x82663))+P1(f319(f319(f227(f932(x82661,a923)),x82662),x82663))
% 28.73/28.53 [8267]~P1(f319(f319(f226(f932(x82671,a923)),x82672),x82674))+~P1(f319(f319(f227(f932(x82671,a923)),x82674),x82673))+P1(f319(f319(f227(f932(x82671,a923)),x82672),x82673))
% 28.73/28.53 [8268]~P1(f319(f319(f227(f932(x82681,a923)),x82682),x82684))+P1(f319(f319(f227(f932(x82681,a923)),x82682),x82683))+~P1(f319(f319(f227(f932(x82681,a923)),x82684),x82683))
% 28.73/28.53 [8312]~P1(f319(f319(f321(x83121),x83124),x83123))+~P1(f319(f319(f227(f932(x83121,a923)),x83122),f319(f319(f301(x83121),x83124),x83123)))+P1(f319(f319(f227(f932(x83121,a923)),x83122),x83123))
% 28.73/28.53 [8322]~P90(x83221)+P1(f319(f319(f226(x83221),x83222),x83223))+~P1(f319(f319(f226(x83221),f319(f319(f74(x83221),x83224),x83222)),f319(f319(f74(x83221),x83224),x83223)))
% 28.73/28.53 [8323]~P90(x83231)+P1(f319(f319(f226(x83231),x83232),x83233))+~P1(f319(f319(f226(x83231),f319(f319(f74(x83231),x83234),x83232)),f319(f319(f74(x83231),x83234),x83233)))
% 28.73/28.53 [8324]~P90(x83241)+P1(f319(f319(f226(x83241),x83242),x83243))+~P1(f319(f319(f226(x83241),f319(f319(f74(x83241),x83242),x83244)),f319(f319(f74(x83241),x83243),x83244)))
% 28.73/28.53 [8325]~P90(x83251)+P1(f319(f319(f226(x83251),x83252),x83253))+~P1(f319(f319(f226(x83251),f319(f319(f74(x83251),x83252),x83254)),f319(f319(f74(x83251),x83253),x83254)))
% 28.73/28.53 [8326]~P90(x83261)+P1(f319(f319(f227(x83261),x83262),x83263))+~P1(f319(f319(f227(x83261),f319(f319(f74(x83261),x83264),x83262)),f319(f319(f74(x83261),x83264),x83263)))
% 28.73/28.53 [8327]~P90(x83271)+P1(f319(f319(f227(x83271),x83272),x83273))+~P1(f319(f319(f227(x83271),f319(f319(f74(x83271),x83274),x83272)),f319(f319(f74(x83271),x83274),x83273)))
% 28.73/28.53 [8328]~P90(x83281)+P1(f319(f319(f227(x83281),x83282),x83283))+~P1(f319(f319(f227(x83281),f319(f319(f74(x83281),x83282),x83284)),f319(f319(f74(x83281),x83283),x83284)))
% 28.73/28.53 [8329]~P90(x83291)+P1(f319(f319(f227(x83291),x83292),x83293))+~P1(f319(f319(f227(x83291),f319(f319(f74(x83291),x83292),x83294)),f319(f319(f74(x83291),x83293),x83294)))
% 28.73/28.53 [8379]P1(f319(x83791,x83792))+~E(f319(f319(f130(x83793),f319(f181(f926(x83793)),f169(x83793,x83791,x83794))),x83794),f105(x83793))+~P1(f319(f319(f321(x83793),x83792),f319(f164(x83793),x83794)))
% 28.73/28.53 [8499]P1(f319(x84991,x84992))+~P1(f319(f319(f321(x84993),x84992),f319(f164(x84993),x84994)))+P1(f319(f319(f227(a925),f319(f181(f926(x84993)),f319(f128(x84993,x84991),x84994))),f319(f181(f926(x84993)),x84994)))
% 28.73/28.53 [8994]~P1(f319(x89941,f762(x89941,x89943,x89942,x89944)))+P1(f319(x89941,f319(f319(f156(x89942),x89943),x89944)))+~P1(f319(f319(f227(a925),x89944),f319(f181(f926(x89942)),x89943)))
% 28.73/28.53 [9019]~P26(x90194,x90193,x90191,f234(f932(x90194,a923)))+E(f319(x90191,f892(x90192,x90191,x90193,x90194)),x90192)+~P1(f319(f319(f321(x90193),x90192),f319(f302(x90194,x90193,x90191),f234(f932(x90194,a923)))))
% 28.73/28.53 [9087]E(f169(x90871,x90872,x90873),f319(f319(f167(x90871),x90874),x90873))+P1(f319(f319(f227(a925),f744(x90872,x90873,x90871,x90874)),x90874))+P1(f319(f319(f227(a925),x90874),f319(f181(f926(x90871)),x90873)))
% 28.73/28.53 [9090]E(f169(x90901,x90902,x90903),f319(f319(f167(x90901),x90904),x90903))+P1(f319(f319(f227(a925),f744(x90902,x90903,x90901,x90904)),x90904))+P1(f319(x90902,f319(f319(f156(x90901),x90903),x90904)))
% 28.73/28.53 [9126]P1(f319(x91261,x91262))+~P1(f319(f319(f321(x91264),x91262),f319(f164(x91264),x91263)))+P1(f319(f319(f227(a925),f719(x91262,x91261,x91263,x91264)),f319(f181(f926(x91264)),x91263)))
% 28.73/28.53 [9128]E(f169(x91281,x91282,x91283),f319(f319(f167(x91281),x91284),x91283))+P1(f319(f319(f227(a925),x91284),f319(f181(f926(x91281)),x91283)))+P1(f319(f319(f227(a925),f744(x91282,x91283,x91281,x91284)),f319(f181(f926(x91281)),x91283)))
% 28.73/28.53 [9135]E(f169(x91351,x91352,x91353),f319(f319(f167(x91351),x91354),x91353))+P1(f319(x91352,f319(f319(f156(x91351),x91353),x91354)))+P1(f319(f319(f227(a925),f744(x91352,x91353,x91351,x91354)),f319(f181(f926(x91351)),x91353)))
% 28.73/28.53 [9162]~P129(x91624)+P1(f319(f319(f321(x91621),f665(x91622,x91623,x91621,x91624)),x91623))+P1(f319(f319(f227(x91624),f2(x91624)),f319(f319(f9(x91621,x91624),x91622),x91623)))
% 28.73/28.53 [9163]~P129(x91634)+P1(f319(f319(f321(x91631),f669(x91632,x91633,x91631,x91634)),x91633))+P1(f319(f319(f226(x91634),f2(x91634)),f319(f319(f9(x91631,x91634),x91632),x91633)))
% 28.73/28.53 [9190]~P1(f319(f55(x91901),x91904))+P1(f319(f319(f321(x91901),f577(x91902,x91903,x91904,x91901)),x91904))+P1(f319(f55(f931(x91901,x91903)),f319(f319(f246(x91901,x91903),x91904),x91902)))
% 28.73/28.53 [9223]P1(f319(f319(f321(x92232),f762(x92231,x92233,x92232,x92234)),f319(f164(x92232),x92233)))+P1(f319(x92231,f319(f319(f156(x92232),x92233),x92234)))+~P1(f319(f319(f227(a925),x92234),f319(f181(f926(x92232)),x92233)))
% 28.73/28.53 [9354]P1(f319(f319(f226(a925),x93544),f319(f181(f926(x93542)),f169(x93542,x93543,x93541))))+P1(f319(f319(f227(a925),f745(x93541,x93542,x93543,x93544)),x93544))+~P1(f319(f319(f226(a925),x93544),f319(f181(f926(x93542)),x93541)))
% 28.73/28.53 [9508]E(f169(x95081,x95082,x95083),f319(f319(f167(x95081),x95084),x95083))+~P1(f319(x95082,f319(f319(f156(x95081),x95083),f744(x95082,x95083,x95081,x95084))))+P1(f319(f319(f227(a925),x95084),f319(f181(f926(x95081)),x95083)))
% 28.73/28.53 [9516]E(f169(x95161,x95162,x95163),f319(f319(f167(x95161),x95164),x95163))+~P1(f319(x95162,f319(f319(f156(x95161),x95163),f744(x95162,x95163,x95161,x95164))))+P1(f319(x95162,f319(f319(f156(x95161),x95163),x95164)))
% 28.73/28.53 [9520]~P1(f319(f55(x95201),x95203))+~P1(f319(f55(x95202),f319(x95204,f577(x95204,x95202,x95203,x95201))))+P1(f319(f55(f931(x95201,x95202)),f319(f319(f246(x95201,x95202),x95203),x95204)))
% 28.73/28.53 [9528]~P129(x95281)+~P1(f319(f319(f226(x95281),f2(x95281)),f319(x95283,f669(x95283,x95284,x95282,x95281))))+P1(f319(f319(f226(x95281),f2(x95281)),f319(f319(f9(x95282,x95281),x95283),x95284)))
% 28.73/28.53 [9529]~P129(x95291)+~P1(f319(f319(f227(x95291),f2(x95291)),f319(x95293,f665(x95293,x95294,x95292,x95291))))+P1(f319(f319(f227(x95291),f2(x95291)),f319(f319(f9(x95292,x95291),x95293),x95294)))
% 28.73/28.53 [9537]~E(f319(f181(f926(x95374)),x95372),f319(f181(f926(x95374)),x95373))+P1(f319(f319(f321(f931(f926(x95374),f926(x95374))),f319(f319(f244(f926(x95374),f926(x95374)),x95373),x95372)),f150(x95374,x95371)))+P1(f319(f319(f227(a925),f671(x95371,x95372,x95373,x95374)),f319(f181(f926(x95374)),x95373)))
% 28.73/28.53 [9590]~P1(f319(x95903,f319(f319(f156(x95902),x95904),f745(x95904,x95902,x95903,x95901))))+P1(f319(f319(f226(a925),x95901),f319(f181(f926(x95902)),f169(x95902,x95903,x95904))))+~P1(f319(f319(f226(a925),x95901),f319(f181(f926(x95902)),x95904)))
% 28.73/28.53 [9672]E(f319(f319(f167(x96721),f681(x96722,x96723,x96724,x96721)),x96723),f319(f319(f167(x96721),f681(x96722,x96723,x96724,x96721)),x96724))+~P1(f319(f319(f321(f931(f926(x96721),f926(x96721))),f319(f319(f244(f926(x96721),f926(x96721)),x96724),x96723)),f139(x96721,x96722)))+P1(f319(f319(f227(a925),f319(f181(f926(x96721)),x96724)),f319(f181(f926(x96721)),x96723)))
% 28.73/28.53 [9729]~P1(f319(f319(f227(a925),f2(a925)),x97293))+~P1(f319(f319(f227(a925),x97294),x97291))+P1(f319(f319(f227(a925),f319(f319(f74(a925),f319(f319(f75(a925),x97291),f39(a925,x97292,x97293))),x97294)),f319(f319(f75(a925),x97291),x97293)))
% 28.73/28.53 [9925]~P3(x99252)+~P1(f319(f319(f226(x99252),f319(x99253,f545(x99254,x99253,x99251,x99252))),f319(x99254,f545(x99254,x99253,x99251,x99252))))+P1(f319(f319(f226(f932(x99251,x99252)),x99253),x99254))
% 28.73/28.53 [9926]~P3(x99262)+~P1(f319(f319(f226(x99262),f319(x99263,f657(x99261,x99264,x99263,x99262))),f319(x99264,f657(x99261,x99264,x99263,x99262))))+P1(f319(f319(f226(f932(x99261,x99262)),x99263),x99264))
% 28.73/28.53 [10041]~P70(x100411)+E(f319(f319(f6(a925,x100411),f319(f319(f18(a925,x100411,x100411),f319(f319(f8(x100411,f932(x100411,x100411),a925),f23(x100411)),x100412)),f319(f319(f8(a925,x100411,a925),x100412),f319(f319(f7(a925,a925,a925),f74(a925)),f72(a925))))),f295(a925,x100413,x100414)),f319(f319(f23(x100411),f319(x100412,x100413)),f319(x100412,f319(f319(f74(a925),x100414),f72(a925)))))+~P1(f319(f319(f226(a925),x100413),x100414))
% 28.73/28.53 [10121]~P38(x101213,f319(f319(f281(x101213,x101213,x101213),x101212),f299(x101213,x101212)))+~P1(f319(f319(f321(f931(x101213,x101213)),f319(f319(f244(x101213,x101213),f319(x101211,f319(a104,f844(x101212,x101211,x101213)))),f319(x101211,f844(x101212,x101211,x101213)))),f299(x101213,x101212)))+E(f319(x101211,f319(f319(f74(a925),f843(x101212,x101211,x101213)),x101214)),f319(x101211,f843(x101212,x101211,x101213)))
% 28.73/28.53 [6964]~P65(x69641)+E(f319(f319(f30(x69641),f319(f319(f75(x69641),x69642),x69643)),x69644),f319(f319(f75(x69641),x69642),f319(f319(f30(x69641),x69643),x69644)))+~P1(f319(f319(f279(x69641),x69644),x69643))
% 28.73/28.53 [7049]E(f319(f319(f126(x70491),x70492),x70493),x70494)+~E(x70493,f319(f319(f130(x70491),f319(f181(f926(x70491)),x70492)),x70494))+~E(f319(f319(f167(x70491),f319(f181(f926(x70491)),x70492)),x70494),x70492)
% 28.73/28.53 [7107]~P73(x71072)+E(x71071,f2(x71072))+E(f319(f319(f283(x71072),f319(f319(f236(x71072),x71073),x71074)),f319(f319(f236(x71072),x71071),x71074)),f319(f319(f236(x71072),f319(f319(f283(x71072),x71073),x71071)),x71074))
% 28.73/28.53 [7248]~P65(x72481)+E(f319(f319(f30(x72481),f319(f319(f75(x72481),x72482),x72483)),x72484),f319(f319(f75(x72481),f319(f319(f30(x72481),x72482),x72484)),x72483))+~P1(f319(f319(f279(x72481),x72484),x72482))
% 28.73/28.53 [7256]~P108(x72561)+~P1(f319(f319(f226(x72561),x72563),x72564))+P1(f319(f319(f226(x72561),f319(f319(f93(x72561),x72562),x72563)),x72564))
% 28.73/28.53 [7257]~P108(x72571)+~P1(f319(f319(f226(x72571),x72572),x72574))+P1(f319(f319(f226(x72571),f319(f319(f93(x72571),x72572),x72573)),x72574))
% 28.73/28.53 [7258]~P4(x72581)+~P1(f319(f319(f226(x72581),x72583),x72584))+P1(f319(f319(f226(x72581),f319(f319(f224(x72581),x72582),x72583)),x72584))
% 28.73/28.53 [7259]~P4(x72591)+~P1(f319(f319(f226(x72591),x72593),x72594))+P1(f319(f319(f226(x72591),f319(f319(f224(x72591),x72592),x72593)),x72594))
% 28.73/28.53 [7260]~P4(x72601)+~P1(f319(f319(f226(x72601),x72602),x72604))+P1(f319(f319(f226(x72601),f319(f319(f224(x72601),x72602),x72603)),x72604))
% 28.73/28.53 [7261]~P4(x72611)+~P1(f319(f319(f226(x72611),x72612),x72614))+P1(f319(f319(f226(x72611),f319(f319(f224(x72611),x72612),x72613)),x72614))
% 28.73/28.53 [7262]~P108(x72621)+~P1(f319(f319(f227(x72621),x72623),x72624))+P1(f319(f319(f227(x72621),f319(f319(f93(x72621),x72622),x72623)),x72624))
% 28.73/28.53 [7263]~P108(x72631)+~P1(f319(f319(f227(x72631),x72632),x72634))+P1(f319(f319(f227(x72631),f319(f319(f93(x72631),x72632),x72633)),x72634))
% 28.73/28.53 [7264]~P4(x72641)+~P1(f319(f319(f227(x72641),x72643),x72644))+P1(f319(f319(f227(x72641),f319(f319(f224(x72641),x72642),x72643)),x72644))
% 28.73/28.53 [7265]~P4(x72651)+~P1(f319(f319(f227(x72651),x72653),x72654))+P1(f319(f319(f227(x72651),f319(f319(f224(x72651),x72652),x72653)),x72654))
% 28.73/28.53 [7266]~P4(x72661)+~P1(f319(f319(f227(x72661),x72662),x72664))+P1(f319(f319(f227(x72661),f319(f319(f224(x72661),x72662),x72663)),x72664))
% 28.73/28.53 [7267]~P4(x72671)+~P1(f319(f319(f227(x72671),x72672),x72674))+P1(f319(f319(f227(x72671),f319(f319(f224(x72671),x72672),x72673)),x72674))
% 28.73/28.53 [7290]~P1(f319(x72903,x72904))+~P1(f319(x72902,x72904))+P1(f319(f319(f319(f93(f932(x72901,a923)),x72902),x72903),x72904))
% 28.73/28.53 [7417]P15(x74171,x74172,x74173)+~P15(x74171,x74172,x74174)+~P1(f319(f319(f226(f932(f924(x74171),a923)),x74173),x74174))
% 28.73/28.53 [7780]~P79(x77801)+E(f319(f319(f74(x77801),f319(x77802,x77803)),f319(f319(f6(a925,x77801),x77802),f319(f294(a925,f319(a104,x77803)),x77804))),f319(f319(f6(a925,x77801),x77802),f319(f294(a925,x77803),x77804)))+~P1(f319(f319(f227(a925),x77803),x77804))
% 28.73/28.53 [7798]E(x77981,x77982)+P1(f319(f319(f164(x77983),x77984),x77982))+~P1(f319(f319(f164(x77983),f319(f319(f143(x77983),x77981),x77984)),x77982))
% 28.73/28.53 [7809]~P4(x78091)+P1(f319(f319(f226(x78091),x78092),x78093))+~P1(f319(f319(f226(x78091),f319(f319(f225(x78091),x78094),x78092)),x78093))
% 28.73/28.53 [7810]~P4(x78101)+P1(f319(f319(f226(x78101),x78102),x78103))+~P1(f319(f319(f226(x78101),f319(f319(f225(x78101),x78104),x78102)),x78103))
% 28.73/28.53 [7811]~P4(x78111)+P1(f319(f319(f226(x78111),x78112),x78113))+~P1(f319(f319(f226(x78111),f319(f319(f225(x78111),x78112),x78114)),x78113))
% 28.73/28.53 [7812]~P4(x78121)+P1(f319(f319(f226(x78121),x78122),x78123))+~P1(f319(f319(f226(x78121),f319(f319(f225(x78121),x78122),x78124)),x78123))
% 28.73/28.53 [7813]~P107(x78131)+P1(f319(f319(f226(x78131),x78132),x78133))+~P1(f319(f319(f226(x78131),f319(f319(f102(x78131),x78134),x78132)),x78133))
% 28.73/28.53 [7814]~P107(x78141)+P1(f319(f319(f226(x78141),x78142),x78143))+~P1(f319(f319(f226(x78141),f319(f319(f102(x78141),x78144),x78142)),x78143))
% 28.73/28.53 [7815]~P107(x78151)+P1(f319(f319(f226(x78151),x78152),x78153))+~P1(f319(f319(f226(x78151),f319(f319(f102(x78151),x78152),x78154)),x78153))
% 28.73/28.53 [7816]~P107(x78161)+P1(f319(f319(f226(x78161),x78162),x78163))+~P1(f319(f319(f226(x78161),f319(f319(f102(x78161),x78162),x78164)),x78163))
% 28.73/28.53 [7817]~P4(x78171)+P1(f319(f319(f227(x78171),x78172),x78173))+~P1(f319(f319(f227(x78171),f319(f319(f225(x78171),x78174),x78172)),x78173))
% 28.73/28.53 [7818]~P4(x78181)+P1(f319(f319(f227(x78181),x78182),x78183))+~P1(f319(f319(f227(x78181),f319(f319(f225(x78181),x78182),x78184)),x78183))
% 28.73/28.53 [7819]~P121(x78191)+P1(f319(f319(f279(x78191),x78192),x78193))+~P1(f319(f319(f279(x78191),f319(f319(f75(x78191),x78194),x78192)),x78193))
% 28.73/28.53 [7820]~P121(x78201)+P1(f319(f319(f279(x78201),x78202),x78203))+~P1(f319(f319(f279(x78201),f319(f319(f75(x78201),x78202),x78204)),x78203))
% 28.73/28.53 [7894]~P1(f319(f319(f321(x78941),x78942),x78944))+P1(f319(f319(f321(x78941),x78942),x78943))+P1(f319(f319(f321(x78941),x78942),f319(f319(f23(f932(x78941,a923)),x78944),x78943)))
% 28.73/28.53 [7895]~P1(f319(f319(f321(x78951),x78952),x78954))+P1(f319(f319(f321(x78951),x78952),x78953))+P1(f319(f319(f321(x78951),x78952),f319(f319(f23(f932(x78951,a923)),x78954),x78953)))
% 28.73/28.53 [7979]P1(f319(x79791,x79792))+P1(f319(x79793,x79792))+~P1(f319(f319(f319(f102(f932(x79794,a923)),x79793),x79791),x79792))
% 28.73/28.53 [7989]~P1(f319(f319(f321(x79891),x79892),x79894))+~P1(f319(f319(f321(x79891),x79892),x79893))+P1(f319(f319(f321(x79891),x79892),f319(f319(f93(f932(x79891,a923)),x79893),x79894)))
% 28.73/28.53 [7990]~P1(f319(f319(f321(x79901),x79902),x79904))+~P1(f319(f319(f321(x79901),x79902),x79903))+P1(f319(f319(f321(x79901),x79902),f319(f319(f93(f932(x79901,a923)),x79903),x79904)))
% 28.73/28.53 [8038]~P107(x80381)+~P1(f319(f55(x80381),x80384))+E(f319(f319(f58(x80381,x80381,f102(x80381)),x80382),f319(f319(f301(x80381),x80383),x80384)),f319(f319(f102(x80381),x80383),f319(f319(f58(x80381,x80381,f102(x80381)),x80382),x80384)))
% 28.73/28.53 [8039]~P108(x80391)+~P1(f319(f55(x80391),x80394))+E(f319(f319(f58(x80391,x80391,f93(x80391)),x80392),f319(f319(f301(x80391),x80393),x80394)),f319(f319(f93(x80391),x80393),f319(f319(f58(x80391,x80391,f93(x80391)),x80392),x80394)))
% 28.73/28.53 [8040]~P4(x80401)+~P1(f319(f55(x80401),x80404))+E(f319(f319(f58(x80401,x80401,f224(x80401)),x80402),f319(f319(f301(x80401),x80403),x80404)),f319(f319(f224(x80401),x80403),f319(f319(f58(x80401,x80401,f224(x80401)),x80402),x80404)))
% 28.73/28.53 [8041]~P4(x80411)+~P1(f319(f55(x80411),x80414))+E(f319(f319(f58(x80411,x80411,f225(x80411)),x80412),f319(f319(f301(x80411),x80413),x80414)),f319(f319(f225(x80411),x80413),f319(f319(f58(x80411,x80411,f225(x80411)),x80412),x80414)))
% 28.73/28.53 [8043]~P116(x80431)+~P100(x80431)+E(f319(f319(f23(x80431),f319(f319(f75(x80431),f319(f95(x80431),x80432)),x80433)),f319(f319(f75(x80431),f319(f95(x80431),x80432)),x80434)),f319(f319(f75(x80431),f319(f95(x80431),x80432)),f319(f319(f23(x80431),x80433),x80434)))
% 28.73/28.53 [8044]~P146(x80441)+~P100(x80441)+E(f319(f319(f74(x80441),f319(f319(f75(x80441),f319(f95(x80441),x80442)),x80443)),f319(f319(f75(x80441),f319(f95(x80441),x80442)),x80444)),f319(f319(f75(x80441),f319(f95(x80441),x80442)),f319(f319(f74(x80441),x80443),x80444)))
% 28.73/28.53 [8160]E(x81601,x81602)+P1(f319(f319(f321(x81603),x81601),f319(f164(x81603),x81604)))+~P1(f319(f319(f321(x81603),x81601),f319(f164(x81603),f319(f319(f143(x81603),x81602),x81604))))
% 28.73/28.53 [8334]P59(x83341,x83342,x83343)+~P59(x83341,x83342,x83344)+~P1(f319(f319(f226(f932(f931(x83341,x83342),a923)),x83343),x83344))
% 28.73/28.53 [8380]P1(f319(f319(f321(x83801),x83802),x83803))+P1(f319(f319(f321(x83801),x83802),x83804))+~P1(f319(f319(f321(x83801),x83802),f319(f319(f102(f932(x83801,a923)),x83804),x83803)))
% 28.73/28.53 [8381]P1(f319(f319(f321(x83811),x83812),x83813))+P1(f319(f319(f321(x83811),x83812),x83814))+~P1(f319(f319(f321(x83811),x83812),f319(f319(f102(f932(x83811,a923)),x83814),x83813)))
% 28.73/28.53 [8390]~P57(x83901,x83904,x83903)+~P1(f319(f319(f321(x83901),x83902),x83904))+P1(f319(f319(f321(f931(x83901,x83901)),f319(f319(f244(x83901,x83901),x83902),x83902)),x83903))
% 28.73/28.53 [8391]~P57(x83911,x83914,x83913)+~P1(f319(f319(f321(x83911),x83912),x83914))+P1(f319(f319(f321(f931(x83911,x83911)),f319(f319(f244(x83911,x83911),x83912),x83912)),x83913))
% 28.73/28.53 [8392]~P57(x83921,x83924,x83923)+~P1(f319(f319(f321(x83921),x83922),x83924))+P1(f319(f319(f321(f931(x83921,x83921)),f319(f319(f244(x83921,x83921),x83922),x83922)),x83923))
% 28.73/28.53 [8404]~P1(f319(f55(x84042),x84044))+~P1(f319(f55(x84041),x84043))+P1(f319(f55(f931(x84041,x84042)),f319(f319(f246(x84041,x84042),x84043),f319(f16(f932(x84042,a923),x84041),x84044))))
% 28.73/28.53 [8405]~P1(f319(f319(f321(x84051),x84052),x84054))+~P1(f319(f319(f226(f932(x84051,a923)),x84053),x84054))+P1(f319(f319(f226(f932(x84051,a923)),f319(f319(f301(x84051),x84052),x84053)),x84054))
% 28.73/28.53 [8412]~P78(x84122)+~P149(x84122)+E(f319(f319(f9(x84121,x84122),f319(f319(f8(a925,x84122,x84121),f92(x84122)),x84123)),x84124),f319(f92(x84122),f319(f319(f9(x84121,a925),x84123),x84124)))
% 28.73/28.53 [8413]~P78(x84132)+~P145(x84132)+E(f319(f319(f9(x84131,x84132),f319(f319(f8(a1,x84132,x84131),f94(x84132)),x84133)),x84134),f319(f94(x84132),f319(f319(f9(x84131,a1),x84133),x84134)))
% 28.73/28.53 [8437]E(f319(f319(f23(f932(x84371,a923)),x84372),f319(f319(f23(f932(x84371,a923)),x84373),x84374)),x84374)+~P1(f319(f319(f226(f932(x84371,a923)),x84372),x84373))+~P1(f319(f319(f226(f932(x84371,a923)),x84374),x84372))
% 28.73/28.53 [8535]~P1(f319(f55(x85351),x85354))+E(f319(f319(f23(a925),f319(f319(f6(x85351,a925),x85352),x85353)),f319(f319(f6(x85351,a925),x85352),x85354)),f319(f319(f6(x85351,a925),x85352),f319(f319(f23(f932(x85351,a923)),x85353),x85354)))+~P1(f319(f319(f226(f932(x85351,a923)),x85354),x85353))
% 28.73/28.53 [8689]~P9(x86891,x86894,x86893)+~P1(f319(f319(f321(x86891),x86892),x86894))+P1(f319(f319(f321(x86891),x86892),f319(f277(x86891,x86891,x86893),f319(f319(f301(x86891),x86892),f180(f932(x86891,a923))))))
% 28.73/28.53 [8752]~P1(f319(f319(f226(f932(x87521,a923)),x87522),x87523))+~P1(f319(f319(f226(f932(x87521,a923)),x87522),x87524))+P1(f319(f319(f226(f932(x87521,a923)),x87522),f319(f319(f93(f932(x87521,a923)),x87523),x87524)))
% 28.73/28.53 [8855]E(x88551,f180(f932(x88552,a923)))+P1(f319(f55(x88553),x88554))+~P1(f319(f55(f931(x88553,x88552)),f319(f319(f246(x88553,x88552),x88554),f319(f16(f932(x88552,a923),x88553),x88551))))
% 28.73/28.53 [8856]E(x88561,f180(f932(x88562,a923)))+P1(f319(f55(x88563),x88564))+~P1(f319(f55(f931(x88562,x88563)),f319(f319(f246(x88562,x88563),x88561),f319(f16(f932(x88563,a923),x88562),x88564))))
% 28.73/28.53 [8928]P1(f319(f319(f321(x89281),x89282),f308(x89281,x89283)))+~P1(f319(f319(f321(x89281),x89284),f308(x89281,x89283)))+~P1(f319(f319(f321(f931(x89281,x89281)),f319(f319(f244(x89281,x89281),x89282),x89284)),x89283))
% 28.73/28.53 [8929]P1(f319(f319(f321(x89291),x89292),f308(x89291,x89293)))+~P1(f319(f319(f321(x89291),x89294),f308(x89291,x89293)))+~P1(f319(f319(f321(f931(x89291,x89291)),f319(f319(f244(x89291,x89291),x89292),x89294)),x89293))
% 28.73/28.53 [8986]~P38(x89861,x89864)+P1(f319(f319(f321(f931(x89861,x89861)),f319(f319(f244(x89861,x89861),x89863),x89862)),f299(x89861,x89864)))+P38(x89861,f319(f319(f301(f931(x89861,x89861)),f319(f319(f244(x89861,x89861),x89862),x89863)),x89864))
% 28.73/28.53 [8987]~P62(x89871,x89874)+P1(f319(f319(f321(f931(x89871,x89871)),f319(f319(f244(x89871,x89871),x89873),x89872)),f299(x89871,x89874)))+P62(x89871,f319(f319(f301(f931(x89871,x89871)),f319(f319(f244(x89871,x89871),x89872),x89873)),x89874))
% 28.73/28.53 [9070]~E(x90702,x90703)+~P1(f319(f319(f321(x90701),x90702),f319(f164(x90701),x90704)))+P1(f319(f319(f321(f931(x90701,x90701)),f319(f319(f244(x90701,x90701),x90702),x90703)),f319(f164(f931(x90701,x90701)),f319(f319(f173(x90701,x90701),x90704),x90704))))
% 28.73/28.53 [9097]~P41(f932(x90971,a923),f932(x90971,a923),x90973)+~P1(f319(f319(f321(x90971),x90972),f88(f932(x90971,a923),x90973)))+P1(f319(f319(f321(x90971),x90972),f319(x90973,f319(f319(f102(f932(x90971,a923)),x90974),f88(f932(x90971,a923),x90973)))))
% 28.73/28.53 [9161]~E(x91613,x91614)+P1(f319(f319(f249(x91611,x91611,a923),a316),x91612))+~P1(f319(f319(f321(f931(x91611,x91611)),x91612),f319(f164(f931(x91611,x91611)),f319(f319(f173(x91611,x91611),x91613),x91614))))
% 28.73/28.53 [9207]P1(f319(f319(f321(f931(f926(x92071),f926(x92071))),f319(f319(f244(f926(x92071),f926(x92071)),x92072),x92073)),f139(x92071,x92074)))+~E(f319(f319(f167(x92071),f319(f181(f926(x92071)),x92072)),x92073),x92072)+~P1(f319(f319(f227(a925),f319(f181(f926(x92071)),x92072)),f319(f181(f926(x92071)),x92073)))
% 28.73/28.53 [9209]~P56(x92091,x92094)+~P1(f319(f319(f321(f931(x92091,x92091)),f319(f319(f244(x92091,x92091),x92093),x92092)),x92094))+P1(f319(f319(f321(f931(x92091,x92091)),f319(f319(f244(x92091,x92091),x92092),x92093)),x92094))
% 28.73/28.53 [9210]~P56(x92101,x92104)+~P1(f319(f319(f321(f931(x92101,x92101)),f319(f319(f244(x92101,x92101),x92103),x92102)),x92104))+P1(f319(f319(f321(f931(x92101,x92101)),f319(f319(f244(x92101,x92101),x92102),x92103)),x92104))
% 28.73/28.53 [9303]~P1(f319(f55(x93031),x93034))+P1(f319(f319(f321(x93031),f905(x93032,x93033,x93034,x93031)),x93034))+P1(f319(f55(x93033),f319(f319(f33(x93031,f932(x93033,a923)),x93034),x93032)))
% 28.73/28.53 [9304]~P1(f319(f55(x93041),x93044))+P1(f319(f319(f321(x93041),f341(x93042,x93043,x93044,x93041)),x93044))+P1(f319(f55(x93043),f319(f319(f33(x93041,f932(x93043,a923)),x93044),x93042)))
% 28.73/28.53 [9392]P1(f319(f319(f321(f931(x93921,x93921)),x93922),f319(f319(f281(x93921,x93921,x93921),x93923),f299(x93921,x93923))))+~P1(f319(f319(f227(a925),f2(a925)),x93924))+~P1(f319(f319(f321(f931(x93921,x93921)),x93922),f319(f319(f175(f931(x93921,x93921),a923),x93924),x93923)))
% 28.73/28.53 [9399]~P38(x93991,x93992)+~P1(f319(f319(f321(f931(x93991,x93991)),f319(f319(f244(x93991,x93991),x93994),x93993)),x93992))+~P1(f319(f319(f321(f931(x93991,x93991)),f319(f319(f244(x93991,x93991),x93993),x93994)),x93992))
% 28.73/28.53 [9400]~P38(x94001,x94002)+~P1(f319(f319(f321(f931(x94001,x94001)),f319(f319(f244(x94001,x94001),x94004),x94003)),x94002))+~P1(f319(f319(f321(f931(x94001,x94001)),f319(f319(f244(x94001,x94001),x94003),x94004)),x94002))
% 28.73/28.53 [9527]~P1(f319(f55(x95271),x95274))+E(f319(f319(f6(x95271,a925),f319(f319(f8(f932(x95272,a923),a925,x95271),f29(x95272)),x95273)),x95274),f319(f29(f931(x95271,x95272)),f319(f319(f246(x95271,x95272),x95274),x95273)))+P1(f319(f319(f321(x95271),f578(x95273,x95272,x95274,x95271)),x95274))
% 28.73/28.53 [9531]~P1(f319(f129(x95311),x95312))+P1(f319(f129(x95311),f319(f319(f151(x95311,x95312),x95313),x95314)))+P1(f319(f319(f321(x95311),x95314),f319(f319(f23(f932(x95311,a923)),f319(f164(x95311),x95312)),f319(f319(f301(x95311),f319(f319(f156(x95311),x95312),x95313)),f180(f932(x95311,a923))))))
% 28.73/28.53 [9549]~P1(f319(f55(x95492),x95493))+~P1(f319(f55(x95491),f319(x95494,f905(x95494,x95491,x95493,x95492))))+P1(f319(f55(x95491),f319(f319(f33(x95492,f932(x95491,a923)),x95493),x95494)))
% 28.73/28.53 [9550]~P1(f319(f55(x95502),x95503))+~P1(f319(f55(x95501),f319(x95504,f341(x95504,x95501,x95503,x95502))))+P1(f319(f55(x95501),f319(f319(f33(x95502,f932(x95501,a923)),x95503),x95504)))
% 28.73/28.53 [9628]~P1(f319(f319(f321(f931(x96281,x96281)),x96282),f319(f319(f281(x96281,x96281,x96281),x96284),f299(x96281,x96284))))+P1(f319(f319(f321(f931(x96281,x96281)),x96282),f319(f319(f281(x96281,x96281,x96281),x96283),f299(x96281,x96283))))+~P1(f319(f319(f226(f932(f931(x96281,x96281),a923)),x96284),x96283))
% 28.73/28.53 [9638]E(f319(f319(f167(x96381),f681(x96384,x96383,x96382,x96381)),x96383),f319(f319(f167(x96381),f681(x96384,x96383,x96382,x96381)),x96382))+~P1(f319(f319(f321(f931(f926(x96381),f926(x96381))),f319(f319(f244(f926(x96381),f926(x96381)),x96382),x96383)),f139(x96381,x96384)))+E(f319(f319(f167(x96381),f319(f181(f926(x96381)),x96382)),x96383),x96382)
% 28.73/28.53 [9655]~P1(f319(f55(x96551),x96554))+E(f319(f319(f6(x96551,a925),f319(f319(f8(f932(x96552,a923),a925,x96551),f29(x96552)),x96553)),x96554),f319(f29(f931(x96551,x96552)),f319(f319(f246(x96551,x96552),x96554),x96553)))+~P1(f319(f55(x96552),f319(x96553,f578(x96553,x96552,x96554,x96551))))
% 28.73/28.53 [9659]~E(f319(f181(f926(x96591)),x96593),f319(f181(f926(x96591)),x96592))+P1(f319(f319(f321(f931(f926(x96591),f926(x96591))),f319(f319(f244(f926(x96591),f926(x96591)),x96592),x96593)),f150(x96591,x96594)))+P1(f319(f319(f321(f931(x96591,x96591)),f686(x96594,x96593,x96592,x96591)),f319(f164(f931(x96591,x96591)),f319(f319(f173(x96591,x96591),x96592),x96593))))
% 28.73/28.53 [9740]~P1(f319(f319(f321(f931(f926(x97401),f926(x97401))),f319(f319(f244(f926(x97401),f926(x97401)),x97402),x97403)),f139(x97401,x97404)))+E(f319(f319(f167(x97401),f319(f181(f926(x97401)),x97402)),x97403),x97402)+P1(f319(f319(f227(a925),f681(x97404,x97403,x97402,x97401)),f319(f319(f224(a925),f319(f181(f926(x97401)),x97402)),f319(f181(f926(x97401)),x97403))))
% 28.73/28.53 [9764]~P1(f319(f319(f321(f931(f926(x97641),f926(x97641))),f319(f319(f244(f926(x97641),f926(x97641)),x97642),x97643)),f139(x97641,x97644)))+P1(f319(f319(f227(a925),f319(f181(f926(x97641)),x97642)),f319(f181(f926(x97641)),x97643)))+P1(f319(f319(f227(a925),f681(x97644,x97643,x97642,x97641)),f319(f319(f224(a925),f319(f181(f926(x97641)),x97642)),f319(f181(f926(x97641)),x97643))))
% 28.73/28.53 [10188]~P1(f319(f319(f321(f931(f926(x101881),f926(x101881))),f319(f319(f244(f926(x101881),f926(x101881)),x101882),x101883)),f139(x101881,x101884)))+E(f319(f319(f167(x101881),f319(f181(f926(x101881)),x101882)),x101883),x101882)+P1(f319(f319(f321(f931(x101881,x101881)),f319(f319(f244(x101881,x101881),f319(f319(f156(x101881),x101882),f681(x101884,x101883,x101882,x101881))),f319(f319(f156(x101881),x101883),f681(x101884,x101883,x101882,x101881)))),x101884))
% 28.73/28.53 [10189]~P1(f319(f319(f321(f931(f926(x101891),f926(x101891))),f319(f319(f244(f926(x101891),f926(x101891)),x101892),x101893)),f139(x101891,x101894)))+P1(f319(f319(f227(a925),f319(f181(f926(x101891)),x101892)),f319(f181(f926(x101891)),x101893)))+P1(f319(f319(f321(f931(x101891,x101891)),f319(f319(f244(x101891,x101891),f319(f319(f156(x101891),x101892),f681(x101894,x101893,x101892,x101891))),f319(f319(f156(x101891),x101893),f681(x101894,x101893,x101892,x101891)))),x101894))
% 28.73/28.53 [10259]~E(f319(f181(f926(x102591)),x102592),f319(f181(f926(x102591)),x102593))+P1(f319(f319(f321(f931(f926(x102591),f926(x102591))),f319(f319(f244(f926(x102591),f926(x102591)),x102592),x102593)),f150(x102591,x102594)))+~P1(f319(f319(f321(f931(x102591,x102591)),f319(f319(f244(x102591,x102591),f319(f319(f156(x102591),x102592),f671(x102594,x102593,x102592,x102591))),f319(f319(f156(x102591),x102593),f671(x102594,x102593,x102592,x102591)))),x102594))
% 28.73/28.53 [10408]~P79(x104081)+~P1(f319(f55(x104082),x104084))+E(f319(f157(x104081),f319(f319(f146(x104082,x104081),x104083),f84(f926(x104082),f319(f319(f18(f926(x104082),a923,a923),f319(f319(f8(a923,f932(a923,a923),f926(x104082)),a317),f319(f319(f7(f926(x104082),f932(x104082,a923),a923),f319(f319(f8(f932(x104082,a923),f932(f932(x104082,a923),a923),f926(x104082)),a316),f164(x104082))),x104084))),f129(x104082))))),f223(x104082,x104081,x104083,x104084))
% 28.73/28.53 [7631]~P72(x76312)+E(x76311,f2(x76312))+E(f319(f319(f283(x76312),f319(f319(f74(x76312),x76313),f319(f319(f75(x76312),x76314),x76311))),x76311),f319(f319(f74(x76312),x76314),f319(f319(f283(x76312),x76313),x76311)))
% 28.73/28.53 [7632]~P65(x76322)+E(x76321,f2(x76322))+E(f319(f319(f30(x76322),f319(f319(f74(x76322),x76323),f319(f319(f75(x76322),x76324),x76321))),x76321),f319(f319(f74(x76322),x76324),f319(f319(f30(x76322),x76323),x76321)))
% 28.73/28.53 [7633]~P65(x76332)+E(x76331,f2(x76332))+E(f319(f319(f30(x76332),f319(f319(f74(x76332),x76333),f319(f319(f75(x76332),x76331),x76334))),x76331),f319(f319(f74(x76332),x76334),f319(f319(f30(x76332),x76333),x76331)))
% 28.73/28.53 [7859]~P73(x78592)+E(x78591,f2(x78592))+E(f319(f319(f283(x78592),f319(f319(f23(x78592),x78593),f319(f319(f75(x78592),x78591),x78594))),x78591),f319(f319(f23(x78592),f319(f319(f283(x78592),x78593),x78591)),x78594))
% 28.73/28.53 [7860]~P72(x78602)+E(x78601,f2(x78602))+E(f319(f319(f283(x78602),f319(f319(f74(x78602),x78603),f319(f319(f75(x78602),x78604),x78601))),x78601),f319(f319(f74(x78602),f319(f319(f283(x78602),x78603),x78601)),x78604))
% 28.73/28.53 [7861]~P73(x78612)+E(x78611,f2(x78612))+E(f319(f319(f283(x78612),f319(f319(f74(x78612),x78613),f319(f319(f75(x78612),x78611),x78614))),x78611),f319(f319(f74(x78612),f319(f319(f283(x78612),x78613),x78611)),x78614))
% 28.73/28.53 [8567]~P1(f319(f152(x85671,x85673),x85674))+~P1(f319(f152(x85671,x85672),x85674))+P1(f319(f152(x85671,f319(f319(f93(f932(x85671,a923)),x85672),x85673)),x85674))
% 28.73/28.53 [8944]~E(f319(f319(f281(x89441,x89441,x89441),x89442),x89444),f180(f932(f931(x89441,x89441),a923)))+~E(f319(f319(f281(x89441,x89441,x89441),x89442),x89443),f180(f932(f931(x89441,x89441),a923)))+E(f319(f319(f281(x89441,x89441,x89441),x89442),f319(f319(f102(f932(f931(x89441,x89441),a923)),x89443),x89444)),f180(f932(f931(x89441,x89441),a923)))
% 28.73/28.53 [9071]~P1(f319(f319(f226(f932(x90711,a923)),x90713),x90714))+~P1(f319(f319(f226(f932(x90711,a923)),x90712),x90714))+P1(f319(f319(f226(f932(x90711,a923)),f319(f319(f102(f932(x90711,a923)),x90712),x90713)),x90714))
% 28.73/28.53 [9455]~P1(f319(f55(x94551),x94554))+~P1(f319(f55(x94551),x94553))+E(f319(f319(f23(a925),f319(f319(f74(a925),f319(f319(f6(x94551,a925),x94552),x94553)),f319(f319(f6(x94551,a925),x94552),x94554))),f319(f319(f6(x94551,a925),x94552),f319(f319(f93(f932(x94551,a923)),x94553),x94554))),f319(f319(f6(x94551,a925),x94552),f319(f319(f102(f932(x94551,a923)),x94553),x94554)))
% 28.73/28.53 [9545]~P1(f319(f319(f321(x95451),x95453),x95452))+~P1(f319(f319(f226(f932(x95451,a923)),x95452),f319(f319(f301(x95451),x95453),x95454)))+P1(f319(f319(f226(f932(x95451,a923)),f319(f319(f23(f932(x95451,a923)),x95452),f319(f319(f301(x95451),x95453),f180(f932(x95451,a923))))),x95454))
% 28.73/28.53 [9715]~P1(f319(f319(f321(x97151),x97153),x97152))+P1(f319(f319(f226(f932(x97151,a923)),x97152),f319(f319(f301(x97151),x97153),x97154)))+~P1(f319(f319(f226(f932(x97151,a923)),f319(f319(f23(f932(x97151,a923)),x97152),f319(f319(f301(x97151),x97153),f180(f932(x97151,a923))))),x97154))
% 28.73/28.53 [9716]~P1(f319(f319(f321(x97161),x97163),x97162))+P1(f319(f319(f226(f932(x97161,a923)),x97162),f319(f319(f301(x97161),x97163),x97164)))+~P1(f319(f319(f226(f932(x97161,a923)),f319(f319(f23(f932(x97161,a923)),x97162),f319(f319(f301(x97161),x97163),f180(f932(x97161,a923))))),x97164))
% 28.73/28.53 [9739]~P1(f319(f319(f226(f932(x97391,a923)),x97392),x97394))+P1(f319(f319(f226(f932(x97391,a923)),x97392),f319(f319(f301(x97391),x97393),x97394)))+~P1(f319(f319(f226(f932(x97391,a923)),f319(f319(f23(f932(x97391,a923)),x97392),f319(f319(f301(x97391),x97393),f180(f932(x97391,a923))))),x97394))
% 28.73/28.53 [9806]~P1(f319(f319(f226(a925),x98061),x98063))+~P1(f319(f319(f227(a925),x98062),x98064))+P1(f319(f319(f321(f931(f931(a925,a925),f931(a925,a925))),f319(f319(f244(f931(a925,a925),f931(a925,a925)),f319(f319(f244(a925,a925),x98061),x98062)),f319(f319(f244(a925,a925),x98063),x98064))),a26))
% 28.73/28.53 [9807]~P1(f319(f319(f226(a925),x98072),x98074))+~P1(f319(f319(f226(a925),x98071),x98073))+P1(f319(f319(f321(f931(f931(a925,a925),f931(a925,a925))),f319(f319(f244(f931(a925,a925),f931(a925,a925)),f319(f319(f244(a925,a925),x98071),x98072)),f319(f319(f244(a925,a925),x98073),x98074))),a64))
% 28.73/28.53 [10119]~P1(f319(f319(f321(f926(x101191)),x101194),f153(x101191,x101193)))+~P1(f319(f319(f321(f926(x101191)),x101194),f153(x101191,x101192)))+P1(f319(f152(x101191,f319(f319(f93(f932(x101191,a923)),f319(f319(f7(x101191,f932(x101191,a923),a923),f321(x101191)),x101192)),f319(f319(f7(x101191,f932(x101191,a923),a923),f321(x101191)),x101193))),x101194))
% 28.73/28.53 [10225]~P26(x102251,f932(f932(x102251,a923),a923),f319(f319(f7(x102251,f932(f931(x102251,x102251),a923),f932(f932(x102251,a923),a923)),f319(f319(f8(f932(x102251,a923),f932(f932(f931(x102251,x102251),a923),f932(f932(x102251,a923),a923)),x102251),f54(x102251)),f319(f319(f7(x102251,f932(x102251,a923),f932(x102251,a923)),f301(x102251)),f180(f932(x102251,a923))))),x102253),x102252)+~P1(f319(f319(f321(x102251),x102254),x102252))+E(f319(f319(f23(f932(f932(x102251,a923),a923)),f319(f319(f54(x102251),x102252),x102253)),f319(f319(f54(x102251),f319(f319(f301(x102251),x102254),f180(f932(x102251,a923)))),x102253)),f319(f319(f54(x102251),f319(f319(f23(f932(x102251,a923)),x102252),f319(f319(f301(x102251),x102254),f180(f932(x102251,a923))))),x102253))
% 28.73/28.53 [10363]~P57(x103631,x103632,x103634)+~P1(f319(f319(f321(f931(x103631,x103631)),x103633),x103634))+P1(f319(f319(f249(x103631,x103631,a923),f319(f319(f7(x103631,f932(x103631,a923),f932(x103631,a923)),f319(f319(f8(f932(a923,a923),f932(f932(x103631,a923),f932(x103631,a923)),x103631),f8(a923,a923,x103631)),f319(f319(f8(a923,f932(a923,a923),x103631),a317),f319(f319(f7(x103631,f932(x103631,a923),a923),f321(x103631)),x103632)))),f319(f319(f7(x103631,f932(x103631,a923),a923),f321(x103631)),x103632))),x103633))
% 28.73/28.53 [10376]P1(f319(f55(x103761),x103762))+~P1(f319(f55(x103763),f319(f302(x103761,x103763,x103764),x103762)))+~P1(f319(f55(x103761),f319(f254(x103761),f319(f319(f18(x103761,a923,a923),f319(f319(f8(a923,f932(a923,a923),x103761),a317),f319(f319(f7(x103761,f932(x103761,a923),a923),f321(x103761)),x103762))),f319(f319(f7(x103761,x103763,a923),f319(f319(f8(x103763,f932(x103763,a923),x103761),a316),x103764)),f319(x103764,f467(x103764,x103763,x103762,x103761)))))))
% 28.73/28.53 [8318]~P73(x83182)+E(x83181,f2(x83182))+E(f319(f319(f283(x83182),f319(f319(f23(x83182),f319(f319(f75(x83182),x83181),x83183)),x83184)),x83181),f319(f319(f23(x83182),x83183),f319(f319(f283(x83182),x83184),x83181)))
% 28.73/28.53 [8319]~P73(x83192)+E(x83191,f2(x83192))+E(f319(f319(f283(x83192),f319(f319(f74(x83192),f319(f319(f75(x83192),x83191),x83193)),x83194)),x83191),f319(f319(f74(x83192),x83193),f319(f319(f283(x83192),x83194),x83191)))
% 28.73/28.53 [9237]~E(f319(f319(f281(x92371,x92371,x92371),x92373),x92374),f180(f932(f931(x92371,x92371),a923)))+~E(f319(f319(f281(x92371,x92371,x92371),x92372),x92374),f180(f932(f931(x92371,x92371),a923)))+E(f319(f319(f281(x92371,x92371,x92371),f319(f319(f102(f932(f931(x92371,x92371),a923)),x92372),x92373)),x92374),f180(f932(f931(x92371,x92371),a923)))
% 28.73/28.53 [10030]~P1(f319(f152(x100301,x100303),x100304))+~P1(f319(f152(x100301,x100302),x100304))+P1(f319(f152(x100301,f319(f319(f18(x100301,a923,a923),f319(f319(f8(a923,f932(a923,a923),x100301),a317),x100302)),x100303)),x100304))
% 28.73/28.53 [10300]P1(f319(x103001,f463(x103002,x103003,x103001,x103004)))+~P1(f319(f55(x103004),f319(f254(x103004),x103001)))+P1(f319(f55(x103003),f319(f254(x103003),f319(f319(f8(f932(x103004,a923),a923,x103003),f81(x103004)),f319(f319(f8(f932(x103004,a923),f932(x103004,a923),x103003),f319(f18(x103004,a923,a923),f319(f319(f8(a923,f932(a923,a923),x103004),a317),x103001))),x103002)))))
% 28.73/28.53 [10318]~P1(f319(f55(x103182),f319(f254(x103182),x103183)))+~P1(f319(f55(x103181),f319(f254(x103181),f319(f319(f7(x103181,x103182,a923),x103184),f463(x103184,x103181,x103183,x103182)))))+P1(f319(f55(x103181),f319(f254(x103181),f319(f319(f8(f932(x103182,a923),a923,x103181),f81(x103182)),f319(f319(f8(f932(x103182,a923),f932(x103182,a923),x103181),f319(f18(x103182,a923,a923),f319(f319(f8(a923,f932(a923,a923),x103182),a317),x103183))),x103184)))))
% 28.73/28.53 [10387]~P1(f319(f55(x103871),x103874))+P1(f319(f319(f321(x103871),f815(x103872,x103873,x103874,x103871)),x103874))+P1(f319(f55(x103873),f319(f254(x103873),f319(f319(f8(f932(x103871,a923),a923,x103873),f81(x103871)),f319(f319(f8(f932(x103871,a923),f932(x103871,a923),x103873),f319(f18(x103871,a923,a923),f319(f319(f8(a923,f932(a923,a923),x103871),a317),f319(f319(f7(x103871,f932(x103871,a923),a923),f321(x103871)),x103874)))),x103872)))))
% 28.73/28.53 [10393]~P1(f319(f55(x103932),x103933))+~P1(f319(f55(x103931),f319(f254(x103931),f319(f319(f7(x103931,x103932,a923),x103934),f815(x103934,x103931,x103933,x103932)))))+P1(f319(f55(x103931),f319(f254(x103931),f319(f319(f8(f932(x103932,a923),a923,x103931),f81(x103932)),f319(f319(f8(f932(x103932,a923),f932(x103932,a923),x103931),f319(f18(x103932,a923,a923),f319(f319(f8(a923,f932(a923,a923),x103932),a317),f319(f319(f7(x103932,f932(x103932,a923),a923),f321(x103932)),x103933)))),x103934)))))
% 28.73/28.53 [5243]~E(x52432,x52434)+E(f161(x52431,x52432,x52433),f161(x52431,x52434,x52435))+~E(x52432,f2(a925))
% 28.73/28.53 [5496]E(x54961,x54962)+~E(f161(x54964,x54963,x54961),f161(x54964,x54965,x54962))+E(x54963,f2(a925))
% 28.73/28.53 [6760]E(x67601,x67602)+~E(f319(x67603,x67601),f319(x67603,x67602))+~P26(x67604,x67605,x67603,f234(f932(x67604,a923)))
% 28.73/28.53 [6761]E(x67611,x67612)+~E(f319(x67613,x67611),f319(x67613,x67612))+~P26(x67614,x67615,x67613,f234(f932(x67614,a923)))
% 28.73/28.53 [7663]E(x76631,x76632)+~P26(x76633,x76634,x76635,f234(f932(x76633,a923)))+~E(f319(f302(x76633,x76634,x76635),x76631),f319(f302(x76633,x76634,x76635),x76632))
% 28.73/28.53 [7913]P26(x79132,x79133,f888(x79134,x79133,x79132,x79131),x79131)+~E(f319(f302(x79133,x79132,x79135),x79134),x79131)+E(x79131,f180(f932(x79132,a923)))
% 28.73/28.53 [8448]~P1(f319(f319(x84483,x84482),x84485))+~P1(f319(f319(x84483,x84484),x84482))+P1(f319(f319(f321(x84481),x84482),f291(x84481,x84483,x84484,x84485)))
% 28.73/28.53 [8449]~P1(f319(f319(x84493,x84492),x84495))+~P1(f319(f319(x84493,x84494),x84492))+P1(f319(f319(f321(x84491),x84492),f282(x84491,x84493,x84494,x84495)))
% 28.73/28.53 [8760]~P26(x87601,x87602,x87603,x87604)+P27(x87601,x87602,x87603,x87604,x87605)+~E(f319(f302(x87601,x87602,x87603),x87604),x87605)
% 28.73/28.53 [8894]~P27(x88941,x88943,x88944,x88942,x88945)+~P1(f319(f55(x88943),x88945))+P1(f319(f55(x88941),x88942))
% 28.73/28.53 [8895]~P27(x88953,x88951,x88954,x88955,x88952)+~P1(f319(f55(x88953),x88955))+P1(f319(f55(x88951),x88952))
% 28.73/28.53 [9028]~P26(x90281,x90283,x90285,f234(f932(x90281,a923)))+~P26(x90283,x90282,x90284,f234(f932(x90283,a923)))+P26(x90281,x90282,f319(f66(x90283,x90282,x90281,x90284),x90285),f234(f932(x90281,a923)))
% 28.73/28.53 [9605]P1(f319(f319(f321(f931(x96051,x96051)),f319(f319(f244(x96051,x96051),x96052),x96053)),f299(x96051,x96054)))+~P1(f319(f319(f321(f931(x96051,x96051)),f319(f319(f244(x96051,x96051),x96052),x96055)),f299(x96051,x96054)))+~P1(f319(f319(f321(f931(x96051,x96051)),f319(f319(f244(x96051,x96051),x96055),x96053)),f299(x96051,x96054)))
% 28.73/28.53 [9645]~P4(x96452)+~P1(f319(f129(x96451),x96455))+P1(f319(f129(x96451),f141(x96451,x96452,x96453,x96454,x96455)))
% 28.73/28.53 [9777]~P27(x97773,x97772,x97774,f234(f932(x97773,a923)),f234(f932(x97772,a923)))+~P27(x97771,x97773,x97775,f234(f932(x97771,a923)),f234(f932(x97773,a923)))+P27(x97771,x97772,f319(f66(x97773,x97772,x97771,x97774),x97775),f234(f932(x97771,a923)),f234(f932(x97772,a923)))
% 28.73/28.53 [5570]~E(x55702,f105(x55701))+E(f319(f319(f126(x55701),x55702),x55703),f319(f319(f143(x55701),x55704),x55705))+~E(x55703,f319(f319(f143(x55701),x55704),x55705))
% 28.73/28.53 [5571]~E(x55712,f105(x55711))+E(f319(f319(f126(x55711),x55712),x55713),f319(f319(f143(x55711),x55714),x55715))+~E(f319(f319(f143(x55711),x55714),x55715),x55713)
% 28.73/28.53 [6718]~E(f319(f181(f926(x67181)),x67185),f319(f181(f926(x67182)),x67184))+E(f319(f319(f146(f931(x67181,x67182),x67182),f248(x67181,x67182)),x67183),x67184)+~E(f319(f319(f173(x67181,x67182),x67185),x67184),x67183)
% 28.73/28.53 [6719]~E(f319(f181(f926(x67191)),x67194),f319(f181(f926(x67192)),x67195))+E(f319(f319(f146(f931(x67191,x67192),x67191),f243(x67191,x67192)),x67193),x67194)+~E(f319(f319(f173(x67191,x67192),x67194),x67195),x67193)
% 28.73/28.53 [7201]~P4(x72011)+~P14(x72011,f319(f319(f146(x72012,x72011),x72013),x72015))+P14(x72011,f319(f319(f146(x72012,x72011),x72013),f319(f128(x72012,x72014),x72015)))
% 28.73/28.53 [7344]~P4(x73441)+P14(x73441,f319(f319(f146(x73442,x73441),x73443),f162(x73442,x73444,x73445)))+~P14(x73441,f319(f319(f146(x73442,x73441),x73443),x73445))
% 28.73/28.53 [7367]~P59(x73673,x73672,x73675)+~P59(x73671,x73673,x73674)+P59(x73671,x73672,f319(f319(f281(x73671,x73673,x73672),x73674),x73675))
% 28.73/28.53 [7463]E(x74631,x74632)+~P26(x74633,x74634,x74635,f234(f932(x74633,a923)))+~E(f319(f319(f146(x74633,x74634),x74635),x74631),f319(f319(f146(x74633,x74634),x74635),x74632))
% 28.73/28.53 [7464]E(x74641,x74642)+~P26(x74643,x74644,x74645,f234(f932(x74643,a923)))+~E(f319(f319(f146(x74643,x74644),x74645),x74641),f319(f319(f146(x74643,x74644),x74645),x74642))
% 28.73/28.53 [7618]~P1(f319(f319(f226(a925),x76181),f319(x76183,x76185)))+P1(f319(f319(f226(a925),x76181),f147(x76182,x76183,x76184)))+~P1(f319(f319(f321(x76182),x76185),f319(f164(x76182),x76184)))
% 28.73/28.53 [7619]~P1(f319(f319(f227(a925),x76191),f319(x76193,x76195)))+P1(f319(f319(f227(a925),x76191),f147(x76192,x76193,x76194)))+~P1(f319(f319(f321(x76192),x76195),f319(f164(x76192),x76194)))
% 28.73/28.53 [7973]~E(x79733,f2(a925))+P1(f319(x79731,x79732))+~P1(f319(f319(f321(x79734),x79732),f319(f164(x79734),f161(x79734,x79733,x79735))))
% 28.73/28.53 [7988]~E(x79881,f2(a925))+~P1(f319(x79882,x79883))+~P1(f319(f319(f321(x79884),x79883),f319(f164(x79884),f161(x79884,x79881,x79885))))
% 28.73/28.53 [8009]P1(f319(x80091,x80092))+~P1(f319(x80091,x80093))+~P1(f319(f319(f321(x80094),x80092),f319(f164(x80094),f161(x80094,x80095,x80093))))
% 28.73/28.53 [8010]P1(f319(x80101,x80102))+~P1(f319(x80101,x80103))+~P1(f319(f319(f321(x80104),x80103),f319(f164(x80104),f161(x80104,x80105,x80102))))
% 28.73/28.53 [8014]~P113(x80141)+P1(f319(f319(f226(f932(x80141,a923)),f295(x80141,x80142,x80143)),f295(x80141,x80144,x80145)))+P1(f319(f319(f226(x80141),x80142),x80143))
% 28.73/28.53 [8036]~P6(x80361)+P1(f319(f319(f226(x80361),f319(f319(f34(x80362,x80361),x80363),x80364)),f319(x80364,x80365)))+~P1(f319(f319(f321(x80362),x80365),x80363))
% 28.73/28.53 [8106]~P26(x81061,x81062,x81064,x81063)+E(f319(f71(x81061,x81062,x81063,x81064),f319(x81064,x81065)),x81065)+~P1(f319(f319(f321(x81061),x81065),x81063))
% 28.73/28.53 [8107]~P26(x81071,x81072,x81074,x81073)+E(f319(f85(x81071,x81072,x81073,x81074),f319(x81074,x81075)),x81075)+~P1(f319(f319(f321(x81071),x81075),x81073))
% 28.73/28.53 [8307]~P1(f319(x83071,x83075))+P1(f319(x83071,f615(x83071,x83072,x83073,x83074)))+~P1(f319(f319(f321(x83074),x83075),x83073))
% 28.73/28.53 [8308]~P1(f319(x83081,x83085))+P1(f319(x83081,f615(x83081,x83082,x83083,x83084)))+~P1(f319(f319(f321(x83084),x83085),x83082))
% 28.73/28.53 [8402]P1(f319(f55(x84021),x84022))+~P1(f319(f55(x84023),x84024))+~P1(f319(f319(f226(f932(x84021,a923)),x84022),f319(f302(x84023,x84021,x84025),x84024)))
% 28.73/28.53 [8411]~P26(x84114,x84111,x84112,f234(f932(x84114,a923)))+~P1(f319(f319(f321(x84114),x84113),x84115))+P1(f319(f319(f321(x84111),f319(x84112,x84113)),f319(f302(x84114,x84111,x84112),x84115)))
% 28.73/28.53 [8570]E(x85701,x85702)+~P26(x85703,x85704,x85705,f319(f319(f102(f932(x85703,a923)),f319(f164(x85703),x85701)),f319(f164(x85703),x85702)))+~E(f319(f319(f146(x85703,x85704),x85705),x85701),f319(f319(f146(x85703,x85704),x85705),x85702))
% 28.73/28.53 [8571]E(x85711,x85712)+~P26(x85713,x85714,x85715,f319(f319(f102(f932(x85713,a923)),f319(f164(x85713),x85711)),f319(f164(x85713),x85712)))+~E(f319(f319(f146(x85713,x85714),x85715),x85711),f319(f319(f146(x85713,x85714),x85715),x85712))
% 28.73/28.53 [8625]~P113(x86251)+~P1(f319(f319(f227(f932(x86251,a923)),f295(x86251,x86254,x86255)),f295(x86251,x86252,x86253)))+P1(f319(f319(f226(x86251),x86252),x86253))
% 28.73/28.53 [8688]~P26(x86881,x86884,x86885,f234(f932(x86881,a923)))+~P1(f319(f319(f321(x86884),f319(x86885,x86882)),f319(f302(x86881,x86884,x86885),x86883)))+P1(f319(f319(f321(x86881),x86882),x86883))
% 28.73/28.53 [8766]P1(f319(x87661,x87662))+~P1(f319(x87661,f567(x87661,x87663,x87664,x87665)))+~P1(f319(f319(f321(x87665),x87662),x87664))
% 28.73/28.53 [8767]P1(f319(x87671,x87672))+~P1(f319(x87671,f567(x87671,x87673,x87674,x87675)))+~P1(f319(f319(f321(x87675),x87672),x87673))
% 28.73/28.53 [9068]~P26(x90682,x90683,x90681,x90684)+E(f319(x90681,f319(f71(x90682,x90683,x90684,x90681),x90685)),x90685)+~P1(f319(f319(f321(x90683),x90685),f319(f302(x90682,x90683,x90681),x90684)))
% 28.73/28.53 [9176]E(x91761,f105(x91762))+E(f319(f319(f143(x91762),x91763),f700(x91764,x91763,x91765,x91761,x91762)),x91761)+~E(f319(f319(f126(x91762),x91761),x91765),f319(f319(f143(x91762),x91763),x91764))
% 28.73/28.53 [9177]E(x91771,f105(x91772))+E(f319(f319(f143(x91772),x91773),f701(x91774,x91771,x91775,x91773,x91772)),x91771)+~E(f319(f319(f126(x91772),x91771),x91774),f319(f319(f143(x91772),x91773),x91775))
% 28.73/28.53 [9195]E(f319(f319(f143(x91952),x91953),f700(x91954,x91953,x91951,x91955,x91952)),x91955)+~E(f319(f319(f126(x91952),x91955),x91951),f319(f319(f143(x91952),x91953),x91954))+E(x91951,f319(f319(f143(x91952),x91953),x91954))
% 28.73/28.53 [9196]E(f319(f319(f143(x91961),x91962),f701(x91964,x91965,x91963,x91962,x91961)),x91965)+~E(f319(f319(f126(x91961),x91965),x91964),f319(f319(f143(x91961),x91962),x91963))+E(f319(f319(f143(x91961),x91962),x91963),x91964)
% 28.73/28.53 [9274]~E(f319(f302(x92743,x92742,x92744),f234(f932(x92743,a923))),f234(f932(x92742,a923)))+~E(f319(f302(x92741,x92743,x92745),f234(f932(x92741,a923))),f234(f932(x92743,a923)))+E(f319(f302(x92741,x92742,f319(f66(x92743,x92742,x92741,x92744),x92745)),f234(f932(x92741,a923))),f234(f932(x92742,a923)))
% 28.73/28.53 [9652]E(x96521,f105(x96522))+~E(f319(f319(f126(x96522),x96521),x96523),f319(f319(f143(x96522),x96525),x96524))+E(f319(f319(f126(x96522),f701(x96523,x96521,x96524,x96525,x96522)),x96523),x96524)
% 28.73/28.53 [9653]E(x96531,f105(x96532))+~E(f319(f319(f126(x96532),x96531),x96535),f319(f319(f143(x96532),x96534),x96533))+E(f319(f319(f126(x96532),f700(x96533,x96534,x96535,x96531,x96532)),x96535),x96533)
% 28.73/28.53 [9660]E(f319(f319(f126(x96602),f700(x96604,x96603,x96601,x96605,x96602)),x96601),x96604)+~E(f319(f319(f126(x96602),x96605),x96601),f319(f319(f143(x96602),x96603),x96604))+E(x96601,f319(f319(f143(x96602),x96603),x96604))
% 28.73/28.53 [9661]~E(f319(f319(f126(x96611),x96615),x96614),f319(f319(f143(x96611),x96612),x96613))+E(f319(f319(f126(x96611),f701(x96614,x96615,x96613,x96612,x96611)),x96614),x96613)+E(f319(f319(f143(x96611),x96612),x96613),x96614)
% 28.73/28.53 [9662]E(f319(f319(f126(x96621),x96625),f703(x96623,x96622,x96624,x96625,x96621)),x96622)+E(f319(f319(f126(x96621),x96622),f702(x96623,x96622,x96624,x96625,x96621)),x96625)+~E(f319(f319(f126(x96621),x96625),x96624),f319(f319(f126(x96621),x96622),x96623))
% 28.73/28.53 [9699]~P4(x96991)+P14(x96991,f319(f319(f146(x96992,x96991),x96993),f141(x96992,x96991,x96993,x96994,x96995)))+~P14(x96991,f319(f319(f146(x96992,x96991),x96993),x96995))
% 28.73/28.53 [9713]~P63(x97135,x97131,x97134,x97133)+P1(f319(f319(x97131,x97132),f562(x97133,x97134,x97131,x97135,x97132)))+~P1(f319(f319(f321(x97135),x97132),x97134))
% 28.73/28.53 [9714]~P63(x97145,x97141,x97144,x97143)+P1(f319(f319(x97141,x97142),f819(x97143,x97144,x97141,x97145,x97142)))+~P1(f319(f319(f321(x97145),x97142),x97144))
% 28.73/28.53 [9818]~P1(f319(f319(f321(f931(x98181,x98181)),f319(f319(f244(x98181,x98181),x98185),x98183)),f299(x98181,x98184)))+P1(f319(f319(f321(f931(x98181,x98181)),f319(f319(f244(x98181,x98181),x98182),x98183)),f319(f319(f281(x98181,x98181,x98181),x98184),f299(x98181,x98184))))+~P1(f319(f319(f321(f931(x98181,x98181)),f319(f319(f244(x98181,x98181),x98182),x98185)),f319(f319(f281(x98181,x98181,x98181),x98184),f299(x98181,x98184))))
% 28.73/28.53 [9819]~P1(f319(f319(f321(f931(x98191,x98191)),f319(f319(f244(x98191,x98191),x98192),x98195)),f299(x98191,x98194)))+P1(f319(f319(f321(f931(x98191,x98191)),f319(f319(f244(x98191,x98191),x98192),x98193)),f319(f319(f281(x98191,x98191,x98191),x98194),f299(x98191,x98194))))+~P1(f319(f319(f321(f931(x98191,x98191)),f319(f319(f244(x98191,x98191),x98195),x98193)),f319(f319(f281(x98191,x98191,x98191),x98194),f299(x98191,x98194))))
% 28.73/28.53 [9821]P1(f319(f319(f321(f931(f926(x98211),f926(x98211))),f319(f319(f244(f926(x98211),f926(x98211)),x98212),x98213)),f150(x98211,f299(x98211,x98214))))+~P1(f319(f319(f321(f931(f926(x98211),f926(x98211))),f319(f319(f244(f926(x98211),f926(x98211)),x98212),x98215)),f150(x98211,f299(x98211,x98214))))+~P1(f319(f319(f321(f931(f926(x98211),f926(x98211))),f319(f319(f244(f926(x98211),f926(x98211)),x98215),x98213)),f150(x98211,f299(x98211,x98214))))
% 28.73/28.53 [9825]E(f319(f319(f126(x98251),x98252),f702(x98253,x98252,x98254,x98255,x98251)),x98255)+E(f319(f319(f126(x98251),f703(x98253,x98252,x98254,x98255,x98251)),x98253),x98254)+~E(f319(f319(f126(x98251),x98252),x98253),f319(f319(f126(x98251),x98255),x98254))
% 28.73/28.53 [9826]E(f319(f319(f126(x98261),x98262),f703(x98263,x98264,x98265,x98262,x98261)),x98264)+E(f319(f319(f126(x98261),f702(x98263,x98264,x98265,x98262,x98261)),x98265),x98263)+~E(f319(f319(f126(x98261),x98262),x98265),f319(f319(f126(x98261),x98264),x98263))
% 28.73/28.53 [9881]P1(f319(f319(f321(f931(x98811,x98811)),f319(f319(f244(x98811,x98811),x98812),x98813)),f319(f319(f281(x98811,x98811,x98811),x98814),f299(x98811,x98814))))+~P1(f319(f319(f321(f931(x98811,x98811)),f319(f319(f244(x98811,x98811),x98812),x98815)),f319(f319(f281(x98811,x98811,x98811),x98814),f299(x98811,x98814))))+~P1(f319(f319(f321(f931(x98811,x98811)),f319(f319(f244(x98811,x98811),x98815),x98813)),f319(f319(f281(x98811,x98811,x98811),x98814),f299(x98811,x98814))))
% 28.73/28.53 [9910]P35(x99101,x99102,x99103,x99104,x99105)+~E(f319(f181(f926(x99101)),x99104),f319(f181(f926(x99102)),x99105))+~P1(f319(f319(f249(x99101,x99102,a923),x99103),f720(x99105,x99104,x99103,x99102,x99101)))
% 28.73/28.53 [9911]P35(x99111,x99112,x99113,x99114,x99115)+~E(f319(f181(f926(x99111)),x99114),f319(f181(f926(x99112)),x99115))+~P1(f319(f319(f249(x99111,x99112,a923),x99113),f721(x99113,x99115,x99114,x99112,x99111)))
% 28.73/28.53 [9916]E(f319(f319(f126(x99161),f702(x99162,x99163,x99164,x99165,x99161)),x99164),x99162)+~E(f319(f319(f126(x99161),x99163),x99162),f319(f319(f126(x99161),x99165),x99164))+E(f319(f319(f126(x99161),f703(x99162,x99163,x99164,x99165,x99161)),x99162),x99164)
% 28.73/28.53 [9932]~P4(x99322)+E(f319(f319(f140(x99321,x99322,x99323),x99324),x99325),f319(f319(f143(x99321),x99324),x99325))+P1(f319(f319(f321(x99321),f766(x99324,x99323,x99325,x99321,x99322)),f319(f164(x99321),x99325)))
% 28.73/28.53 [9937]~P63(x99371,x99374,x99373,x99372)+~P1(f319(f319(f321(x99371),x99375),x99373))+P1(f319(f319(f321(x99371),f562(x99372,x99373,x99374,x99371,x99375)),x99372))
% 28.73/28.53 [9938]~P63(x99381,x99384,x99383,x99382)+~P1(f319(f319(f321(x99381),x99385),x99383))+P1(f319(f319(f321(x99381),f819(x99382,x99383,x99384,x99381,x99385)),x99382))
% 28.73/28.53 [10066]~P1(f319(f319(f321(f931(f932(x100661,a923),f932(x100661,a923))),f319(f319(f244(f932(x100661,a923),f932(x100661,a923)),x100664),x100663)),f311(x100661,x100662)))+~P1(f319(f319(f321(x100661),x100665),x100664))+P1(f319(f319(f321(x100661),f619(x100662,x100663,x100664,x100661,x100665)),x100663))
% 28.73/28.53 [10076]~P4(x100762)+E(f319(f319(f140(x100761,x100762,x100763),x100764),x100765),f319(f319(f143(x100761),x100764),x100765))+~P1(f319(f319(f226(x100762),f319(x100763,x100764)),f319(x100763,f766(x100764,x100763,x100765,x100761,x100762))))
% 28.73/28.53 [10128]~P26(x101283,x101284,x101285,f234(f932(x101283,a923)))+P1(f319(x101281,x101282))+~P1(f319(x101281,f319(f85(x101283,x101284,f234(f932(x101283,a923)),x101285),f793(x101282,x101281,x101285,x101284,x101283))))
% 28.73/28.53 [10276]P35(x102761,x102762,x102763,x102764,x102765)+~E(f319(f181(f926(x102761)),x102764),f319(f181(f926(x102762)),x102765))+~P1(f319(f319(x102763,f319(f319(f156(x102761),x102764),f722(x102765,x102764,x102763,x102762,x102761))),f319(f319(f156(x102762),x102765),f722(x102765,x102764,x102763,x102762,x102761))))
% 28.73/28.53 [10277]P35(x102771,x102772,x102773,x102774,x102775)+~E(f319(f181(f926(x102771)),x102774),f319(f181(f926(x102772)),x102775))+~P1(f319(f319(x102773,f319(f319(f156(x102771),x102774),f755(x102773,x102775,x102772,x102774,x102771))),f319(f319(f156(x102772),x102775),f755(x102773,x102775,x102772,x102774,x102771))))
% 28.73/28.53 [6791]~P19(x67912,x67915,x67911)+~P1(f319(f55(x67912),x67914))+E(f319(x67911,f319(f319(f301(x67912),x67913),x67914)),f319(f319(f58(x67912,x67912,x67915),x67913),x67914))
% 28.73/28.53 [6792]~E(x67923,x67924)+~E(x67922,x67925)+E(f319(f319(f301(x67921),x67922),f319(f319(f301(x67921),x67923),f180(f932(x67921,a923)))),f319(f319(f301(x67921),x67924),f319(f319(f301(x67921),x67925),f180(f932(x67921,a923)))))
% 28.73/28.53 [6802]P1(f319(x68022,x68025))+E(f169(x68021,x68022,f319(f319(f126(x68021),x68023),x68024)),f169(x68021,x68022,x68023))+~P1(f319(f319(f321(x68021),x68025),f319(f164(x68021),x68023)))
% 28.73/28.53 [6842]E(f319(x68421,x68422),f234(f932(x68423,a923)))+~E(f319(f319(f34(x68424,f932(x68423,a923)),x68425),x68421),f234(f932(x68423,a923)))+~P1(f319(f319(f321(x68424),x68422),x68425))
% 28.73/28.53 [6843]E(f319(x68431,x68432),f180(f932(x68433,a923)))+~E(f319(f319(f33(x68434,f932(x68433,a923)),x68435),x68431),f180(f932(x68433,a923)))+~P1(f319(f319(f321(x68434),x68432),x68435))
% 28.73/28.53 [6844]E(f319(x68441,x68442),f234(f932(x68443,a923)))+~E(f319(f319(f34(x68444,f932(x68443,a923)),x68445),x68441),f234(f932(x68443,a923)))+~P1(f319(f319(f321(x68444),x68442),x68445))
% 28.73/28.53 [6845]E(f319(x68451,x68452),f180(f932(x68453,a923)))+~E(f319(f319(f33(x68454,f932(x68453,a923)),x68455),x68451),f180(f932(x68453,a923)))+~P1(f319(f319(f321(x68454),x68452),x68455))
% 28.73/28.53 [7041]~E(x70414,f319(f319(f126(x70411),x70415),f319(f319(f143(x70411),x70412),x70413)))+P1(f319(f319(f321(x70411),x70412),f319(f164(x70411),x70413)))+P1(f319(f319(f321(x70411),x70412),f319(f164(x70411),x70414)))
% 28.73/28.53 [7042]~E(x70424,f319(f319(f126(x70421),x70423),f319(f319(f143(x70421),x70422),x70425)))+P1(f319(f319(f321(x70421),x70422),f319(f164(x70421),x70423)))+P1(f319(f319(f321(x70421),x70422),f319(f164(x70421),x70424)))
% 28.73/28.53 [7353]~E(x73532,x73534)+~P148(x73531)+E(f319(f319(f74(x73531),f319(f319(f75(x73531),x73532),x73533)),f319(f319(f75(x73531),x73534),x73535)),f319(f319(f74(x73531),f319(f319(f75(x73531),x73532),x73535)),f319(f319(f75(x73531),x73534),x73533)))
% 28.73/28.53 [7354]~E(x73542,x73544)+~P148(x73541)+E(f319(f319(f74(x73541),f319(f319(f75(x73541),x73542),x73543)),f319(f319(f75(x73541),x73544),x73545)),f319(f319(f74(x73541),f319(f319(f75(x73541),x73542),x73545)),f319(f319(f75(x73541),x73544),x73543)))
% 28.73/28.53 [7416]~P6(x74161)+~P1(f319(f319(f321(x74164),x74163),x74165))+P1(f319(f319(f226(x74161),f319(x74162,x74163)),f319(f319(f33(x74164,x74161),x74165),x74162)))
% 28.73/28.53 [7467]~P3(x74671)+P1(f319(f319(f226(x74671),f319(x74672,x74673)),f319(x74674,x74673)))+~P1(f319(f319(f226(f932(x74675,x74671)),x74672),x74674))
% 28.73/28.53 [7468]~P3(x74681)+P1(f319(f319(f226(x74681),f319(x74682,x74683)),f319(x74684,x74683)))+~P1(f319(f319(f226(f932(x74685,x74681)),x74682),x74684))
% 28.73/28.53 [7469]~P3(x74691)+P1(f319(f319(f226(x74691),f319(x74692,x74693)),f319(x74694,x74693)))+~P1(f319(f319(f226(f932(x74695,x74691)),x74692),x74694))
% 28.73/28.53 [7588]E(x75881,x75882)+E(x75883,x75881)+~E(f319(f319(f301(x75884),x75881),f319(f319(f301(x75884),x75885),f180(f932(x75884,a923)))),f319(f319(f301(x75884),x75882),f319(f319(f301(x75884),x75883),f180(f932(x75884,a923)))))
% 28.73/28.53 [7589]E(x75891,x75892)+E(x75893,x75891)+~E(f319(f319(f301(x75894),x75893),f319(f319(f301(x75894),x75892),f180(f932(x75894,a923)))),f319(f319(f301(x75894),x75895),f319(f319(f301(x75894),x75891),f180(f932(x75894,a923)))))
% 28.73/28.53 [7590]E(x75901,x75902)+E(x75901,x75903)+~E(f319(f319(f301(x75904),x75903),f319(f319(f301(x75904),x75902),f180(f932(x75904,a923)))),f319(f319(f301(x75904),x75905),f319(f319(f301(x75904),x75901),f180(f932(x75904,a923)))))
% 28.73/28.53 [7591]E(x75911,x75912)+E(x75911,x75913)+~E(f319(f319(f301(x75914),x75911),f319(f319(f301(x75914),x75915),f180(f932(x75914,a923)))),f319(f319(f301(x75914),x75912),f319(f319(f301(x75914),x75913),f180(f932(x75914,a923)))))
% 28.73/28.53 [8116]P26(x81161,x81162,x81163,x81164)+~P26(x81161,x81162,x81163,x81165)+~P1(f319(f319(f226(f932(x81161,a923)),x81164),x81165))
% 28.73/28.53 [8146]~E(f319(x81463,x81465),x81464)+~P26(x81461,x81462,x81463,f234(f932(x81461,a923)))+E(f319(f85(x81461,x81462,f234(f932(x81461,a923)),x81463),x81464),x81465)
% 28.73/28.53 [8295]E(x82951,x82952)+~E(f319(f302(x82953,x82954,x82955),x82951),f319(f302(x82953,x82954,x82955),x82952))+~P26(x82953,x82954,x82955,f319(f319(f102(f932(x82953,a923)),x82951),x82952))
% 28.73/28.53 [8370]P1(f319(x83702,x83704))+E(f319(f319(f130(x83701),f319(f181(f926(x83701)),f169(x83701,x83702,x83703))),x83703),f319(f319(f143(x83701),x83704),x83705))+~E(f319(f319(f126(x83701),f169(x83701,x83702,x83703)),f319(f319(f143(x83701),x83704),x83705)),x83703)
% 28.73/28.53 [8400]~P26(x84001,x84002,x84003,x84005)+~P26(x84001,x84002,x84003,x84004)+P26(x84001,x84002,x84003,f319(f319(f93(f932(x84001,a923)),x84004),x84005))
% 28.73/28.53 [8509]~P79(x85091)+E(f319(f319(f74(x85091),f319(x85092,x85093)),f319(f157(x85091),f319(f319(f146(x85094,x85091),x85092),f162(x85094,x85093,x85095)))),f319(f157(x85091),f319(f319(f146(x85094,x85091),x85092),x85095)))+~P1(f319(f319(f321(x85094),x85093),f319(f164(x85094),x85095)))
% 28.73/28.53 [8597]~P4(x85971)+~P14(x85971,f319(f319(f146(x85972,x85971),x85973),x85975))+P14(x85971,f319(f319(f146(x85972,x85971),x85973),f319(f319(f140(x85972,x85971,x85973),x85974),x85975)))
% 28.73/28.53 [8684]~P6(x86841)+P1(f319(f319(f226(x86841),f319(f319(f33(x86842,x86841),x86843),x86844)),f319(f319(f33(x86842,x86841),x86845),x86844)))+~P1(f319(f319(f226(f932(x86842,a923)),x86843),x86845))
% 28.73/28.53 [8685]~P6(x86851)+P1(f319(f319(f226(x86851),f319(f319(f34(x86852,x86851),x86853),x86854)),f319(f319(f34(x86852,x86851),x86855),x86854)))+~P1(f319(f319(f226(f932(x86852,a923)),x86855),x86853))
% 28.73/28.53 [8721]~P4(x87213)+P1(f319(f129(x87211),x87212))+~P1(f319(f129(x87211),f319(f319(f140(x87211,x87213,x87214),x87215),x87212)))
% 28.73/28.53 [8866]~P4(x88661)+~P1(f319(f319(f321(x88662),x88663),f319(f164(x88662),x88664)))+~P1(f319(f129(x88662),f319(f319(f140(x88662,x88661,x88665),x88663),x88664)))
% 28.73/28.53 [8956]~P4(x89561)+P14(x89561,f319(f319(f146(x89562,x89561),x89563),x89564))+~P14(x89561,f319(f319(f146(x89562,x89561),x89563),f319(f319(f140(x89562,x89561,x89563),x89565),x89564)))
% 28.73/28.53 [9003]~P26(x90032,x90031,x90034,x90033)+E(f319(f302(x90031,x90032,f85(x90032,x90031,x90033,x90034)),f319(f302(x90032,x90031,x90034),x90035)),x90035)+~P1(f319(f319(f226(f932(x90032,a923)),x90035),x90033))
% 28.73/28.53 [9056]~P4(x90562)+E(f319(f319(f140(x90561,x90562,x90563),x90564),x90565),f141(x90561,x90562,x90563,x90564,x90565))+P1(f319(f319(f321(x90562),f319(x90563,x90564)),f319(f302(x90561,x90562,x90563),f319(f164(x90561),x90565))))
% 28.73/28.53 [9138]~P4(x91382)+E(f141(x91381,x91382,x91383,x91384,x91385),x91385)+~P1(f319(f319(f321(x91382),f319(x91383,x91384)),f319(f302(x91381,x91382,x91383),f319(f164(x91381),x91385))))
% 28.73/28.53 [9154]~P26(x91542,x91541,x91543,x91545)+P1(f319(f319(f227(f932(x91541,a923)),f319(f302(x91542,x91541,x91543),x91544)),f319(f302(x91542,x91541,x91543),x91545)))+~P1(f319(f319(f227(f932(x91542,a923)),x91544),x91545))
% 28.73/28.53 [9187]~P26(x91872,x91871,x91873,f234(f932(x91872,a923)))+P1(f319(f319(f226(f932(x91871,a923)),f319(f302(x91872,x91871,x91873),x91874)),f319(f302(x91872,x91871,x91873),x91875)))+~P1(f319(f319(f226(f932(x91872,a923)),x91874),x91875))
% 28.73/28.53 [9315]~P26(x93151,x93152,x93153,f234(f932(x93151,a923)))+~P1(f319(f319(f226(f932(x93152,a923)),x93154),f319(f302(x93151,x93152,x93153),x93155)))+P1(f319(f319(f226(f932(x93151,a923)),f319(f303(x93151,x93152,x93153),x93154)),x93155))
% 28.73/28.53 [9339]~E(f319(f302(x93393,x93391,x93394),f234(f932(x93393,a923))),f234(f932(x93391,a923)))+P1(f319(f319(f226(f932(x93391,a923)),x93392),f319(f302(x93393,x93391,x93394),x93395)))+~P1(f319(f319(f226(f932(x93393,a923)),f319(f303(x93393,x93391,x93394),x93392)),x93395))
% 28.73/28.53 [9448]~P26(x94481,x94484,x94485,f234(f932(x94481,a923)))+~P1(f319(f319(f226(f932(x94484,a923)),f319(f302(x94481,x94484,x94485),x94482)),f319(f302(x94481,x94484,x94485),x94483)))+P1(f319(f319(f226(f932(x94481,a923)),x94482),x94483))
% 28.73/28.53 [9573]~P88(x95731)+~E(f319(x95733,f741(x95733,x95734,x95735,x95732,x95731)),f2(x95731))+E(f319(f157(x95731),f319(f319(f146(x95732,x95731),x95733),f319(f128(x95732,x95734),x95735))),f319(f157(x95731),f319(f319(f146(x95732,x95731),x95733),x95735)))
% 28.73/28.53 [9600]~P27(x96001,x96002,x96003,f234(f932(x96001,a923)),f234(f932(x96002,a923)))+~P1(f319(f319(f226(f932(x96002,a923)),x96004),f319(f302(x96001,x96002,x96003),x96005)))+P1(f319(f319(f226(f932(x96001,a923)),f319(f303(x96001,x96002,x96003),x96004)),x96005))
% 28.73/28.53 [9629]~P27(x96293,x96291,x96294,f234(f932(x96293,a923)),f234(f932(x96291,a923)))+P1(f319(f319(f226(f932(x96291,a923)),x96292),f319(f302(x96293,x96291,x96294),x96295)))+~P1(f319(f319(f226(f932(x96293,a923)),f319(f303(x96293,x96291,x96294),x96292)),x96295))
% 28.73/28.53 [9757]~P18(x97571,x97572,x97573)+~P1(f319(f55(x97571),x97575))+P1(f319(f60(x97571,x97572,x97573,x97574,x97575),f319(f319(f58(x97571,x97572,x97573),x97574),x97575)))
% 28.73/28.53 [9838]~P27(x98382,x98381,x98384,f234(f932(x98382,a923)),f234(f932(x98381,a923)))+~P27(x98381,x98383,x98385,f234(f932(x98381,a923)),f234(f932(x98383,a923)))+E(f319(f66(x98381,x98382,x98383,f85(x98382,x98381,f234(f932(x98382,a923)),x98384)),f85(x98381,x98383,f234(f932(x98381,a923)),x98385)),f85(x98382,x98383,f234(f932(x98382,a923)),f319(f66(x98381,x98383,x98382,x98385),x98384)))
% 28.73/28.53 [9839]P1(f319(x98391,f664(x98392,x98391,x98393,x98394,x98395)))+~P1(f319(f319(f226(f932(x98395,a923)),x98394),x98393))+P1(f319(f319(f226(f932(x98395,a923)),f319(f319(f93(f932(x98395,a923)),x98394),f319(f254(x98395),x98391))),f319(f319(f93(f932(x98395,a923)),x98393),f319(f254(x98395),x98392))))
% 28.73/28.53 [9854]~P88(x98541)+~P1(f319(x98544,f741(x98543,x98544,x98545,x98542,x98541)))+E(f319(f157(x98541),f319(f319(f146(x98542,x98541),x98543),f319(f128(x98542,x98544),x98545))),f319(f157(x98541),f319(f319(f146(x98542,x98541),x98543),x98545)))
% 28.73/28.53 [9934]~P6(x99345)+P1(f319(f319(f321(x99341),f912(x99342,x99343,x99341,x99344,x99345)),x99343))+P1(f319(f319(f226(x99345),x99344),f319(f319(f34(x99341,x99345),x99343),x99342)))
% 28.73/28.53 [9935]~P6(x99355)+P1(f319(f319(f321(x99351),f557(x99352,x99353,x99354,x99351,x99355)),x99354))+P1(f319(f319(f226(x99355),x99353),f319(f319(f34(x99351,x99355),x99354),x99352)))
% 28.73/28.53 [9939]~P88(x99391)+E(f319(f157(x99391),f319(f319(f146(x99392,x99391),x99393),f319(f128(x99392,x99394),x99395))),f319(f157(x99391),f319(f319(f146(x99392,x99391),x99393),x99395)))+P1(f319(f319(f321(x99392),f741(x99393,x99394,x99395,x99392,x99391)),f319(f164(x99392),x99395)))
% 28.73/28.53 [9950]~P1(f319(x99505,f664(x99505,x99503,x99504,x99502,x99501)))+~P1(f319(f319(f226(f932(x99501,a923)),x99502),x99504))+P1(f319(f319(f226(f932(x99501,a923)),f319(f319(f93(f932(x99501,a923)),x99502),f319(f254(x99501),x99503))),f319(f319(f93(f932(x99501,a923)),x99504),f319(f254(x99501),x99505))))
% 28.73/28.53 [9970]~P26(x99705,x99703,x99704,f234(f932(x99705,a923)))+P1(f319(x99701,x99702))+P1(f319(f319(f321(x99703),f793(x99702,x99701,x99704,x99703,x99705)),f319(f302(x99705,x99703,x99704),f234(f932(x99705,a923)))))
% 28.73/28.53 [9997]P35(x99971,x99972,x99973,x99974,x99975)+~E(f319(f181(f926(x99972)),x99975),f319(f181(f926(x99971)),x99974))+P1(f319(f319(f227(a925),f722(x99975,x99974,x99973,x99972,x99971)),f319(f181(f926(x99971)),x99974)))
% 28.73/28.53 [9998]P35(x99981,x99982,x99983,x99984,x99985)+~E(f319(f181(f926(x99982)),x99985),f319(f181(f926(x99981)),x99984))+P1(f319(f319(f227(a925),f755(x99983,x99985,x99982,x99984,x99981)),f319(f181(f926(x99981)),x99984)))
% 28.73/28.53 [10032]P1(f319(f319(f321(x100321),f664(x100322,x100323,x100324,x100325,x100321)),x100325))+~P1(f319(f319(f226(f932(x100321,a923)),x100325),x100324))+P1(f319(f319(f226(f932(x100321,a923)),f319(f319(f93(f932(x100321,a923)),x100325),f319(f254(x100321),x100323))),f319(f319(f93(f932(x100321,a923)),x100324),f319(f254(x100321),x100322))))
% 28.73/28.53 [10077]~P6(x100771)+~P1(f319(f319(f226(x100771),x100772),f319(x100775,f912(x100775,x100774,x100773,x100772,x100771))))+P1(f319(f319(f226(x100771),x100772),f319(f319(f34(x100773,x100771),x100774),x100775)))
% 28.73/28.53 [10078]~P6(x100781)+~P1(f319(f319(f226(x100781),x100782),f319(x100785,f557(x100785,x100782,x100784,x100783,x100781))))+P1(f319(f319(f226(x100781),x100782),f319(f319(f34(x100783,x100781),x100784),x100785)))
% 28.73/28.53 [10117]~P78(x101171)+~P1(f319(f55(x101172),x101175))+E(f319(f319(f319(f59(x101171,x101172,f75(x101171)),f319(f319(f18(x101172,x101171,x101171),f319(f319(f8(x101171,f932(x101171,x101171),x101172),f75(x101171)),x101173)),x101174)),f72(x101171)),x101175),f319(f319(f75(x101171),f319(f319(f319(f59(x101171,x101172,f75(x101171)),x101173),f72(x101171)),x101175)),f319(f319(f319(f59(x101171,x101172,f75(x101171)),x101174),f72(x101171)),x101175)))
% 28.73/28.53 [10172]~P1(f319(f319(f321(f931(f932(x101721,a923),f932(x101721,a923))),f319(f319(f244(f932(x101721,a923),f932(x101721,a923)),x101725),x101724)),f311(x101721,x101723)))+~P1(f319(f319(f321(x101721),x101722),x101725))+P1(f319(f319(f321(f931(x101721,x101721)),f319(f319(f244(x101721,x101721),x101722),f619(x101723,x101724,x101725,x101721,x101722))),x101723))
% 28.73/28.53 [10315]~P1(f319(f319(f321(f931(f926(x103151),f926(x103151))),f319(f319(f244(f926(x103151),f926(x103151)),f319(f319(f126(x103151),x103155),x103152)),f319(f319(f126(x103151),x103155),x103153))),f139(x103151,x103154)))+P1(f319(f319(f321(f931(f926(x103151),f926(x103151))),f319(f319(f244(f926(x103151),f926(x103151)),x103152),x103153)),f139(x103151,x103154)))+P1(f319(f319(f321(f931(x103151,x103151)),f319(f319(f244(x103151,x103151),f709(x103154,x103153,x103152,x103155,x103151)),f709(x103154,x103153,x103152,x103155,x103151))),x103154))
% 28.73/28.53 [7472]~E(x74723,x74725)+E(f319(f319(f156(x74721),f319(f319(f151(x74721,x74722),x74723),x74724)),x74725),x74724)+~P1(f319(f319(f227(a925),x74723),f319(f181(f926(x74721)),x74722)))
% 28.73/28.53 [7585]~E(f319(f319(f126(x75851),x75852),x75854),f319(f319(f126(x75851),x75853),x75855))+E(f319(f319(f167(x75851),f319(f181(f926(x75851)),x75852)),x75853),x75852)+P1(f319(f319(f226(a925),f319(f181(f926(x75851)),x75853)),f319(f181(f926(x75851)),x75852)))
% 28.73/28.53 [7586]E(x75861,x75862)+E(f319(f319(f156(x75863),f319(f319(f151(x75863,x75864),x75861),x75865)),x75862),f319(f319(f156(x75863),x75864),x75862))+~P1(f319(f319(f227(a925),x75861),f319(f181(f926(x75863)),x75864)))
% 28.73/28.53 [8077]~E(f319(f319(f126(x80771),x80772),x80774),f319(f319(f126(x80771),x80773),x80775))+E(f319(f319(f167(x80771),f319(f181(f926(x80771)),x80772)),x80773),x80772)+~P1(f319(f319(f226(a925),f319(f181(f926(x80771)),x80772)),f319(f181(f926(x80771)),x80773)))
% 28.73/28.53 [8101]~P1(f319(f55(x81011),f319(x81014,x81015)))+~P1(f319(f319(f321(x81012),x81015),x81013))+P1(f319(f55(x81011),f319(f319(f34(x81012,f932(x81011,a923)),x81013),x81014)))
% 28.73/28.53 [8279]~P57(x82791,x82793,x82795)+~P57(x82791,x82792,x82794)+P57(x82791,f319(f319(f102(f932(x82791,a923)),x82792),x82793),f319(f319(f102(f932(f931(x82791,x82791),a923)),x82794),x82795))
% 28.73/28.53 [8280]~P57(x82801,x82803,x82805)+~P57(x82801,x82802,x82804)+P57(x82801,f319(f319(f93(f932(x82801,a923)),x82802),x82803),f319(f319(f93(f932(f931(x82801,x82801),a923)),x82804),x82805))
% 28.73/28.53 [8637]E(f319(f319(f244(x86371,x86372),f319(f319(f156(x86371),x86373),x86374)),f319(f319(f156(x86372),x86375),x86374)),f319(f319(f156(f931(x86371,x86372)),f319(f319(f173(x86371,x86372),x86373),x86375)),x86374))+~P1(f319(f319(f227(a925),x86374),f319(f181(f926(x86371)),x86373)))+~P1(f319(f319(f227(a925),x86374),f319(f181(f926(x86372)),x86375)))
% 28.73/28.53 [8794]~P57(x87941,x87943,x87944)+P1(f319(f319(f321(x87941),x87942),x87943))+~P1(f319(f319(f321(f931(x87941,x87941)),f319(f319(f244(x87941,x87941),x87945),x87942)),x87944))
% 28.73/28.53 [8795]~P57(x87951,x87953,x87954)+P1(f319(f319(f321(x87951),x87952),x87953))+~P1(f319(f319(f321(f931(x87951,x87951)),f319(f319(f244(x87951,x87951),x87952),x87955)),x87954))
% 28.73/28.53 [8796]~P9(x87961,x87963,x87964)+P1(f319(f319(f321(x87961),x87962),x87963))+~P1(f319(f319(f321(f931(x87961,x87961)),f319(f319(f244(x87961,x87961),x87965),x87962)),x87964))
% 28.73/28.53 [8797]~P9(x87971,x87973,x87974)+P1(f319(f319(f321(x87971),x87972),x87973))+~P1(f319(f319(f321(f931(x87971,x87971)),f319(f319(f244(x87971,x87971),x87972),x87975)),x87974))
% 28.73/28.53 [9079]~P9(x90791,x90795,x90792)+E(f319(f277(x90791,x90791,x90792),f319(f319(f301(x90791),x90793),f180(f932(x90791,a923)))),f319(f277(x90791,x90791,x90792),f319(f319(f301(x90791),x90794),f180(f932(x90791,a923)))))+~P1(f319(f319(f321(f931(x90791,x90791)),f319(f319(f244(x90791,x90791),x90793),x90794)),x90792))
% 28.73/28.53 [9080]~P9(x90801,x90805,x90802)+E(f319(f277(x90801,x90801,x90802),f319(f319(f301(x90801),x90803),f180(f932(x90801,a923)))),f319(f277(x90801,x90801,x90802),f319(f319(f301(x90801),x90804),f180(f932(x90801,a923)))))+~P1(f319(f319(f321(f931(x90801,x90801)),f319(f319(f244(x90801,x90801),x90803),x90804)),x90802))
% 28.73/28.53 [9271]P1(f319(x92711,x92712))+~P1(f319(f319(f321(x92713),x92712),x92715))+P1(f319(f319(f321(x92713),f567(x92711,x92714,x92715,x92713)),f319(f319(f102(f932(x92713,a923)),x92715),x92714)))
% 28.73/28.53 [9272]P1(f319(x92721,x92722))+~P1(f319(f319(f321(x92723),x92722),x92724))+P1(f319(f319(f321(x92723),f567(x92721,x92724,x92725,x92723)),f319(f319(f102(f932(x92723,a923)),x92725),x92724)))
% 28.73/28.53 [9280]~P1(f319(x92802,x92805))+~P1(f319(f319(f321(x92801),x92805),x92804))+P1(f319(f319(f321(x92801),f615(x92802,x92803,x92804,x92801)),f319(f319(f102(f932(x92801,a923)),x92804),x92803)))
% 28.73/28.53 [9281]~P1(f319(x92812,x92815))+~P1(f319(f319(f321(x92811),x92815),x92813))+P1(f319(f319(f321(x92811),f615(x92812,x92813,x92814,x92811)),f319(f319(f102(f932(x92811,a923)),x92814),x92813)))
% 28.73/28.53 [9296]~P1(f319(f319(f226(f932(x92961,a923)),x92963),x92965))+~P1(f319(f319(f226(f932(x92961,a923)),x92962),x92964))+P1(f319(f319(f226(f932(x92961,a923)),f319(f319(f102(f932(x92961,a923)),x92962),x92963)),f319(f319(f102(f932(x92961,a923)),x92964),x92965)))
% 28.73/28.53 [9297]~P1(f319(f319(f226(f932(x92971,a923)),x92973),x92975))+~P1(f319(f319(f226(f932(x92971,a923)),x92972),x92974))+P1(f319(f319(f226(f932(x92971,a923)),f319(f319(f93(f932(x92971,a923)),x92972),x92973)),f319(f319(f93(f932(x92971,a923)),x92974),x92975)))
% 28.73/28.53 [9298]~P1(f319(f319(f226(f932(x92981,a923)),x92985),x92983))+~P1(f319(f319(f226(f932(x92981,a923)),x92982),x92984))+P1(f319(f319(f226(f932(x92981,a923)),f319(f319(f23(f932(x92981,a923)),x92982),x92983)),f319(f319(f23(f932(x92981,a923)),x92984),x92985)))
% 28.73/28.53 [9395]P1(f319(f319(f321(f931(x93951,x93951)),f319(f319(f244(x93951,x93951),x93952),x93953)),f313(x93951,x93954,x93955)))+~P1(f319(f319(f226(a925),f319(x93954,x93952)),f319(x93954,x93953)))+~P1(f319(f319(f321(f931(x93951,x93951)),f319(f319(f244(x93951,x93951),x93952),x93953)),x93955))
% 28.73/28.53 [9583]P1(f319(f319(f321(f931(x95831,x95831)),f319(f319(f244(x95831,x95831),x95832),x95833)),f299(x95831,x95834)))+~P1(f319(f319(f321(f931(x95831,x95831)),f319(f319(f244(x95831,x95831),x95832),x95835)),f299(x95831,x95834)))+~P1(f319(f319(f321(f931(x95831,x95831)),f319(f319(f244(x95831,x95831),x95835),x95833)),x95834))
% 28.73/28.53 [9584]P1(f319(f319(f321(f931(x95841,x95841)),f319(f319(f244(x95841,x95841),x95842),x95843)),f299(x95841,x95844)))+~P1(f319(f319(f321(f931(x95841,x95841)),f319(f319(f244(x95841,x95841),x95845),x95843)),f299(x95841,x95844)))+~P1(f319(f319(f321(f931(x95841,x95841)),f319(f319(f244(x95841,x95841),x95842),x95845)),x95844))
% 28.73/28.53 [9685]E(x96851,x96852)+E(f319(a104,f635(x96853,x96854,x96851,x96852,x96855)),x96854)+~P1(f319(f319(f321(f931(x96855,x96855)),f319(f319(f244(x96855,x96855),x96852),x96851)),f319(f319(f175(f931(x96855,x96855),a923),x96854),x96853)))
% 28.73/28.53 [9686]E(x96861,x96862)+E(f319(a104,f637(x96863,x96864,x96861,x96862,x96865)),x96864)+~P1(f319(f319(f321(f931(x96865,x96865)),f319(f319(f244(x96865,x96865),x96862),x96861)),f319(f319(f175(f931(x96865,x96865),a923),x96864),x96863)))
% 28.73/28.53 [9687]E(x96871,f2(a925))+E(f319(a104,f635(x96872,x96871,x96873,x96874,x96875)),x96871)+~P1(f319(f319(f321(f931(x96875,x96875)),f319(f319(f244(x96875,x96875),x96874),x96873)),f319(f319(f175(f931(x96875,x96875),a923),x96871),x96872)))
% 28.73/28.53 [9688]E(x96881,f2(a925))+E(f319(a104,f637(x96882,x96881,x96883,x96884,x96885)),x96881)+~P1(f319(f319(f321(f931(x96885,x96885)),f319(f319(f244(x96885,x96885),x96884),x96883)),f319(f319(f175(f931(x96885,x96885),a923),x96881),x96882)))
% 28.73/28.53 [9710]P1(f319(f319(f321(f931(x97101,x97101)),f319(f319(f244(x97101,x97101),x97102),x97103)),f319(f319(f281(x97101,x97101,x97101),x97104),f299(x97101,x97104))))+~P1(f319(f319(f321(f931(x97101,x97101)),f319(f319(f244(x97101,x97101),x97102),x97105)),x97104))+~P1(f319(f319(f321(f931(x97101,x97101)),f319(f319(f244(x97101,x97101),x97105),x97103)),x97104))
% 28.73/28.53 [9717]~P1(f319(f319(f321(f931(x97171,x97171)),f319(f319(f244(x97171,x97171),x97172),x97175)),f299(x97171,x97174)))+P1(f319(f319(f321(f931(x97171,x97171)),f319(f319(f244(x97171,x97171),x97172),x97173)),f319(f319(f281(x97171,x97171,x97171),x97174),f299(x97171,x97174))))+~P1(f319(f319(f321(f931(x97171,x97171)),f319(f319(f244(x97171,x97171),x97175),x97173)),x97174))
% 28.73/28.53 [9718]~P1(f319(f319(f321(f931(x97181,x97181)),f319(f319(f244(x97181,x97181),x97185),x97183)),f299(x97181,x97184)))+P1(f319(f319(f321(f931(x97181,x97181)),f319(f319(f244(x97181,x97181),x97182),x97183)),f319(f319(f281(x97181,x97181,x97181),x97184),f299(x97181,x97184))))+~P1(f319(f319(f321(f931(x97181,x97181)),f319(f319(f244(x97181,x97181),x97182),x97185)),x97184))
% 28.73/28.53 [9751]~P9(x97511,x97515,x97512)+~P1(f319(f319(f321(f931(x97511,x97511)),f319(f319(f244(x97511,x97511),x97513),x97514)),x97512))+P1(f319(f319(f226(f932(x97511,a923)),f319(f277(x97511,x97511,x97512),f319(f319(f301(x97511),x97513),f180(f932(x97511,a923))))),f319(f277(x97511,x97511,x97512),f319(f319(f301(x97511),x97514),f180(f932(x97511,a923))))))
% 28.73/28.53 [9811]P1(f319(f319(f321(f931(x98111,x98111)),f319(f319(f244(x98111,x98111),x98112),x98113)),f319(f319(f281(x98111,x98111,x98111),x98114),f299(x98111,x98114))))+~P1(f319(f319(f321(f931(x98111,x98111)),f319(f319(f244(x98111,x98111),x98112),x98115)),f319(f319(f281(x98111,x98111,x98111),x98114),f299(x98111,x98114))))+~P1(f319(f319(f321(f931(x98111,x98111)),f319(f319(f244(x98111,x98111),x98115),x98113)),x98114))
% 28.73/28.53 [9812]P1(f319(f319(f321(f931(x98121,x98121)),f319(f319(f244(x98121,x98121),x98122),x98123)),f319(f319(f281(x98121,x98121,x98121),x98124),f299(x98121,x98124))))+~P1(f319(f319(f321(f931(x98121,x98121)),f319(f319(f244(x98121,x98121),x98125),x98123)),f319(f319(f281(x98121,x98121,x98121),x98124),f299(x98121,x98124))))+~P1(f319(f319(f321(f931(x98121,x98121)),f319(f319(f244(x98121,x98121),x98122),x98125)),x98124))
% 28.73/28.53 [9863]~P1(f319(f60(x98631,x98631,x98634,x98632,x98633),x98635))+P1(f319(f319(f321(x98631),x98632),x98633))+P1(f319(f56(x98631,x98634,f319(f319(f301(x98631),x98632),x98633)),x98635))
% 28.73/28.53 [9901]~E(f319(f302(x99013,x99012,x99015),x99014),x99011)+E(x99011,f180(f932(x99012,a923)))+P1(f319(f319(f226(f932(x99013,a923)),f319(f302(x99012,x99013,f888(x99014,x99013,x99012,x99011)),x99011)),x99014))
% 28.73/28.53 [9954]~P6(x99545)+P1(f319(f319(f321(x99541),f921(x99542,x99543,x99544,x99541,x99545)),x99544))+P1(f319(f319(f226(x99545),f319(f319(f33(x99541,x99545),x99544),x99543)),x99542))
% 28.73/28.53 [9955]~P6(x99555)+P1(f319(f319(f321(x99551),f638(x99552,x99553,x99554,x99551,x99555)),x99554))+P1(f319(f319(f226(x99555),f319(f319(f33(x99551,x99555),x99554),x99553)),x99552))
% 28.73/28.53 [10018]P35(x100181,x100182,x100183,x100184,x100185)+~E(f319(f181(f926(x100181)),x100184),f319(f181(f926(x100182)),x100185))+P1(f319(f319(f321(f931(x100181,x100182)),f720(x100185,x100184,x100183,x100182,x100181)),f319(f164(f931(x100181,x100182)),f319(f319(f173(x100181,x100182),x100184),x100185))))
% 28.73/28.53 [10019]P35(x100191,x100192,x100193,x100194,x100195)+~E(f319(f181(f926(x100191)),x100194),f319(f181(f926(x100192)),x100195))+P1(f319(f319(f321(f931(x100191,x100192)),f721(x100193,x100195,x100194,x100192,x100191)),f319(f164(f931(x100191,x100192)),f319(f319(f173(x100191,x100192),x100194),x100195))))
% 28.73/28.53 [10151]E(x101511,x101512)+P1(f319(f319(f321(f931(x101513,x101513)),f319(f319(f244(x101513,x101513),x101511),f639(x101514,x101515,x101512,x101511,x101513))),x101514))+~P1(f319(f319(f321(f931(x101513,x101513)),f319(f319(f244(x101513,x101513),x101511),x101512)),f319(f319(f175(f931(x101513,x101513),a923),x101515),x101514)))
% 28.73/28.53 [10152]E(x101521,f2(a925))+P1(f319(f319(f321(f931(x101522,x101522)),f319(f319(f244(x101522,x101522),x101523),f639(x101524,x101521,x101525,x101523,x101522))),x101524))+~P1(f319(f319(f321(f931(x101522,x101522)),f319(f319(f244(x101522,x101522),x101523),x101525)),f319(f319(f175(f931(x101522,x101522),a923),x101521),x101524)))
% 28.73/28.53 [10191]~P6(x101911)+~P1(f319(f319(f226(x101911),f319(x101914,f921(x101915,x101914,x101913,x101912,x101911))),x101915))+P1(f319(f319(f226(x101911),f319(f319(f33(x101912,x101911),x101913),x101914)),x101915))
% 28.73/28.53 [10192]~P6(x101921)+~P1(f319(f319(f226(x101921),f319(x101924,f638(x101925,x101924,x101923,x101922,x101921))),x101925))+P1(f319(f319(f226(x101921),f319(f319(f33(x101922,x101921),x101923),x101924)),x101925))
% 28.73/28.53 [10246]E(x102461,x102462)+P1(f319(f319(f321(f931(x102463,x102463)),f319(f319(f244(x102463,x102463),f636(x102464,x102465,x102461,x102462,x102463)),x102461)),x102464))+~P1(f319(f319(f321(f931(x102463,x102463)),f319(f319(f244(x102463,x102463),x102462),x102461)),f319(f319(f175(f931(x102463,x102463),a923),x102465),x102464)))
% 28.73/28.53 [10247]E(x102471,f2(a925))+P1(f319(f319(f321(f931(x102472,x102472)),f319(f319(f244(x102472,x102472),f636(x102473,x102471,x102474,x102475,x102472)),x102474)),x102473))+~P1(f319(f319(f321(f931(x102472,x102472)),f319(f319(f244(x102472,x102472),x102475),x102474)),f319(f319(f175(f931(x102472,x102472),a923),x102471),x102473)))
% 28.73/28.53 [10251]E(x102511,x102512)+P1(f319(f319(f321(f931(x102513,x102513)),f319(f319(f244(x102513,x102513),x102511),f636(x102514,x102515,x102512,x102511,x102513))),f319(f319(f175(f931(x102513,x102513),a923),f635(x102514,x102515,x102512,x102511,x102513)),x102514)))+~P1(f319(f319(f321(f931(x102513,x102513)),f319(f319(f244(x102513,x102513),x102511),x102512)),f319(f319(f175(f931(x102513,x102513),a923),x102515),x102514)))
% 28.73/28.53 [10252]E(x102521,f2(a925))+P1(f319(f319(f321(f931(x102522,x102522)),f319(f319(f244(x102522,x102522),x102523),f636(x102524,x102521,x102525,x102523,x102522))),f319(f319(f175(f931(x102522,x102522),a923),f635(x102524,x102521,x102525,x102523,x102522)),x102524)))+~P1(f319(f319(f321(f931(x102522,x102522)),f319(f319(f244(x102522,x102522),x102523),x102525)),f319(f319(f175(f931(x102522,x102522),a923),x102521),x102524)))
% 28.73/28.53 [10306]E(x103061,x103062)+P1(f319(f319(f321(f931(x103063,x103063)),f319(f319(f244(x103063,x103063),f639(x103064,x103065,x103061,x103062,x103063)),x103061)),f319(f319(f175(f931(x103063,x103063),a923),f637(x103064,x103065,x103061,x103062,x103063)),x103064)))+~P1(f319(f319(f321(f931(x103063,x103063)),f319(f319(f244(x103063,x103063),x103062),x103061)),f319(f319(f175(f931(x103063,x103063),a923),x103065),x103064)))
% 28.73/28.53 [10307]E(x103071,f2(a925))+P1(f319(f319(f321(f931(x103072,x103072)),f319(f319(f244(x103072,x103072),f639(x103073,x103071,x103074,x103075,x103072)),x103074)),f319(f319(f175(f931(x103072,x103072),a923),f637(x103073,x103071,x103074,x103075,x103072)),x103073)))+~P1(f319(f319(f321(f931(x103072,x103072)),f319(f319(f244(x103072,x103072),x103075),x103074)),f319(f319(f175(f931(x103072,x103072),a923),x103071),x103073)))
% 28.73/28.53 [10341]~P79(x103412)+~P1(f319(f55(x103411),x103415))+E(f319(f319(f6(x103411,x103412),f319(f319(f7(x103411,x103412,x103412),f319(f319(f18(x103411,x103412,f932(x103412,x103412)),f319(f319(f8(a923,f932(x103412,f932(x103412,x103412)),x103411),f86(x103412)),f319(f319(f7(x103411,f932(x103411,a923),a923),f321(x103411)),x103413))),x103414)),f2(x103412))),x103415),f319(f319(f6(x103411,x103412),x103414),f319(f319(f93(f932(x103411,a923)),x103415),x103413)))
% 28.73/28.53 [8863]~P79(x88631)+~P1(f319(f55(x88634),x88635))+E(f319(f319(f74(x88631),f319(x88632,x88633)),f319(f319(f6(x88634,x88631),x88632),f319(f319(f23(f932(x88634,a923)),x88635),f319(f319(f301(x88634),x88633),f180(f932(x88634,a923)))))),f319(f319(f6(x88634,x88631),x88632),f319(f319(f301(x88634),x88633),x88635)))
% 28.73/28.53 [8864]~P78(x88641)+~P1(f319(f55(x88644),x88645))+E(f319(f319(f75(x88641),f319(x88642,x88643)),f319(f319(f9(x88644,x88641),x88642),f319(f319(f23(f932(x88644,a923)),x88645),f319(f319(f301(x88644),x88643),f180(f932(x88644,a923)))))),f319(f319(f9(x88644,x88641),x88642),f319(f319(f301(x88644),x88643),x88645)))
% 28.73/28.53 [9202]~P4(x92022)+~P14(x92022,f319(f160(x92022),f319(f319(f146(x92021,x92022),x92024),x92025)))+E(f319(f128(x92021,f319(f319(f8(x92022,a923,x92021),f319(f227(x92022),x92023)),x92024)),x92025),f169(x92021,f319(f319(f8(x92022,a923,x92021),f319(f227(x92022),x92023)),x92024),x92025))
% 28.73/28.53 [9227]~P79(x92271)+E(f319(f319(f74(x92271),f319(f319(f6(a925,x92271),x92272),f295(a925,x92273,x92274))),f319(f319(f6(a925,x92271),x92272),f295(a925,f319(f319(f74(a925),x92274),f72(a925)),f319(f319(f74(a925),x92274),x92275)))),f319(f319(f6(a925,x92271),x92272),f295(a925,x92273,f319(f319(f74(a925),x92274),x92275))))+~P1(f319(f319(f226(a925),x92273),f319(f319(f74(a925),x92274),f72(a925))))
% 28.73/28.53 [9228]~P1(f319(f319(f321(x92281),x92284),x92285))+~P1(f319(f319(f226(f932(x92281,a923)),f319(f164(x92281),x92282)),x92285))+P1(f319(f319(f226(f932(x92281,a923)),f319(f164(x92281),f319(f319(f151(x92281,x92282),x92283),x92284))),x92285))
% 28.73/28.53 [9456]~P6(x94562)+~P1(f319(f55(x94561),x94565))+E(f319(f319(f58(x94561,x94562,f319(f319(f8(x94562,f932(x94562,x94562),x94561),f102(x94562)),x94563)),x94564),x94565),f319(f319(f102(x94562),x94564),f319(f319(f33(x94561,x94562),x94565),x94563)))
% 28.73/28.53 [9457]~P6(x94572)+~P1(f319(f55(x94571),x94575))+E(f319(f319(f58(x94571,x94572,f319(f319(f8(x94572,f932(x94572,x94572),x94571),f93(x94572)),x94573)),x94574),x94575),f319(f319(f93(x94572),x94574),f319(f319(f34(x94571,x94572),x94575),x94573)))
% 28.73/28.53 [9506]E(f319(x95061,x95062),f319(x95061,x95063))+P1(f319(f319(f227(a925),f319(x95061,x95062)),f319(x95061,x95063)))+~P1(f319(f319(f321(f931(x95064,x95064)),f319(f319(f244(x95064,x95064),x95062),x95063)),f145(x95064,f319(f319(f143(f932(x95064,a925)),x95061),x95065))))
% 28.73/28.53 [9540]~E(f319(x95404,x95402),f319(x95404,x95403))+~P1(f319(f319(f321(f931(x95401,x95401)),f319(f319(f244(x95401,x95401),x95402),x95403)),f145(x95401,x95405)))+P1(f319(f319(f321(f931(x95401,x95401)),f319(f319(f244(x95401,x95401),x95402),x95403)),f145(x95401,f319(f319(f143(f932(x95401,a925)),x95404),x95405))))
% 28.73/28.53 [9561]~P26(x95611,x95612,x95613,x95615)+P26(x95611,x95612,x95613,f319(f319(f301(x95611),x95614),x95615))+P1(f319(f319(f321(x95612),f319(x95613,x95614)),f319(f302(x95611,x95612,x95613),f319(f319(f23(f932(x95611,a923)),x95615),f319(f319(f301(x95611),x95614),f180(f932(x95611,a923)))))))
% 28.73/28.53 [9564]P1(f319(x95642,x95645))+~P1(f319(f319(f321(x95641),x95645),f319(f164(x95641),x95643)))+E(f319(f319(f130(x95641),f319(f181(f926(x95641)),f169(x95641,x95642,f319(f319(f126(x95641),x95643),x95644)))),f319(f319(f126(x95641),x95643),x95644)),f319(f319(f126(x95641),f319(f319(f130(x95641),f319(f181(f926(x95641)),f169(x95641,x95642,x95643))),x95643)),x95644))
% 28.73/28.53 [9569]~P1(f319(f319(f321(f931(x95691,x95691)),f319(f319(f244(x95691,x95691),x95692),x95693)),f145(x95691,x95695)))+~P1(f319(f319(f226(a925),f319(x95694,x95692)),f319(x95694,x95693)))+P1(f319(f319(f321(f931(x95691,x95691)),f319(f319(f244(x95691,x95691),x95692),x95693)),f145(x95691,f319(f319(f143(f932(x95691,a925)),x95694),x95695))))
% 28.73/28.53 [9636]P1(f319(f319(f321(f931(x96364,x96364)),f319(f319(f244(x96364,x96364),x96362),x96363)),f145(x96364,x96365)))+P1(f319(f319(f227(a925),f319(x96361,x96362)),f319(x96361,x96363)))+~P1(f319(f319(f321(f931(x96364,x96364)),f319(f319(f244(x96364,x96364),x96362),x96363)),f145(x96364,f319(f319(f143(f932(x96364,a925)),x96361),x96365))))
% 28.73/28.53 [9783]~P1(f319(f319(f321(f931(f926(x97831),f926(x97831))),f319(f319(f244(f926(x97831),f926(x97831)),x97832),x97834)),f150(x97831,x97835)))+~P1(f319(f319(f227(a925),x97833),f319(f181(f926(x97831)),x97832)))+P1(f319(f319(f321(f931(x97831,x97831)),f319(f319(f244(x97831,x97831),f319(f319(f156(x97831),x97832),x97833)),f319(f319(f156(x97831),x97834),x97833))),x97835))
% 28.73/28.53 [10042]E(x100421,f2(a1))+~P1(f319(f43(x100423,x100421),f319(f319(f244(a1,a1),x100424),x100425)))+P1(f319(f43(f319(f319(f75(a1),x100422),x100423),x100421),f319(f319(f244(a1,a1),f319(f319(f74(a1),f319(f319(f75(a1),x100422),x100424)),f319(f319(f30(a1),f319(f319(f75(a1),x100422),x100425)),x100421))),f39(a1,f319(f319(f75(a1),x100422),x100425),x100421))))
% 28.73/28.53 [10044]~P1(f319(f319(f227(a925),f2(a925)),x100443))+~P1(f319(f42(x100442,x100443),f319(f319(f244(a925,a925),x100444),x100445)))+P1(f319(f42(f319(f319(f75(a925),x100441),x100442),x100443),f319(f319(f244(a925,a925),f319(f319(f74(a925),f319(f319(f75(a925),x100441),x100444)),f319(f319(f30(a925),f319(f319(f75(a925),x100441),x100445)),x100443))),f39(a925,f319(f319(f75(a925),x100441),x100445),x100443))))
% 28.73/28.53 [10364]~P79(x103642)+~P1(f319(f55(x103641),x103644))+E(f319(f319(f6(x103641,x103642),x103643),f319(f254(x103641),f319(f319(f18(x103641,a923,a923),f319(f319(f8(a923,f932(a923,a923),x103641),a317),f319(f319(f7(x103641,f932(x103641,a923),a923),f321(x103641)),x103644))),f319(f319(f7(x103641,f932(x103641,a923),a923),f321(x103641)),x103645)))),f319(f319(f6(x103641,x103642),f319(f319(f7(x103641,x103642,x103642),f319(f319(f18(x103641,x103642,f932(x103642,x103642)),f319(f319(f8(a923,f932(x103642,f932(x103642,x103642)),x103641),f86(x103642)),f319(f319(f7(x103641,f932(x103641,a923),a923),f321(x103641)),x103645))),x103643)),f2(x103642))),x103644))
% 28.73/28.53 [8487]~E(f319(f319(f126(x84871),x84872),x84875),f319(f319(f126(x84871),x84873),x84874))+E(f319(f319(f126(x84871),f319(f319(f130(x84871),f319(f181(f926(x84871)),x84872)),x84873)),x84874),x84875)+P1(f319(f319(f226(a925),f319(f181(f926(x84871)),x84873)),f319(f181(f926(x84871)),x84872)))
% 28.73/28.53 [8687]~E(f319(f319(f126(x86872),x86873),x86871),f319(f319(f126(x86872),x86874),x86875))+E(x86871,f319(f319(f126(x86872),f319(f319(f130(x86872),f319(f181(f926(x86872)),x86873)),x86874)),x86875))+~P1(f319(f319(f226(a925),f319(f181(f926(x86872)),x86873)),f319(f181(f926(x86872)),x86874)))
% 28.73/28.53 [8777]~E(f319(f319(f74(a925),f319(f319(f75(a925),x87773),x87774)),x87771),f319(f319(f74(a925),f319(f319(f75(a925),x87772),x87774)),x87775))+~P1(f319(f319(f226(a925),x87773),x87772))+E(x87771,f319(f319(f74(a925),f319(f319(f75(a925),f319(f319(f23(a925),x87772),x87773)),x87774)),x87775))
% 28.73/28.53 [8778]~E(f319(f319(f74(a925),f319(f319(f75(a925),x87781),x87783)),x87784),f319(f319(f74(a925),f319(f319(f75(a925),x87782),x87783)),x87785))+~P1(f319(f319(f226(a925),x87782),x87781))+E(f319(f319(f74(a925),f319(f319(f75(a925),f319(f319(f23(a925),x87781),x87782)),x87783)),x87784),x87785)
% 28.73/28.53 [8947]E(f319(f319(f74(a925),f319(f319(f75(a925),x89471),x89472)),x89473),f319(f319(f74(a925),f319(f319(f75(a925),x89474),x89472)),x89475))+~P1(f319(f319(f226(a925),x89474),x89471))+~E(x89475,f319(f319(f74(a925),f319(f319(f75(a925),f319(f319(f23(a925),x89471),x89474)),x89472)),x89473))
% 28.73/28.53 [8948]E(f319(f319(f74(a925),f319(f319(f75(a925),x89481),x89482)),x89483),f319(f319(f74(a925),f319(f319(f75(a925),x89484),x89482)),x89485))+~P1(f319(f319(f226(a925),x89484),x89481))+~E(f319(f319(f74(a925),f319(f319(f75(a925),f319(f319(f23(a925),x89481),x89484)),x89482)),x89483),x89485)
% 28.73/28.53 [9835]~P79(x98352)+~P1(f319(f55(x98351),x98355))+E(f319(f319(f6(x98351,x98352),f319(f319(f18(x98351,x98352,x98352),f319(f319(f8(x98352,f932(x98352,x98352),x98351),f74(x98352)),x98353)),x98354)),x98355),f319(f319(f74(x98352),f319(f319(f6(x98351,x98352),x98353),x98355)),f319(f319(f6(x98351,x98352),x98354),x98355)))
% 28.73/28.53 [9836]~P78(x98362)+~P1(f319(f55(x98361),x98365))+E(f319(f319(f9(x98361,x98362),f319(f319(f18(x98361,x98362,x98362),f319(f319(f8(x98362,f932(x98362,x98362),x98361),f75(x98362)),x98363)),x98364)),x98365),f319(f319(f75(x98362),f319(f319(f9(x98361,x98362),x98363),x98365)),f319(f319(f9(x98361,x98362),x98364),x98365)))
% 28.73/28.53 [9837]~P72(x98372)+~P1(f319(f55(x98371),x98375))+E(f319(f319(f9(x98371,x98372),f319(f319(f18(x98371,x98372,x98372),f319(f319(f8(x98372,f932(x98372,x98372),x98371),f283(x98372)),x98373)),x98374)),x98375),f319(f319(f283(x98372),f319(f319(f9(x98371,x98372),x98373),x98375)),f319(f319(f9(x98371,x98372),x98374),x98375)))
% 28.73/28.53 [9978]~E(f641(x99785,x99784,x99783,x99782,x99781),f642(x99785,x99784,x99783,x99782,x99781))+P1(f319(f319(f321(f931(x99781,x99781)),f319(f319(f244(x99781,x99781),x99782),x99783)),f299(x99781,x99784)))+~P1(f319(f319(f321(f931(x99781,x99781)),f319(f319(f244(x99781,x99781),x99782),x99783)),f299(x99781,f319(f319(f102(f932(f931(x99781,x99781),a923)),x99784),x99785))))
% 28.73/28.53 [9979]~E(f643(x99795,x99794,x99793,x99792,x99791),f644(x99795,x99794,x99793,x99792,x99791))+P1(f319(f319(f321(f931(x99791,x99791)),f319(f319(f244(x99791,x99791),x99792),x99793)),f299(x99791,x99794)))+~P1(f319(f319(f321(f931(x99791,x99791)),f319(f319(f244(x99791,x99791),x99792),x99793)),f299(x99791,f319(f319(f102(f932(f931(x99791,x99791),a923)),x99794),x99795))))
% 28.73/28.53 [10181]P1(f319(f319(f321(f931(x101811,x101811)),f319(f319(f244(x101811,x101811),x101812),f644(x101815,x101814,x101813,x101812,x101811))),f299(x101811,x101814)))+P1(f319(f319(f321(f931(x101811,x101811)),f319(f319(f244(x101811,x101811),x101812),x101813)),f299(x101811,x101814)))+~P1(f319(f319(f321(f931(x101811,x101811)),f319(f319(f244(x101811,x101811),x101812),x101813)),f299(x101811,f319(f319(f102(f932(f931(x101811,x101811),a923)),x101814),x101815))))
% 28.73/28.53 [10273]P1(f319(f319(f321(f931(x102731,x102731)),f319(f319(f244(x102731,x102731),f642(x102735,x102734,x102733,x102732,x102731)),x102733)),f299(x102731,x102734)))+P1(f319(f319(f321(f931(x102731,x102731)),f319(f319(f244(x102731,x102731),x102732),x102733)),f299(x102731,x102734)))+~P1(f319(f319(f321(f931(x102731,x102731)),f319(f319(f244(x102731,x102731),x102732),x102733)),f299(x102731,f319(f319(f102(f932(f931(x102731,x102731),a923)),x102734),x102735))))
% 28.73/28.53 [10313]P1(f319(f319(f321(f931(x103131,x103131)),f319(f319(f244(x103131,x103131),x103132),x103133)),f299(x103131,x103134)))+P1(f319(f319(f321(f931(x103131,x103131)),f319(f319(f244(x103131,x103131),f641(x103135,x103134,x103133,x103132,x103131)),f642(x103135,x103134,x103133,x103132,x103131))),x103135))+~P1(f319(f319(f321(f931(x103131,x103131)),f319(f319(f244(x103131,x103131),x103132),x103133)),f299(x103131,f319(f319(f102(f932(f931(x103131,x103131),a923)),x103134),x103135))))
% 28.73/28.53 [10314]P1(f319(f319(f321(f931(x103141,x103141)),f319(f319(f244(x103141,x103141),x103142),x103143)),f299(x103141,x103144)))+P1(f319(f319(f321(f931(x103141,x103141)),f319(f319(f244(x103141,x103141),f644(x103145,x103144,x103143,x103142,x103141)),f643(x103145,x103144,x103143,x103142,x103141))),x103145))+~P1(f319(f319(f321(f931(x103141,x103141)),f319(f319(f244(x103141,x103141),x103142),x103143)),f299(x103141,f319(f319(f102(f932(f931(x103141,x103141),a923)),x103144),x103145))))
% 28.73/28.53 [10459]~P1(f319(f319(f321(f931(f926(x104591),f926(x104591))),f319(f319(f244(f926(x104591),f926(x104591)),x104594),x104595)),f150(x104591,x104592)))+~P1(f319(f319(f321(f931(x104591,x104591)),x104593),f319(f164(f931(x104591,x104591)),f319(f319(f173(x104591,x104591),x104594),x104595))))+P1(f319(f319(f249(x104591,x104591,a923),f319(f319(f7(x104591,f932(f931(x104591,x104591),a923),f932(x104591,a923)),f319(f319(f8(f932(x104591,f932(f932(f931(x104591,x104591),a923),a923)),f932(f932(f931(x104591,x104591),a923),f932(x104591,a923)),x104591),f7(x104591,f932(f931(x104591,x104591),a923),a923)),f319(f319(f8(f932(x104591,f931(x104591,x104591)),f932(x104591,f932(f932(f931(x104591,x104591),a923),a923)),x104591),f319(f8(f931(x104591,x104591),f932(f932(f931(x104591,x104591),a923),a923),x104591),f321(f931(x104591,x104591)))),f244(x104591,x104591)))),x104592)),x104593))
% 28.73/28.53 [9867]~P1(f319(f319(f226(a925),x98673),x98672))+~P1(f319(f319(f226(a925),f319(f319(f74(a925),f319(f319(f75(a925),x98673),x98674)),x98671)),f319(f319(f74(a925),f319(f319(f75(a925),x98672),x98674)),x98675)))+P1(f319(f319(f226(a925),x98671),f319(f319(f74(a925),f319(f319(f75(a925),f319(f319(f23(a925),x98672),x98673)),x98674)),x98675)))
% 28.73/28.53 [9868]~P1(f319(f319(f226(a925),x98683),x98682))+~P1(f319(f319(f227(a925),f319(f319(f74(a925),f319(f319(f75(a925),x98683),x98684)),x98681)),f319(f319(f74(a925),f319(f319(f75(a925),x98682),x98684)),x98685)))+P1(f319(f319(f227(a925),x98681),f319(f319(f74(a925),f319(f319(f75(a925),f319(f319(f23(a925),x98682),x98683)),x98684)),x98685)))
% 28.73/28.53 [9885]~P1(f319(f319(f226(a925),x98851),x98854))+P1(f319(f319(f226(a925),f319(f319(f74(a925),f319(f319(f75(a925),x98851),x98852)),x98853)),f319(f319(f74(a925),f319(f319(f75(a925),x98854),x98852)),x98855)))+~P1(f319(f319(f226(a925),x98853),f319(f319(f74(a925),f319(f319(f75(a925),f319(f319(f23(a925),x98854),x98851)),x98852)),x98855)))
% 28.73/28.53 [9886]~P1(f319(f319(f226(a925),x98861),x98864))+P1(f319(f319(f227(a925),f319(f319(f74(a925),f319(f319(f75(a925),x98861),x98862)),x98863)),f319(f319(f74(a925),f319(f319(f75(a925),x98864),x98862)),x98865)))+~P1(f319(f319(f227(a925),x98863),f319(f319(f74(a925),f319(f319(f75(a925),f319(f319(f23(a925),x98864),x98861)),x98862)),x98865)))
% 28.73/28.53 [10016]~P1(f319(f319(f226(a925),x100162),x100161))+~P1(f319(f319(f226(a925),f319(f319(f74(a925),f319(f319(f75(a925),x100161),x100163)),x100164)),f319(f319(f74(a925),f319(f319(f75(a925),x100162),x100163)),x100165)))+P1(f319(f319(f226(a925),f319(f319(f74(a925),f319(f319(f75(a925),f319(f319(f23(a925),x100161),x100162)),x100163)),x100164)),x100165))
% 28.73/28.53 [10017]~P1(f319(f319(f226(a925),x100172),x100171))+~P1(f319(f319(f227(a925),f319(f319(f74(a925),f319(f319(f75(a925),x100171),x100173)),x100174)),f319(f319(f74(a925),f319(f319(f75(a925),x100172),x100173)),x100175)))+P1(f319(f319(f227(a925),f319(f319(f74(a925),f319(f319(f75(a925),f319(f319(f23(a925),x100171),x100172)),x100173)),x100174)),x100175))
% 28.73/28.53 [10063]~P1(f319(f319(f226(a925),x100634),x100631))+P1(f319(f319(f226(a925),f319(f319(f74(a925),f319(f319(f75(a925),x100631),x100632)),x100633)),f319(f319(f74(a925),f319(f319(f75(a925),x100634),x100632)),x100635)))+~P1(f319(f319(f226(a925),f319(f319(f74(a925),f319(f319(f75(a925),f319(f319(f23(a925),x100631),x100634)),x100632)),x100633)),x100635))
% 28.73/28.53 [10064]~P1(f319(f319(f226(a925),x100644),x100641))+P1(f319(f319(f227(a925),f319(f319(f74(a925),f319(f319(f75(a925),x100641),x100642)),x100643)),f319(f319(f74(a925),f319(f319(f75(a925),x100644),x100642)),x100645)))+~P1(f319(f319(f227(a925),f319(f319(f74(a925),f319(f319(f75(a925),f319(f319(f23(a925),x100641),x100644)),x100642)),x100643)),x100645))
% 28.73/28.53 [10301]~P12(x103011,x103012,x103015,x103013)+~P1(f319(f319(f321(f931(x103011,x103011)),x103014),x103015))+P1(f319(f319(f249(x103011,x103011,a923),f319(f319(f7(x103011,f932(x103011,x103012),f932(x103011,a923)),f319(f319(f8(f932(x103012,a923),f932(f932(x103011,x103012),f932(x103011,a923)),x103011),f8(x103012,a923,x103011)),f319(f319(f8(x103012,f932(x103012,a923),x103011),a316),x103013))),x103013)),x103014))
% 28.73/28.53 [10322]~P113(x103221)+~P41(x103221,f932(x103222,a923),x103223)+P41(x103221,f932(x103222,a923),f319(f319(f7(x103221,f932(x103222,a923),f932(x103222,a923)),f319(f319(f8(f932(x103222,a923),f932(f932(x103222,a923),f932(x103222,a923)),x103221),f102(f932(x103222,a923))),f319(f319(f7(x103221,f932(x103222,a923),f932(x103222,a923)),f319(f319(f8(f932(x103222,a923),f932(f932(x103222,a923),f932(x103222,a923)),x103221),f102(f932(x103222,a923))),x103223)),x103224))),x103225))
% 28.73/28.53 [8649]~P21(x86496,x86491,x86492,x86494)+E(f319(f66(x86491,x86491,x86491,f319(x86492,x86493)),f319(x86494,x86495)),f319(f66(x86491,x86491,x86491,f319(x86494,x86495)),f319(x86492,x86493)))+~P1(f319(f55(x86496),x86495))
% 28.73/28.53 [9091]~P26(x90911,x90913,x90915,x90916)+~P26(x90913,x90912,x90914,f319(f302(x90911,x90913,x90915),x90916))+P26(x90911,x90912,f319(f66(x90913,x90912,x90911,x90914),x90915),x90916)
% 28.73/28.53 [9092]~P26(x90921,x90923,x90925,x90926)+~P26(x90923,x90922,x90924,f319(f302(x90921,x90923,x90925),x90926))+P26(x90921,x90922,f319(f66(x90923,x90922,x90921,x90924),x90925),x90926)
% 28.73/28.53 [9276]~P26(x92764,x92761,x92765,x92766)+~P26(x92764,x92762,f319(f66(x92761,x92762,x92764,x92763),x92765),x92766)+P26(x92761,x92762,x92763,f319(f302(x92764,x92761,x92765),x92766))
% 28.73/28.53 [9669]~P1(f319(f319(x96693,x96692),x96696))+~P1(f319(f319(x96694,x96695),x96692))+P1(f319(f319(f321(x96691),x96692),f292(x96691,x96693,x96694,x96695,x96696)))
% 28.73/28.53 [9670]~P1(f319(f319(x96704,x96702),x96706))+~P1(f319(f319(x96703,x96705),x96702))+P1(f319(f319(f321(x96701),x96702),f289(x96701,x96703,x96704,x96705,x96706)))
% 28.73/28.53 [9784]E(x97841,x97842)+E(x97843,x97844)+~P1(f319(f319(f321(f931(f926(x97845),f926(x97845))),f319(f319(f244(f926(x97845),f926(x97845)),f319(f319(f143(x97845),x97843),x97841)),f319(f319(f143(x97845),x97844),x97842))),f149(x97845,x97846)))
% 28.73/28.53 [9793]~E(x97932,x97934)+P1(f319(f319(f321(f931(f926(x97931),f926(x97931))),f319(f319(f244(f926(x97931),f926(x97931)),f319(f319(f143(x97931),x97932),x97933)),f319(f319(f143(x97931),x97934),x97935))),f137(x97931,x97936)))+~P1(f319(f319(f321(f931(f926(x97931),f926(x97931))),f319(f319(f244(f926(x97931),f926(x97931)),x97933),x97935)),f137(x97931,x97936)))
% 28.73/28.53 [9794]~E(x97942,x97944)+P1(f319(f319(f321(f931(f926(x97941),f926(x97941))),f319(f319(f244(f926(x97941),f926(x97941)),f319(f319(f143(x97941),x97942),x97943)),f319(f319(f143(x97941),x97944),x97945))),f139(x97941,x97946)))+~P1(f319(f319(f321(f931(f926(x97941),f926(x97941))),f319(f319(f244(f926(x97941),f926(x97941)),x97943),x97945)),f139(x97941,x97946)))
% 28.73/28.53 [9795]~E(x97952,x97954)+P1(f319(f319(f321(f931(f926(x97951),f926(x97951))),f319(f319(f244(f926(x97951),f926(x97951)),f319(f319(f143(x97951),x97952),x97953)),f319(f319(f143(x97951),x97954),x97955))),f149(x97951,x97956)))+~P1(f319(f319(f321(f931(f926(x97951),f926(x97951))),f319(f319(f244(f926(x97951),f926(x97951)),x97953),x97955)),f149(x97951,x97956)))
% 28.73/28.53 [9796]~E(x97962,x97964)+P1(f319(f319(f321(f931(f926(x97961),f926(x97961))),f319(f319(f244(f926(x97961),f926(x97961)),f319(f319(f126(x97961),x97962),x97963)),f319(f319(f126(x97961),x97964),x97965))),f149(x97961,x97966)))+~P1(f319(f319(f321(f931(f926(x97961),f926(x97961))),f319(f319(f244(f926(x97961),f926(x97961)),x97963),x97965)),f149(x97961,x97966)))
% 28.73/28.53 [9797]~E(x97973,x97975)+P1(f319(f319(f321(f931(f926(x97971),f926(x97971))),f319(f319(f244(f926(x97971),f926(x97971)),f319(f319(f126(x97971),x97972),x97973)),f319(f319(f126(x97971),x97974),x97975))),f149(x97971,x97976)))+~P1(f319(f319(f321(f931(f926(x97971),f926(x97971))),f319(f319(f244(f926(x97971),f926(x97971)),x97972),x97974)),f149(x97971,x97976)))
% 28.73/28.53 [9855]E(x98551,x98552)+P1(f319(f319(f321(f931(f926(x98553),f926(x98553))),f319(f319(f244(f926(x98553),f926(x98553)),x98551),x98552)),f149(x98553,x98554)))+~P1(f319(f319(f321(f931(f926(x98553),f926(x98553))),f319(f319(f244(f926(x98553),f926(x98553)),f319(f319(f143(x98553),x98555),x98551)),f319(f319(f143(x98553),x98556),x98552))),f149(x98553,x98554)))
% 28.73/28.53 [10020]~E(x100203,x100205)+P1(f319(f319(f321(f931(f926(x100201),f926(x100201))),f319(f319(f244(f926(x100201),f926(x100201)),f319(f319(f126(x100201),x100202),f319(f319(f143(x100201),x100203),f105(x100201)))),f319(f319(f126(x100201),x100204),f319(f319(f143(x100201),x100205),f105(x100201))))),f149(x100201,x100206)))+~P1(f319(f319(f321(f931(f926(x100201),f926(x100201))),f319(f319(f244(f926(x100201),f926(x100201)),x100202),x100204)),f149(x100201,x100206)))
% 28.73/28.53 [10067]E(x100671,x100672)+E(x100673,x100674)+~P1(f319(f319(f321(f931(f926(x100675),f926(x100675))),f319(f319(f244(f926(x100675),f926(x100675)),f319(f319(f126(x100675),x100673),f319(f319(f143(x100675),x100671),f105(x100675)))),f319(f319(f126(x100675),x100674),f319(f319(f143(x100675),x100672),f105(x100675))))),f149(x100675,x100676)))
% 28.73/28.53 [10096]E(x100961,x100962)+~P1(f319(f319(f321(f931(f926(x100963),f926(x100963))),f319(f319(f244(f926(x100963),f926(x100963)),f319(f319(f126(x100963),x100961),f319(f319(f143(x100963),x100965),f105(x100963)))),f319(f319(f126(x100963),x100962),f319(f319(f143(x100963),x100966),f105(x100963))))),f149(x100963,x100964)))+P1(f319(f319(f321(f931(f926(x100963),f926(x100963))),f319(f319(f244(f926(x100963),f926(x100963)),x100961),x100962)),f149(x100963,x100964)))
% 28.73/28.53 [10134]~P1(f319(f319(f321(f931(f932(x101341,a923),f932(x101341,a923))),f319(f319(f244(f932(x101341,a923),f932(x101341,a923)),x101342),x101344)),f311(x101341,x101346)))+~P1(f319(f319(f321(f931(f932(x101341,a923),f932(x101341,a923))),f319(f319(f244(f932(x101341,a923),f932(x101341,a923)),x101343),x101345)),f311(x101341,x101346)))+P1(f319(f319(f321(f931(f932(x101341,a923),f932(x101341,a923))),f319(f319(f244(f932(x101341,a923),f932(x101341,a923)),f319(f319(f102(f932(x101341,a923)),x101342),x101343)),f319(f319(f102(f932(x101341,a923)),x101344),x101345))),f311(x101341,x101346)))
% 28.73/28.53 [5874]~E(f319(f319(f126(x58741),x58746),x58743),x58745)+E(f319(f319(f126(x58741),x58742),x58743),f319(f319(f143(x58741),x58744),x58745))+~E(x58742,f319(f319(f143(x58741),x58744),x58746))
% 28.73/28.53 [5875]~E(f319(f319(f126(x58751),x58756),x58753),x58755)+E(f319(f319(f126(x58751),x58752),x58753),f319(f319(f126(x58751),x58754),x58755))+~E(x58752,f319(f319(f126(x58751),x58754),x58756))
% 28.73/28.53 [5876]E(f319(f319(f126(x58761),x58762),x58763),f319(f319(f143(x58761),x58764),x58765))+~E(f319(f319(f143(x58761),x58764),x58766),x58762)+~E(x58765,f319(f319(f126(x58761),x58766),x58763))
% 28.73/28.53 [5877]E(f319(f319(f126(x58771),x58772),x58773),f319(f319(f143(x58771),x58774),x58775))+~E(f319(f319(f143(x58771),x58774),x58776),x58772)+~E(x58775,f319(f319(f126(x58771),x58776),x58773))
% 28.73/28.53 [5878]~E(f319(f319(f126(x58781),x58782),x58786),x58784)+E(f319(f319(f126(x58781),x58782),x58783),f319(f319(f126(x58781),x58784),x58785))+~E(x58783,f319(f319(f126(x58781),x58786),x58785))
% 28.73/28.53 [5879]~E(f319(f319(f126(x58791),x58792),x58796),x58794)+E(f319(f319(f126(x58791),x58792),x58793),f319(f319(f126(x58791),x58794),x58795))+~E(x58793,f319(f319(f126(x58791),x58796),x58795))
% 28.73/28.53 [7031]E(f319(x70311,x70312),f319(x70313,x70312))+~E(f319(f319(f146(x70314,x70315),x70311),x70316),f319(f319(f146(x70314,x70315),x70313),x70316))+~P1(f319(f319(f321(x70314),x70312),f319(f164(x70314),x70316)))
% 28.73/28.53 [7418]~P21(x74184,x74185,x74186,x74181)+E(f319(f319(x74181,x74182),x74183),f319(f319(f58(x74184,x74185,x74186),x74183),x74182))+~P1(f319(f55(x74184),x74182))
% 28.73/28.53 [7488]~E(x74882,f319(x74884,x74886))+~P1(f319(f319(f321(x74883),x74886),x74885))+P1(f319(f319(f321(x74881),x74882),f319(f302(x74883,x74881,x74884),x74885)))
% 28.73/28.53 [7489]~E(x74892,f319(x74894,x74896))+~P1(f319(f319(f321(x74893),x74896),x74895))+P1(f319(f319(f321(x74891),x74892),f319(f302(x74893,x74891,x74894),x74895)))
% 28.73/28.53 [7490]~E(x74902,f319(x74904,x74906))+~P1(f319(f319(f321(x74903),x74906),x74905))+P1(f319(f319(f321(x74901),x74902),f319(f302(x74903,x74901,x74904),x74905)))
% 28.73/28.53 [7491]~E(f319(x74914,x74912),x74916)+~P1(f319(f319(f321(x74913),x74916),x74915))+P1(f319(f319(f321(x74911),x74912),f319(f303(x74911,x74913,x74914),x74915)))
% 28.73/28.53 [7933]~P33(x79331,x79332,x79334,x79336)+P33(x79331,x79332,f319(f319(f143(x79331),x79333),x79334),f319(f319(f143(x79331),x79335),x79336))+~P1(f319(f319(x79332,x79333),x79335))
% 28.73/28.53 [7934]~P33(x79341,x79342,x79344,x79346)+P33(x79341,x79342,f319(f319(f143(x79341),x79343),x79344),f319(f319(f143(x79341),x79345),x79346))+~P1(f319(f319(x79342,x79343),x79345))
% 28.73/28.53 [8957]~P61(x89574,x89575,x89571,x89572,x89576)+E(f319(x89571,f319(x89572,x89573)),x89573)+~P1(f319(f319(f321(x89575),x89573),x89576))
% 28.73/28.53 [9465]~P27(x94652,x94651,x94655,x94654,x94653)+E(f319(f85(x94651,x94652,x94653,f85(x94652,x94651,x94654,x94655)),x94656),f319(x94655,x94656))+~P1(f319(f319(f321(x94652),x94656),x94654))
% 28.73/28.53 [9476]~P26(x94761,x94762,x94763,x94766)+P26(x94761,x94762,f68(x94761,x94762,x94763,x94764,x94765),x94766)+P1(f319(f319(f321(x94762),x94765),f319(f302(x94761,x94762,x94763),x94766)))
% 28.73/28.53 [9786]E(x97861,x97862)+E(f319(f181(f926(x97863)),x97864),f319(f181(f926(x97863)),x97865))+~P1(f319(f319(f321(f931(f926(x97863),f926(x97863))),f319(f319(f244(f926(x97863),f926(x97863)),f319(f319(f143(x97863),x97861),x97864)),f319(f319(f143(x97863),x97862),x97865))),f137(x97863,x97866)))
% 28.73/28.53 [9849]~P18(x98491,x98492,x98493)+E(f319(f319(f58(x98491,x98492,x98493),x98494),x98495),x98496)+~P1(f319(f60(x98491,x98492,x98493,x98494,x98495),x98496))
% 28.73/28.53 [9858]E(f319(f181(f926(x98581)),x98582),f319(f181(f926(x98581)),x98583))+P1(f319(f319(f321(f931(f926(x98581),f926(x98581))),f319(f319(f244(f926(x98581),f926(x98581)),x98582),x98583)),f137(x98581,x98584)))+~P1(f319(f319(f321(f931(f926(x98581),f926(x98581))),f319(f319(f244(f926(x98581),f926(x98581)),f319(f319(f143(x98581),x98585),x98582)),f319(f319(f143(x98581),x98586),x98583))),f137(x98581,x98584)))
% 28.73/28.53 [9879]~P1(f319(f319(f321(f931(x98791,x98791)),f319(f319(f244(x98791,x98791),x98792),x98794)),f299(x98791,x98796)))+P1(f319(f319(f321(f931(f926(x98791),f926(x98791))),f319(f319(f244(f926(x98791),f926(x98791)),f319(f319(f143(x98791),x98792),x98793)),f319(f319(f143(x98791),x98794),x98795))),f299(f926(x98791),f149(x98791,x98796))))+~P1(f319(f319(f321(f931(f926(x98791),f926(x98791))),f319(f319(f244(f926(x98791),f926(x98791)),x98793),x98795)),f299(f926(x98791),f149(x98791,x98796))))
% 28.73/28.53 [10073]~P1(f319(x100732,x100736))+~E(f319(f128(x100731,x100732),x100733),f319(f319(f143(x100731),x100734),x100735))+~P1(f319(f319(f321(x100731),x100736),f319(f164(x100731),f767(x100735,x100734,x100733,x100732,x100731))))
% 28.73/28.53 [10074]~P1(f319(x100744,x100746))+~E(f319(f319(f143(x100741),x100742),x100743),f319(f128(x100741,x100744),x100745))+~P1(f319(f319(f321(x100741),x100746),f319(f164(x100741),f765(x100745,x100744,x100743,x100742,x100741))))
% 28.73/28.53 [10398]~P79(x103982)+E(f319(f319(f6(x103981,x103982),f319(f319(f8(f932(x103983,a923),x103982,x103981),f319(f6(x103983,x103982),x103984)),f319(f319(f8(f932(x103983,a923),f932(x103983,a923),x103981),f254(x103983)),f319(f319(f8(f932(x103983,a923),f932(x103983,a923),x103981),f319(f18(x103983,a923,a923),f319(f319(f8(a923,f932(a923,a923),x103983),a317),f319(f319(f7(x103983,f932(x103983,a923),a923),f321(x103983)),x103985)))),f319(f7(x103983,x103981,a923),f319(f319(f8(x103981,f932(x103981,a923),x103983),a316),x103986)))))),f319(f302(x103983,x103981,x103986),x103985)),f319(f319(f6(x103983,x103982),x103984),x103985))+~P1(f319(f55(x103983),x103985))
% 28.73/28.53 [7091]~P4(x70913)+P1(f319(x70912,x70915))+E(f319(f128(x70911,x70912),f319(f319(f140(x70911,x70913,x70914),x70915),x70916)),f319(f128(x70911,x70912),x70916))
% 28.73/28.53 [7093]P1(f319(x70931,x70932))+~E(f158(x70933,x70931,x70934),f319(f319(f244(f926(x70933),f926(x70933)),x70935),x70936))+~P1(f319(f319(f321(x70933),x70932),f319(f164(x70933),x70935)))
% 28.73/28.53 [7137]~P1(f319(x71372,x71376))+~E(f158(x71371,x71372,x71373),f319(f319(f244(f926(x71371),f926(x71371)),x71374),x71375))+~P1(f319(f319(f321(x71371),x71376),f319(f164(x71371),x71375)))
% 28.73/28.53 [7797]~P16(x77971,x77972,x77973)+~P1(f319(f55(x77971),x77976))+E(f319(f319(f58(x77971,x77972,x77973),x77974),f319(f319(f301(x77971),x77975),x77976)),f319(f319(f58(x77971,x77972,x77973),f319(f319(x77973,x77975),x77974)),x77976))
% 28.73/28.53 [7850]~P4(x78502)+~P1(f319(f319(f226(x78502),f319(x78503,x78504)),f319(x78503,x78505)))+E(f319(f319(f140(x78501,x78502,x78503),x78504),f319(f319(f143(x78501),x78505),x78506)),f319(f319(f143(x78501),x78504),f319(f319(f143(x78501),x78505),x78506)))
% 28.73/28.53 [7962]E(x79621,x79622)+~E(f319(f319(f246(x79623,x79624),x79621),f319(f16(f932(x79624,a923),x79623),x79625)),f319(f319(f246(x79623,x79624),x79622),f319(f16(f932(x79624,a923),x79623),x79625)))+~P1(f319(f319(f321(x79624),x79626),x79625))
% 28.73/28.53 [8027]~P16(x80271,x80272,x80273)+~P1(f319(f55(x80271),x80276))+E(f319(f319(f58(x80271,x80272,x80273),x80274),f319(f319(f301(x80271),x80275),x80276)),f319(f319(x80273,x80275),f319(f319(f58(x80271,x80272,x80273),x80274),x80276)))
% 28.73/28.53 [8147]~P18(x81471,x81472,x81473)+~P1(f319(f55(x81471),x81476))+E(f319(f319(f58(x81471,x81472,x81473),f319(f319(x81473,x81474),x81475)),x81476),f319(f319(x81473,x81474),f319(f319(f58(x81471,x81472,x81473),x81475),x81476)))
% 28.73/28.53 [8218]~P22(x82182,x82185,x82186,x82181)+~P1(f319(f55(x82182),x82184))+E(f319(x82181,f319(f319(f301(x82182),x82183),x82184)),f319(f66(x82185,x82185,x82185,f319(x82181,x82184)),f319(x82186,x82183)))
% 28.73/28.53 [8250]~P4(x82502)+P1(f319(f319(f226(x82502),f319(x82503,x82504)),f319(x82503,x82505)))+E(f319(f319(f140(x82501,x82502,x82503),x82504),f319(f319(f143(x82501),x82505),x82506)),f319(f319(f143(x82501),x82505),f319(f319(f140(x82501,x82502,x82503),x82504),x82506)))
% 28.73/28.53 [8393]~E(f319(f181(f926(x83931)),x83935),f319(f181(f926(x83932)),x83936))+~E(f319(f181(f926(x83931)),x83933),f319(f181(f926(x83932)),x83934))+E(f319(f319(f126(f931(x83931,x83932)),f319(f319(f173(x83931,x83932),x83933),x83934)),f319(f319(f173(x83931,x83932),x83935),x83936)),f319(f319(f173(x83931,x83932),f319(f319(f126(x83931),x83933),x83935)),f319(f319(f126(x83932),x83934),x83936)))
% 28.73/28.53 [8505]~E(x85052,f319(f302(x85053,x85051,x85054),x85056))+P1(f319(f319(f226(f932(x85051,a923)),x85052),f319(f302(x85053,x85051,x85054),x85055)))+~P1(f319(f319(f226(f932(x85053,a923)),x85056),x85055))
% 28.73/28.53 [8608]~P4(x86085)+E(f319(x86081,x86082),f319(x86081,x86083))+E(f319(f319(f140(x86084,x86085,x86081),x86082),f319(f319(f140(x86084,x86085,x86081),x86083),x86086)),f319(f319(f140(x86084,x86085,x86081),x86083),f319(f319(f140(x86084,x86085,x86081),x86082),x86086)))
% 28.73/28.53 [8785]~P1(f319(f319(f321(x87852),x87854),f319(x87856,x87853)))+~P1(f319(f319(f321(x87851),x87853),x87855))+P1(f319(f319(f321(f931(x87851,x87852)),f319(f319(f244(x87851,x87852),x87853),x87854)),f319(f319(f246(x87851,x87852),x87855),x87856)))
% 28.73/28.53 [8786]~P1(f319(f319(f321(x87862),x87864),f319(x87866,x87863)))+~P1(f319(f319(f321(x87861),x87863),x87865))+P1(f319(f319(f321(f931(x87861,x87862)),f319(f319(f244(x87861,x87862),x87863),x87864)),f319(f319(f246(x87861,x87862),x87865),x87866)))
% 28.73/28.53 [9269]~P79(x92692)+~P26(x92694,x92691,x92695,x92696)+E(f319(f319(f6(x92691,x92692),x92693),f319(f302(x92694,x92691,x92695),x92696)),f319(f319(f6(x92694,x92692),f319(f66(x92691,x92692,x92694,x92693),x92695)),x92696))
% 28.73/28.53 [9270]~P78(x92702)+~P26(x92704,x92701,x92705,x92706)+E(f319(f319(f9(x92701,x92702),x92703),f319(f302(x92704,x92701,x92705),x92706)),f319(f319(f9(x92704,x92702),f319(f66(x92701,x92702,x92704,x92703),x92705)),x92706))
% 28.73/28.53 [9316]~P35(x93162,x93165,x93161,x93163,x93166)+P1(f319(f319(x93161,f319(f319(f156(x93162),x93163),x93164)),f319(f319(f156(x93165),x93166),x93164)))+~P1(f319(f319(f227(a925),x93164),f319(f181(f926(x93162)),x93163)))
% 28.73/28.53 [9317]~P35(x93172,x93175,x93171,x93173,x93176)+P1(f319(f319(x93171,f319(f319(f156(x93172),x93173),x93174)),f319(f319(f156(x93175),x93176),x93174)))+~P1(f319(f319(f227(a925),x93174),f319(f181(f926(x93175)),x93176)))
% 28.73/28.53 [9318]~P35(x93182,x93185,x93181,x93183,x93186)+P1(f319(f319(x93181,f319(f319(f156(x93182),x93183),x93184)),f319(f319(f156(x93185),x93186),x93184)))+~P1(f319(f319(f227(a925),x93184),f319(f181(f926(x93182)),x93183)))
% 28.73/28.53 [9329]~E(f319(f302(x93291,x93292,x93293),x93294),x93296)+E(f319(f302(x93291,x93292,x93293),f319(f302(x93292,x93291,f85(x93291,x93292,x93294,x93293)),x93295)),x93295)+~P1(f319(f319(f226(f932(x93292,a923)),x93295),x93296))
% 28.73/28.53 [9535]~P21(x95353,x95351,x95356,x95352)+~P1(f319(f55(x95353),x95354))+E(f319(f66(x95351,x95351,x95351,f319(x95352,f319(f319(f23(f932(x95353,a923)),x95354),f319(f319(f301(x95353),x95355),f180(f932(x95353,a923)))))),f319(x95356,x95355)),f319(x95352,f319(f319(f301(x95353),x95355),x95354)))
% 28.73/28.53 [9548]~P1(f319(f319(f321(x95485),x95483),x95486))+P1(f319(f319(f321(x95481),f319(x95482,x95483)),f88(f932(x95481,a923),x95484)))+~P1(f319(f319(f226(f932(x95481,a923)),f319(f302(x95485,x95481,x95482),x95486)),f319(x95484,f319(f302(x95485,x95481,x95482),x95486))))
% 28.73/28.53 [10163]~E(f319(f302(x101632,x101634,x101636),f234(f932(x101632,a923))),f234(f932(x101634,a923)))+~E(f319(f302(x101631,x101633,x101635),f234(f932(x101631,a923))),f234(f932(x101633,a923)))+E(f319(f302(f931(x101631,x101632),f931(x101633,x101634),f250(x101631,x101633,x101632,x101634,x101635,x101636)),f234(f932(f931(x101631,x101632),a923))),f234(f932(f931(x101633,x101634),a923)))
% 28.73/28.53 [10217]~E(x102173,x102175)+~E(f319(x102176,f746(x102172,x102174,x102176,x102171,x102173,x102175)),f319(x102174,f746(x102172,x102174,x102176,x102171,x102173,x102175)))+E(f319(f319(f34(x102171,f932(x102172,a923)),x102173),x102174),f319(f319(f34(x102171,f932(x102172,a923)),x102175),x102176))
% 28.73/28.53 [10222]~P26(x102223,x102224,x102225,f319(x102226,f901(x102226,x102225,x102224,x102223,x102222,x102221)))+P26(x102223,x102224,x102225,f319(f319(f34(x102222,f932(x102223,a923)),x102221),x102226))+E(x102221,f180(f932(x102222,a923)))
% 28.73/28.53 [10278]~E(x102783,x102785)+E(f319(f319(f34(x102781,f932(x102782,a923)),x102783),x102784),f319(f319(f34(x102781,f932(x102782,a923)),x102785),x102786))+P1(f319(f319(f321(x102781),f746(x102782,x102784,x102786,x102781,x102783,x102785)),x102783))
% 28.73/28.53 [10281]P26(x102816,x102815,x102814,f319(f319(f34(x102812,f932(x102816,a923)),x102811),x102813))+E(x102811,f180(f932(x102812,a923)))+P1(f319(f319(f321(x102812),f901(x102813,x102814,x102815,x102816,x102812,x102811)),x102811))
% 28.73/28.53 [10287]P1(f319(f319(f321(x102871),f609(x102872,x102873,x102874,x102875,x102876,x102871)),x102876))+P1(f319(f319(f226(f932(f931(x102871,x102874),a923)),f319(f319(f246(x102871,x102874),x102876),x102873)),f319(f319(f246(x102871,x102874),x102875),x102872)))+~P1(f319(f319(f226(f932(x102871,a923)),x102876),x102875))
% 28.73/28.53 [10412]~P1(f319(f319(f226(f932(x104122,a923)),f319(x104124,f609(x104126,x104124,x104122,x104125,x104123,x104121))),f319(x104126,f609(x104126,x104124,x104122,x104125,x104123,x104121))))+~P1(f319(f319(f226(f932(x104121,a923)),x104123),x104125))+P1(f319(f319(f226(f932(f931(x104121,x104122),a923)),f319(f319(f246(x104121,x104122),x104123),x104124)),f319(f319(f246(x104121,x104122),x104125),x104126)))
% 28.73/28.53 [7984]~P1(f319(x79841,x79845))+~P1(f319(x79846,x79844))+P1(f319(x79841,f319(f248(x79842,x79843),f319(f319(f244(x79842,x79843),x79844),x79845))))
% 28.73/28.53 [7985]~P1(f319(x79851,x79854))+~P1(f319(x79856,x79855))+P1(f319(x79851,f319(f243(x79852,x79853),f319(f319(f244(x79852,x79853),x79854),x79855))))
% 28.73/28.53 [8032]~P1(f319(f319(x80324,x80326),x80325))+~P1(f319(f319(f321(x80321),x80326),x80323))+P1(f319(f319(f319(f33(x80321,f932(x80322,a923)),x80323),x80324),x80325))
% 28.73/28.53 [8033]~P1(f319(f319(x80334,x80336),x80335))+~P1(f319(f319(f321(x80331),x80336),x80333))+P1(f319(f319(f319(f33(x80331,f932(x80332,a923)),x80333),x80334),x80335))
% 28.73/28.53 [8342]~P1(f319(f319(f321(x83421),x83422),f319(x83425,x83426)))+~P1(f319(f319(f321(x83423),x83426),x83424))+P1(f319(f319(f321(x83421),x83422),f319(f319(f33(x83423,f932(x83421,a923)),x83424),x83425)))
% 28.73/28.53 [8343]~P1(f319(f319(f321(x83431),x83432),f319(x83435,x83436)))+~P1(f319(f319(f321(x83433),x83436),x83434))+P1(f319(f319(f321(x83431),x83432),f319(f319(f33(x83433,f932(x83431,a923)),x83434),x83435)))
% 28.73/28.53 [8385]P1(f319(f319(x83851,x83852),x83853))+~P1(f319(f319(x83854,x83852),x83853))+~P1(f319(f319(f226(f932(x83855,f932(x83856,a923))),x83854),x83851))
% 28.73/28.53 [8386]P1(f319(f319(x83861,x83862),x83863))+~P1(f319(f319(x83864,x83862),x83863))+~P1(f319(f319(f226(f932(x83865,f932(x83866,a923))),x83864),x83861))
% 28.73/28.53 [8527]P1(f319(f319(x85271,x85272),x85273))+~P1(f319(f319(f321(x85274),x85272),x85275))+~P1(f319(f319(f319(f34(x85274,f932(x85276,a923)),x85275),x85271),x85273))
% 28.73/28.53 [8528]P1(f319(f319(x85281,x85282),x85283))+~P1(f319(f319(f321(x85284),x85282),x85285))+~P1(f319(f319(f319(f34(x85284,f932(x85286,a923)),x85285),x85281),x85283))
% 28.73/28.53 [8529]P1(f319(f319(x85291,x85292),x85293))+~P1(f319(f319(f321(x85294),x85292),x85295))+~P1(f319(f319(f319(f34(x85294,f932(x85296,a923)),x85295),x85291),x85293))
% 28.73/28.53 [8662]P1(f319(f319(f321(x86621),x86622),f319(x86623,x86624)))+~P1(f319(f319(f321(x86625),x86624),x86626))+~P1(f319(f319(f321(x86621),x86622),f319(f319(f34(x86625,f932(x86621,a923)),x86626),x86623)))
% 28.73/28.53 [8663]P1(f319(f319(f321(x86631),x86632),f319(x86633,x86634)))+~P1(f319(f319(f321(x86635),x86634),x86636))+~P1(f319(f319(f321(x86631),x86632),f319(f319(f34(x86635,f932(x86631,a923)),x86636),x86633)))
% 28.73/28.53 [8664]P1(f319(f319(f321(x86641),x86642),f319(x86643,x86644)))+~P1(f319(f319(f321(x86645),x86644),x86646))+~P1(f319(f319(f321(x86641),x86642),f319(f319(f34(x86645,f932(x86641,a923)),x86646),x86643)))
% 28.73/28.53 [8936]~P12(x89364,x89365,x89366,x89361)+E(f319(x89361,x89362),f319(x89361,x89363))+~P1(f319(f319(f321(f931(x89364,x89364)),f319(f319(f244(x89364,x89364),x89362),x89363)),x89366))
% 28.73/28.53 [8971]P1(f319(f319(f226(f932(x89711,a923)),x89712),f319(x89713,x89714)))+~P1(f319(f319(f321(x89715),x89714),x89716))+~P1(f319(f319(f226(f932(x89711,a923)),x89712),f319(f319(f34(x89715,f932(x89711,a923)),x89716),x89713)))
% 28.73/28.53 [9005]~P59(x90053,x90054,f319(f278(x90054,x90053),x90055))+E(x90051,f180(f932(x90052,a923)))+E(f319(f319(f34(x90052,f932(x90053,a923)),x90051),f319(f319(f8(f932(x90054,a923),f932(x90053,a923),x90052),f277(x90054,x90053,x90055)),x90056)),f319(f277(x90054,x90053,x90055),f319(f319(f34(x90052,f932(x90054,a923)),x90051),x90056)))
% 28.73/28.53 [9082]P1(f319(f319(f321(x90821),x90822),f319(f277(x90823,x90821,x90824),x90825)))+~P1(f319(f319(f321(x90823),x90826),x90825))+~P1(f319(f319(f321(f931(x90823,x90821)),f319(f319(f244(x90823,x90821),x90826),x90822)),x90824))
% 28.73/28.53 [9083]P1(f319(f319(f321(x90831),x90832),f319(f277(x90833,x90831,x90834),x90835)))+~P1(f319(f319(f321(x90833),x90836),x90835))+~P1(f319(f319(f321(f931(x90833,x90831)),f319(f319(f244(x90833,x90831),x90836),x90832)),x90834))
% 28.73/28.53 [9397]P1(f319(f319(f226(f932(x93971,a923)),f319(f277(x93972,x93971,x93973),x93974)),f319(f277(x93972,x93971,x93975),x93976)))+~P1(f319(f319(f226(f932(x93972,a923)),x93974),x93976))+~P1(f319(f319(f226(f932(f931(x93972,x93971),a923)),x93973),x93975))
% 28.73/28.53 [9585]~P1(f319(f319(f321(x95852),x95856),x95854))+~P1(f319(f319(f226(f932(x95851,a923)),x95853),x95855))+P1(f319(f319(f226(f932(f931(x95851,x95852),a923)),f319(f319(f246(x95851,x95852),x95853),f319(f16(f932(x95852,a923),x95851),x95854))),f319(f319(f246(x95851,x95852),x95855),f319(f16(f932(x95852,a923),x95851),x95854))))
% 28.73/28.53 [9597]~P35(x95971,x95972,x95973,x95975,x95976)+P1(f319(f319(f249(x95971,x95972,a923),x95973),x95974))+~P1(f319(f319(f321(f931(x95971,x95972)),x95974),f319(f164(f931(x95971,x95972)),f319(f319(f173(x95971,x95972),x95975),x95976))))
% 28.73/28.53 [9738]~E(x97383,x97385)+P1(f319(f319(f321(f931(f926(x97381),f926(x97381))),f319(f319(f244(f926(x97381),f926(x97381)),f319(f319(f143(x97381),x97382),x97383)),f319(f319(f143(x97381),x97384),x97385))),f149(x97381,x97386)))+~P1(f319(f319(f321(f931(x97381,x97381)),f319(f319(f244(x97381,x97381),x97382),x97384)),x97386))
% 28.73/28.53 [9744]~E(f319(f181(f926(x97441)),x97443),f319(f181(f926(x97441)),x97445))+P1(f319(f319(f321(f931(f926(x97441),f926(x97441))),f319(f319(f244(f926(x97441),f926(x97441)),f319(f319(f143(x97441),x97442),x97443)),f319(f319(f143(x97441),x97444),x97445))),f137(x97441,x97446)))+~P1(f319(f319(f321(f931(x97441,x97441)),f319(f319(f244(x97441,x97441),x97442),x97444)),x97446))
% 28.73/28.53 [9778]P1(f319(f319(f321(f931(x97781,x97781)),f319(f319(f244(x97781,x97781),x97782),x97783)),f319(f319(f175(f931(x97781,x97781),a923),f319(a104,x97784)),x97785)))+~P1(f319(f319(f321(f931(x97781,x97781)),f319(f319(f244(x97781,x97781),x97786),x97783)),x97785))+~P1(f319(f319(f321(f931(x97781,x97781)),f319(f319(f244(x97781,x97781),x97782),x97786)),f319(f319(f175(f931(x97781,x97781),a923),x97784),x97785)))
% 28.73/28.53 [9779]P1(f319(f319(f321(f931(x97791,x97791)),f319(f319(f244(x97791,x97791),x97792),x97793)),f319(f319(f175(f931(x97791,x97791),a923),f319(a104,x97794)),x97795)))+~P1(f319(f319(f321(f931(x97791,x97791)),f319(f319(f244(x97791,x97791),x97792),x97796)),x97795))+~P1(f319(f319(f321(f931(x97791,x97791)),f319(f319(f244(x97791,x97791),x97796),x97793)),f319(f319(f175(f931(x97791,x97791),a923),x97794),x97795)))
% 28.73/28.53 [9782]~P1(f319(f319(f321(x97824),x97825),x97826))+P1(f319(f319(f226(f932(x97821,a923)),x97822),x97823))+~P1(f319(f319(f226(f932(f931(x97821,x97824),a923)),f319(f319(f246(x97821,x97824),x97822),f319(f16(f932(x97824,a923),x97821),x97826))),f319(f319(f246(x97821,x97824),x97823),f319(f16(f932(x97824,a923),x97821),x97826))))
% 28.73/28.53 [9827]E(x98271,x98272)+~P1(f319(f319(f321(f931(f926(x98273),f926(x98273))),f319(f319(f244(f926(x98273),f926(x98273)),f319(f319(f143(x98273),x98271),x98275)),f319(f319(f143(x98273),x98272),x98276))),f137(x98273,x98274)))+P1(f319(f319(f321(f931(x98273,x98273)),f319(f319(f244(x98273,x98273),x98271),x98272)),x98274))
% 28.73/28.53 [9828]E(x98281,x98282)+~P1(f319(f319(f321(f931(f926(x98283),f926(x98283))),f319(f319(f244(f926(x98283),f926(x98283)),f319(f319(f143(x98283),x98281),x98285)),f319(f319(f143(x98283),x98282),x98286))),f139(x98283,x98284)))+P1(f319(f319(f321(f931(x98283,x98283)),f319(f319(f244(x98283,x98283),x98281),x98282)),x98284))
% 28.73/28.53 [9829]E(x98291,x98292)+~P1(f319(f319(f321(f931(f926(x98293),f926(x98293))),f319(f319(f244(f926(x98293),f926(x98293)),f319(f319(f143(x98293),x98291),x98295)),f319(f319(f143(x98293),x98292),x98296))),f149(x98293,x98294)))+P1(f319(f319(f321(f931(x98293,x98293)),f319(f319(f244(x98293,x98293),x98291),x98292)),x98294))
% 28.73/28.53 [9866]P1(f319(f319(f321(f931(f926(x98661),f926(x98661))),f319(f319(f244(f926(x98661),f926(x98661)),f319(f319(f143(x98661),x98662),x98663)),f319(f319(f143(x98661),x98664),x98665))),f150(x98661,x98666)))+~P1(f319(f319(f321(f931(f926(x98661),f926(x98661))),f319(f319(f244(f926(x98661),f926(x98661)),x98663),x98665)),f150(x98661,x98666)))+~P1(f319(f319(f321(f931(x98661,x98661)),f319(f319(f244(x98661,x98661),x98662),x98664)),x98666))
% 28.73/28.53 [9883]P1(f319(x98831,x98832))+~P1(f319(x98831,f382(x98831,x98833,x98834,x98835,x98836)))+~P1(f319(f319(f321(x98836),x98832),f319(f319(f33(x98835,f932(x98836,a923)),x98834),x98833)))
% 28.73/28.53 [9888]~P1(f319(f319(f321(f931(f926(x98881),f926(x98881))),f319(f319(f244(f926(x98881),f926(x98881)),f319(f319(f143(x98881),x98882),x98885)),f319(f319(f143(x98881),x98883),x98886))),f137(x98881,x98884)))+P1(f319(f319(f321(f931(f926(x98881),f926(x98881))),f319(f319(f244(f926(x98881),f926(x98881)),x98885),x98886)),f137(x98881,x98884)))+P1(f319(f319(f321(f931(x98881,x98881)),f319(f319(f244(x98881,x98881),x98882),x98883)),x98884))
% 28.73/28.53 [9889]~P1(f319(f319(f321(f931(f926(x98891),f926(x98891))),f319(f319(f244(f926(x98891),f926(x98891)),f319(f319(f143(x98891),x98892),x98895)),f319(f319(f143(x98891),x98893),x98896))),f139(x98891,x98894)))+P1(f319(f319(f321(f931(f926(x98891),f926(x98891))),f319(f319(f244(f926(x98891),f926(x98891)),x98895),x98896)),f139(x98891,x98894)))+P1(f319(f319(f321(f931(x98891,x98891)),f319(f319(f244(x98891,x98891),x98892),x98893)),x98894))
% 28.73/28.53 [9890]~P1(f319(f319(f321(f931(f926(x98901),f926(x98901))),f319(f319(f244(f926(x98901),f926(x98901)),f319(f319(f143(x98901),x98902),x98905)),f319(f319(f143(x98901),x98903),x98906))),f149(x98901,x98904)))+P1(f319(f319(f321(f931(f926(x98901),f926(x98901))),f319(f319(f244(f926(x98901),f926(x98901)),x98905),x98906)),f149(x98901,x98904)))+P1(f319(f319(f321(f931(x98901,x98901)),f319(f319(f244(x98901,x98901),x98902),x98903)),x98904))
% 28.73/28.53 [9990]P1(f319(x99901,x99902))+P1(f319(f319(f321(x99903),f364(x99901,x99904,x99905,x99903,x99906)),x99905))+~P1(f319(f319(f321(x99906),x99902),f319(f319(f33(x99903,f932(x99906,a923)),x99905),x99904)))
% 28.73/28.53 [10002]~E(x100022,x100024)+P1(f319(f319(f321(f931(f926(x100021),f926(x100021))),f319(f319(f244(f926(x100021),f926(x100021)),f319(f319(f126(x100021),x100022),f319(f319(f143(x100021),x100023),f105(x100021)))),f319(f319(f126(x100021),x100024),f319(f319(f143(x100021),x100025),f105(x100021))))),f149(x100021,x100026)))+~P1(f319(f319(f321(f931(x100021,x100021)),f319(f319(f244(x100021,x100021),x100023),x100025)),x100026))
% 28.73/28.53 [10083]E(x100831,x100832)+~P1(f319(f319(f321(f931(f926(x100833),f926(x100833))),f319(f319(f244(f926(x100833),f926(x100833)),f319(f319(f126(x100833),x100835),f319(f319(f143(x100833),x100831),f105(x100833)))),f319(f319(f126(x100833),x100836),f319(f319(f143(x100833),x100832),f105(x100833))))),f149(x100833,x100834)))+P1(f319(f319(f321(f931(x100833,x100833)),f319(f319(f244(x100833,x100833),x100831),x100832)),x100834))
% 28.73/28.53 [10115]~P1(f319(f319(f321(f931(f926(x101151),f926(x101151))),f319(f319(f244(f926(x101151),f926(x101151)),f319(f319(f126(x101151),x101155),f319(f319(f143(x101151),x101152),f105(x101151)))),f319(f319(f126(x101151),x101156),f319(f319(f143(x101151),x101153),f105(x101151))))),f149(x101151,x101154)))+P1(f319(f319(f321(f931(f926(x101151),f926(x101151))),f319(f319(f244(f926(x101151),f926(x101151)),x101155),x101156)),f149(x101151,x101154)))+P1(f319(f319(f321(f931(x101151,x101151)),f319(f319(f244(x101151,x101151),x101152),x101153)),x101154))
% 28.73/28.53 [10135]P1(f319(x101351,x101352))+P1(f319(f319(f321(x101353),f382(x101351,x101354,x101355,x101356,x101353)),f319(x101354,f364(x101351,x101354,x101355,x101356,x101353))))+~P1(f319(f319(f321(x101353),x101352),f319(f319(f33(x101356,f932(x101353,a923)),x101355),x101354)))
% 28.73/28.53 [10291]P1(f319(f319(f321(x102911),f528(x102912,x102913,x102914,x102915,x102916,x102911)),x102915))+~P1(f319(f319(f226(f932(x102911,a923)),x102916),x102915))+P1(f319(f319(f226(f932(x102914,a923)),f319(f319(f34(x102911,f932(x102914,a923)),x102915),x102913)),f319(f319(f34(x102911,f932(x102914,a923)),x102915),x102912)))
% 28.73/28.53 [10292]P1(f319(f319(f321(x102921),f546(x102922,x102923,x102924,x102925,x102926,x102921)),x102926))+~P1(f319(f319(f226(f932(x102921,a923)),x102926),x102925))+P1(f319(f319(f226(f932(x102924,a923)),f319(f319(f33(x102921,f932(x102924,a923)),x102926),x102923)),f319(f319(f33(x102921,f932(x102924,a923)),x102925),x102922)))
% 28.73/28.53 [10413]~P1(f319(f319(f226(f932(x104131,a923)),f319(x104134,f546(x104136,x104134,x104131,x104135,x104133,x104132))),f319(x104136,f546(x104136,x104134,x104131,x104135,x104133,x104132))))+~P1(f319(f319(f226(f932(x104132,a923)),x104133),x104135))+P1(f319(f319(f226(f932(x104131,a923)),f319(f319(f33(x104132,f932(x104131,a923)),x104133),x104134)),f319(f319(f33(x104132,f932(x104131,a923)),x104135),x104136)))
% 28.73/28.53 [10414]~P1(f319(f319(f226(f932(x104141,a923)),f319(x104144,f528(x104145,x104144,x104141,x104143,x104146,x104142))),f319(x104145,f528(x104145,x104144,x104141,x104143,x104146,x104142))))+~P1(f319(f319(f226(f932(x104142,a923)),x104146),x104143))+P1(f319(f319(f226(f932(x104141,a923)),f319(f319(f34(x104142,f932(x104141,a923)),x104143),x104144)),f319(f319(f34(x104142,f932(x104141,a923)),x104143),x104145)))
% 28.73/28.53 [9104]~P18(x91043,x91044,x91041)+~P1(f319(f55(x91043),x91046))+E(f319(f319(x91041,x91042),f319(f319(f58(x91043,x91044,x91041),x91045),f319(f319(f23(f932(x91043,a923)),x91046),f319(f319(f301(x91043),x91042),f180(f932(x91043,a923)))))),f319(f319(f58(x91043,x91044,x91041),x91045),f319(f319(f301(x91043),x91042),x91046)))
% 28.73/28.53 [9406]~P1(f319(f319(f321(x94065),x94063),x94066))+P1(f319(f319(f226(f932(x94061,a923)),f319(x94062,x94063)),x94064))+~P1(f319(f319(f226(f932(x94061,a923)),f319(f319(f33(x94065,f932(x94061,a923)),x94066),x94062)),x94064))
% 28.73/28.53 [10056]~P9(x100561,x100565,x100564)+P1(f319(f319(f321(f931(x100561,x100561)),f319(f319(f244(x100561,x100561),x100562),x100563)),x100564))+~P1(f319(f319(f321(x100561),x100566),f319(f319(f93(f932(x100561,a923)),f319(f277(x100561,x100561,x100564),f319(f319(f301(x100561),x100562),f180(f932(x100561,a923))))),f319(f277(x100561,x100561,x100564),f319(f319(f301(x100561),x100563),f180(f932(x100561,a923)))))))
% 28.73/28.53 [8824]~P116(x88242)+~E(f319(f319(f74(x88242),f319(f319(f75(x88242),x88244),x88245)),x88241),f319(f319(f74(x88242),f319(f319(f75(x88242),x88243),x88245)),x88246))+E(x88241,f319(f319(f74(x88242),f319(f319(f75(x88242),f319(f319(f23(x88242),x88243),x88244)),x88245)),x88246))
% 28.73/28.53 [8825]~P116(x88251)+~E(f319(f319(f74(x88251),f319(f319(f75(x88251),x88252),x88254)),x88255),f319(f319(f74(x88251),f319(f319(f75(x88251),x88253),x88254)),x88256))+E(f319(f319(f74(x88251),f319(f319(f75(x88251),f319(f319(f23(x88251),x88252),x88253)),x88254)),x88255),x88256)
% 28.73/28.53 [9008]~P116(x90081)+E(f319(f319(f74(x90081),f319(f319(f75(x90081),x90082),x90083)),x90084),f319(f319(f74(x90081),f319(f319(f75(x90081),x90085),x90083)),x90086))+~E(x90086,f319(f319(f74(x90081),f319(f319(f75(x90081),f319(f319(f23(x90081),x90082),x90085)),x90083)),x90084))
% 28.73/28.53 [9009]~P116(x90091)+E(f319(f319(f74(x90091),f319(f319(f75(x90091),x90092),x90093)),x90094),f319(f319(f74(x90091),f319(f319(f75(x90091),x90095),x90093)),x90096))+~E(f319(f319(f74(x90091),f319(f319(f75(x90091),f319(f319(f23(x90091),x90092),x90095)),x90093)),x90094),x90096)
% 28.73/28.53 [9341]~P1(f319(f319(x93414,x93415),x93416))+~P1(f319(f319(x93413,x93415),x93416))+P1(f319(f319(f319(f319(f93(f932(x93411,f932(x93412,a923))),x93413),x93414),x93415),x93416))
% 28.73/28.53 [9606]P1(f319(f319(x96061,x96062),x96063))+P1(f319(f319(x96064,x96062),x96063))+~P1(f319(f319(f319(f319(f102(f932(x96065,f932(x96066,a923))),x96064),x96061),x96062),x96063))
% 28.73/28.53 [9903]~P132(x99031)+~P1(f319(f319(f226(x99031),f319(f319(f74(x99031),f319(f319(f75(x99031),x99034),x99035)),x99032)),f319(f319(f74(x99031),f319(f319(f75(x99031),x99033),x99035)),x99036)))+P1(f319(f319(f226(x99031),x99032),f319(f319(f74(x99031),f319(f319(f75(x99031),f319(f319(f23(x99031),x99033),x99034)),x99035)),x99036)))
% 28.73/28.53 [9904]~P132(x99041)+~P1(f319(f319(f227(x99041),f319(f319(f74(x99041),f319(f319(f75(x99041),x99044),x99045)),x99042)),f319(f319(f74(x99041),f319(f319(f75(x99041),x99043),x99045)),x99046)))+P1(f319(f319(f227(x99041),x99042),f319(f319(f74(x99041),f319(f319(f75(x99041),f319(f319(f23(x99041),x99043),x99044)),x99045)),x99046)))
% 28.73/28.53 [9930]~P132(x99301)+P1(f319(f319(f226(x99301),f319(f319(f74(x99301),f319(f319(f75(x99301),x99302),x99303)),x99304)),f319(f319(f74(x99301),f319(f319(f75(x99301),x99305),x99303)),x99306)))+~P1(f319(f319(f226(x99301),x99304),f319(f319(f74(x99301),f319(f319(f75(x99301),f319(f319(f23(x99301),x99305),x99302)),x99303)),x99306)))
% 28.73/28.53 [9931]~P132(x99311)+P1(f319(f319(f227(x99311),f319(f319(f74(x99311),f319(f319(f75(x99311),x99312),x99313)),x99314)),f319(f319(f74(x99311),f319(f319(f75(x99311),x99315),x99313)),x99316)))+~P1(f319(f319(f227(x99311),x99314),f319(f319(f74(x99311),f319(f319(f75(x99311),f319(f319(f23(x99311),x99315),x99312)),x99313)),x99316)))
% 28.73/28.53 [10048]~P132(x100481)+~P1(f319(f319(f226(x100481),f319(f319(f74(x100481),f319(f319(f75(x100481),x100482),x100484)),x100485)),f319(f319(f74(x100481),f319(f319(f75(x100481),x100483),x100484)),x100486)))+P1(f319(f319(f226(x100481),f319(f319(f74(x100481),f319(f319(f75(x100481),f319(f319(f23(x100481),x100482),x100483)),x100484)),x100485)),x100486))
% 28.73/28.53 [10049]~P132(x100491)+~P1(f319(f319(f227(x100491),f319(f319(f74(x100491),f319(f319(f75(x100491),x100492),x100494)),x100495)),f319(f319(f74(x100491),f319(f319(f75(x100491),x100493),x100494)),x100496)))+P1(f319(f319(f227(x100491),f319(f319(f74(x100491),f319(f319(f75(x100491),f319(f319(f23(x100491),x100492),x100493)),x100494)),x100495)),x100496))
% 28.73/28.53 [10098]~P132(x100981)+P1(f319(f319(f226(x100981),f319(f319(f74(x100981),f319(f319(f75(x100981),x100982),x100983)),x100984)),f319(f319(f74(x100981),f319(f319(f75(x100981),x100985),x100983)),x100986)))+~P1(f319(f319(f226(x100981),f319(f319(f74(x100981),f319(f319(f75(x100981),f319(f319(f23(x100981),x100982),x100985)),x100983)),x100984)),x100986))
% 28.73/28.53 [10099]~P132(x100991)+P1(f319(f319(f227(x100991),f319(f319(f74(x100991),f319(f319(f75(x100991),x100992),x100993)),x100994)),f319(f319(f74(x100991),f319(f319(f75(x100991),x100995),x100993)),x100996)))+~P1(f319(f319(f227(x100991),f319(f319(f74(x100991),f319(f319(f75(x100991),f319(f319(f23(x100991),x100992),x100995)),x100993)),x100994)),x100996))
% 28.73/28.53 [10274]~P79(x102742)+~P1(f319(f55(x102741),x102746))+E(f319(f319(f6(x102741,x102742),f319(f319(f18(x102741,x102742,x102742),f319(f319(f18(x102741,x102742,f932(x102742,x102742)),f319(f319(f8(a923,f932(x102742,f932(x102742,x102742)),x102741),f86(x102742)),x102743)),x102744)),x102745)),x102746),f319(f319(f74(x102742),f319(f319(f6(x102741,x102742),x102744),f319(f319(f93(f932(x102741,a923)),x102746),f319(f254(x102741),x102743)))),f319(f319(f6(x102741,x102742),x102745),f319(f319(f93(f932(x102741,a923)),x102746),f319(f73(f932(x102741,a923)),f319(f254(x102741),x102743))))))
% 28.73/28.53 [10337]P1(f319(f319(f321(x103372),x103374),x103376))+P1(f319(f319(f321(x103372),x103375),x103376))+E(f319(f303(x103371,x103372,f319(f319(f7(x103371,x103372,x103372),f319(f319(f7(x103371,x103372,f932(x103372,x103372)),f319(f319(f8(a923,f932(x103372,f932(x103372,x103372)),x103371),f86(x103372)),f319(f319(f7(x103371,f932(x103371,a923),a923),f321(x103371)),x103373))),x103374)),x103375)),x103376),f180(f932(x103371,a923)))
% 28.73/28.53 [10338]P1(f319(f319(f321(x103382),x103385),x103386))+~P1(f319(f319(f321(x103382),x103384),x103386))+E(f319(f303(x103381,x103382,f319(f319(f7(x103381,x103382,x103382),f319(f319(f7(x103381,x103382,f932(x103382,x103382)),f319(f319(f8(a923,f932(x103382,f932(x103382,x103382)),x103381),f86(x103382)),f319(f319(f7(x103381,f932(x103381,a923),a923),f321(x103381)),x103383))),x103384)),x103385)),x103386),x103383)
% 28.73/28.53 [10339]P1(f319(f319(f321(x103392),x103394),x103396))+~P1(f319(f319(f321(x103392),x103395),x103396))+E(f319(f303(x103391,x103392,f319(f319(f7(x103391,x103392,x103392),f319(f319(f7(x103391,x103392,f932(x103392,x103392)),f319(f319(f8(a923,f932(x103392,f932(x103392,x103392)),x103391),f86(x103392)),f319(f319(f7(x103391,f932(x103391,a923),a923),f321(x103391)),x103393))),x103394)),x103395)),x103396),f319(f73(f932(x103391,a923)),x103393))
% 28.73/28.53 [10340]~P1(f319(f319(f321(x103402),x103404),x103406))+~P1(f319(f319(f321(x103402),x103405),x103406))+E(f319(f303(x103401,x103402,f319(f319(f7(x103401,x103402,x103402),f319(f319(f7(x103401,x103402,f932(x103402,x103402)),f319(f319(f8(a923,f932(x103402,f932(x103402,x103402)),x103401),f86(x103402)),f319(f319(f7(x103401,f932(x103401,a923),a923),f321(x103401)),x103403))),x103404)),x103405)),x103406),f234(f932(x103401,a923)))
% 28.73/28.53 [8857]E(x88571,x88572)+~P61(x88574,x88575,x88573,x88576,x88577)+~E(f319(x88573,x88571),f319(x88573,x88572))
% 28.73/28.53 [8885]~P11(x88856,x88855,x88857,x88854,x88851)+E(f319(f319(x88851,x88852),x88853),x88854)+P1(f319(f55(x88855),x88853))
% 28.73/28.53 [8886]~P11(x88866,x88865,x88867,x88864,x88861)+E(f319(f319(x88861,x88862),x88863),x88864)+P1(f319(f55(x88865),x88863))
% 28.73/28.53 [9767]P44(x97671,x97672,x97673,x97674,x97675,f319(f319(x97673,x97676),x97677))+~E(f319(f319(x97673,x97676),x97677),x97674)+~E(x97675,f180(f932(x97671,a923)))
% 28.73/28.53 [9957]~P1(f319(x99576,x99573))+~P1(f319(f319(f321(f931(x99572,x99572)),f319(f319(f244(x99572,x99572),x99574),x99575)),f319(x99577,x99573)))+P1(f319(f319(f321(f931(f931(x99571,x99572),f931(x99571,x99572))),f319(f319(f244(f931(x99571,x99572),f931(x99571,x99572)),f319(f319(f244(x99571,x99572),x99573),x99574)),f319(f319(f244(x99571,x99572),x99573),x99575))),f272(x99571,x99572,x99576,x99577)))
% 28.73/28.53 [10401]~P44(x104012,x104017,x104013,x104016,x104011,f319(f319(x104013,x104015),x104014))+E(f319(f319(x104013,f897(x104014,x104015,x104011,x104016,x104013,x104017,x104012)),f898(x104014,x104015,x104011,x104016,x104013,x104017,x104012)),f319(f319(x104013,x104015),x104014))+E(x104011,f180(f932(x104012,a923)))
% 28.73/28.53 [10402]~P44(x104027,x104026,x104021,x104024,x104025,f319(f319(x104021,x104022),x104023))+E(f319(f319(x104021,f897(x104023,x104022,x104025,x104024,x104021,x104026,x104027)),f898(x104023,x104022,x104025,x104024,x104021,x104026,x104027)),f319(f319(x104021,x104022),x104023))+E(f319(f319(x104021,x104022),x104023),x104024)
% 28.73/28.53 [9440]~P35(x94401,x94402,x94403,x94405,x94407)+P35(x94401,x94402,x94403,f319(f319(f143(x94401),x94404),x94405),f319(f319(f143(x94402),x94406),x94407))+~P1(f319(f319(x94403,x94404),x94406))
% 28.73/28.53 [9458]P35(x94581,x94582,x94583,x94584,x94585)+~P35(x94581,x94582,x94583,f319(f319(f126(x94581),x94586),x94584),f319(f319(f126(x94582),x94587),x94585))+~E(f319(f181(f926(x94581)),x94586),f319(f181(f926(x94582)),x94587))
% 28.73/28.53 [9459]P35(x94591,x94592,x94593,x94594,x94595)+~P35(x94591,x94592,x94593,f319(f319(f126(x94591),x94594),x94596),f319(f319(f126(x94592),x94595),x94597))+~E(f319(f181(f926(x94591)),x94594),f319(f181(f926(x94592)),x94595))
% 28.73/28.53 [9673]~P35(x96731,x96732,x96733,x96735,x96737)+~P35(x96731,x96732,x96733,x96734,x96736)+P35(x96731,x96732,x96733,f319(f319(f126(x96731),x96734),x96735),f319(f319(f126(x96732),x96736),x96737))
% 28.73/28.53 [10039]~P1(f319(f60(x100391,x100394,x100395,x100396,x100393),x100397))+P1(f319(f60(x100391,x100394,x100395,x100396,f319(f319(f301(x100391),x100392),x100393)),f319(f319(x100395,x100392),x100397)))+P1(f319(f319(f321(x100391),x100392),x100393))
% 28.73/28.53 [10430]~P44(x104302,x104307,x104306,x104305,x104301,f319(f319(x104306,x104304),x104303))+E(x104301,f180(f932(x104302,a923)))+P1(f319(f319(f321(x104302),f897(x104303,x104304,x104301,x104305,x104306,x104307,x104302)),x104301))
% 28.73/28.53 [10431]~P44(x104315,x104317,x104311,x104314,x104316,f319(f319(x104311,x104312),x104313))+E(f319(f319(x104311,x104312),x104313),x104314)+P1(f319(f319(f321(x104315),f897(x104313,x104312,x104316,x104314,x104311,x104317,x104315)),x104316))
% 28.73/28.53 [10522]E(f319(f319(f244(x105221,x105222),x105223),x105224),f319(f319(f244(x105221,x105222),x105225),x105226))+P1(f319(f319(f321(f931(f931(x105221,x105222),f931(x105221,x105222))),f319(f319(f244(f931(x105221,x105222),f931(x105221,x105222)),f319(f319(f244(x105221,x105222),f850(x105227,x105224,x105223,x105226,x105225,x105222,x105221)),f851(x105227,x105224,x105223,x105226,x105225,x105222,x105221))),f319(f319(f244(x105221,x105222),x105223),x105224))),f299(f931(x105221,x105222),x105227)))+~P1(f319(f319(f321(f931(f931(x105221,x105222),f931(x105221,x105222))),f319(f319(f244(f931(x105221,x105222),f931(x105221,x105222)),f319(f319(f244(x105221,x105222),x105225),x105226)),f319(f319(f244(x105221,x105222),x105223),x105224))),f299(f931(x105221,x105222),x105227)))
% 28.73/28.53 [9129]~P23(x91294,x91295,x91296,x91297,x91291)+~P1(f319(f55(x91295),x91293))+E(f319(f319(x91291,x91292),x91293),f319(f319(f319(f59(x91294,x91295,x91296),x91292),x91297),x91293))
% 28.73/28.53 [9130]~P11(x91304,x91305,x91306,x91307,x91301)+~P1(f319(f55(x91305),x91303))+E(f319(f319(x91301,x91302),x91303),f319(f319(f319(f59(x91304,x91305,x91306),x91302),x91307),x91303))
% 28.73/28.53 [9924]~P25(x99243,x99244,x99245,x99247,x99246,x99241)+~P1(f319(f55(x99244),x99242))+E(f319(x99241,x99242),f319(f319(f319(f59(x99243,x99244,x99245),x99246),x99247),x99242))
% 28.73/28.53 [10093]P44(x100931,x100932,x100933,x100934,x100935,f319(f319(x100933,x100936),x100937))+~P44(x100931,x100932,x100933,x100934,f319(f319(f23(f932(x100931,a923)),x100935),f319(f319(f301(x100931),x100936),f180(f932(x100931,a923)))),x100937)+~P1(f319(f319(f321(x100931),x100936),x100935))
% 28.73/28.53 [10455]P1(f319(f319(x104557,f809(x104554,x104555,x104551,x104556,x104553,x104552,x104557)),f810(x104554,x104555,x104551,x104556,x104553,x104552,x104557)))+~P1(f319(f319(x104557,f319(f248(x104552,x104553),x104556)),f319(f243(x104552,x104553),x104556)))+P1(f319(x104551,f319(f319(f249(x104552,x104553,x104554),x104555),x104556)))
% 28.73/28.53 [10465]~P44(x104652,x104653,x104654,x104655,x104651,f319(f319(x104654,x104657),x104656))+P44(x104652,x104653,x104654,x104655,f319(f319(f23(f932(x104652,a923)),x104651),f319(f319(f301(x104652),f897(x104656,x104657,x104651,x104655,x104654,x104653,x104652)),f180(f932(x104652,a923)))),f898(x104656,x104657,x104651,x104655,x104654,x104653,x104652))+E(x104651,f180(f932(x104652,a923)))
% 28.73/28.53 [10466]~P44(x104665,x104666,x104661,x104664,x104667,f319(f319(x104661,x104662),x104663))+P44(x104665,x104666,x104661,x104664,f319(f319(f23(f932(x104665,a923)),x104667),f319(f319(f301(x104665),f897(x104663,x104662,x104667,x104664,x104661,x104666,x104665)),f180(f932(x104665,a923)))),f898(x104663,x104662,x104667,x104664,x104661,x104666,x104665))+E(f319(f319(x104661,x104662),x104663),x104664)
% 28.73/28.53 [10488]~P1(f319(x104881,f319(f319(x104885,f810(x104884,x104885,x104881,x104886,x104883,x104882,x104887)),f809(x104884,x104885,x104881,x104886,x104883,x104882,x104887))))+~P1(f319(f319(x104887,f319(f248(x104882,x104883),x104886)),f319(f243(x104882,x104883),x104886)))+P1(f319(x104881,f319(f319(f249(x104882,x104883,x104884),x104885),x104886)))
% 28.73/28.53 [9752]P1(f319(f319(f226(f932(f931(x97521,x97522),a923)),f319(f319(f281(x97521,x97523,x97522),x97524),x97525)),f319(f319(f281(x97521,x97523,x97522),x97526),x97527)))+~P1(f319(f319(f226(f932(f931(x97523,x97522),a923)),x97525),x97527))+~P1(f319(f319(f226(f932(f931(x97521,x97523),a923)),x97524),x97526))
% 28.73/28.53 [10516]E(f319(f319(f244(x105161,x105162),x105163),x105164),f319(f319(f244(x105161,x105162),x105165),x105166))+~P1(f319(f319(f321(f931(f931(x105161,x105162),f931(x105161,x105162))),f319(f319(f244(f931(x105161,x105162),f931(x105161,x105162)),f319(f319(f244(x105161,x105162),x105163),x105164)),f319(f319(f244(x105161,x105162),x105165),x105166))),f299(f931(x105161,x105162),x105167)))+P1(f319(f319(f321(f931(f931(x105161,x105162),f931(x105161,x105162))),f319(f319(f244(f931(x105161,x105162),f931(x105161,x105162)),f319(f319(f244(x105161,x105162),x105163),x105164)),f319(f319(f244(x105161,x105162),f850(x105167,x105166,x105165,x105164,x105163,x105162,x105161)),f851(x105167,x105166,x105165,x105164,x105163,x105162,x105161)))),x105167))
% 28.73/28.53 [10104]~P1(f319(f319(f321(x101041),x101046),x101045))+P1(f319(f60(x101041,x101042,x101043,x101044,x101045),f319(f319(x101043,x101046),x101047)))+~P1(f319(f60(x101041,x101042,x101043,x101044,f319(f319(f23(f932(x101041,a923)),x101045),f319(f319(f301(x101041),x101046),f180(f932(x101041,a923))))),x101047))
% 28.73/28.53 [10529]~P143(x105291)+~P26(f931(x105292,x105293),x105291,f319(f249(x105292,x105293,x105291),f319(f319(f7(x105292,f932(x105293,x105291),f932(x105293,x105291)),f319(f319(f8(f932(x105291,x105291),f932(f932(x105293,x105291),f932(x105293,x105291)),x105292),f8(x105291,x105291,x105293)),f319(f319(f8(x105291,f932(x105291,x105291),x105292),f75(x105291)),x105294))),x105295)),f319(f319(f246(x105292,x105293),x105296),f319(f16(f932(x105293,a923),x105292),x105297)))+E(f319(f319(f6(x105291,x105291),f25(x105291)),f319(f254(x105291),f319(f319(f8(f932(x105292,a923),a923,x105291),f81(x105292)),f319(f319(f8(f932(x105292,f932(x105293,a923)),f932(x105292,a923),x105291),f319(f8(f932(x105293,a923),a923,x105292),f81(x105293))),f319(f319(f7(x105291,f932(x105292,f932(x105293,a923)),f932(x105292,f932(x105293,a923))),f319(f319(f8(f932(x105292,f932(f932(x105293,a923),f932(x105293,a923))),f932(f932(x105292,f932(x105293,a923)),f932(x105292,f932(x105293,a923))),x105291),f18(x105292,f932(x105293,a923),f932(x105293,a923))),f319(f319(f8(f932(x105292,f932(x105293,f932(a923,a923))),f932(x105292,f932(f932(x105293,a923),f932(x105293,a923))),x105291),f319(f8(f932(x105293,f932(a923,a923)),f932(f932(x105293,a923),f932(x105293,a923)),x105292),f18(x105293,a923,a923))),f319(f319(f8(f932(x105292,f932(x105293,a923)),f932(x105292,f932(x105293,f932(a923,a923))),x105291),f319(f8(f932(x105293,a923),f932(x105293,f932(a923,a923)),x105292),f319(f8(a923,f932(a923,a923),x105293),a317))),f319(f319(f7(x105291,f932(x105292,f932(x105293,x105291)),f932(x105292,f932(x105293,a923))),f319(f319(f8(f932(f932(x105293,x105291),f932(x105293,a923)),f932(f932(x105292,f932(x105293,x105291)),f932(x105292,f932(x105293,a923))),x105291),f8(f932(x105293,x105291),f932(x105293,a923),x105292)),f319(f319(f8(f932(x105291,a923),f932(f932(x105293,x105291),f932(x105293,a923)),x105291),f8(x105291,a923,x105293)),a316))),f319(f319(f7(x105292,f932(x105293,x105291),f932(x105293,x105291)),f319(f319(f8(f932(x105291,x105291),f932(f932(x105293,x105291),f932(x105293,x105291)),x105292),f8(x105291,x105291,x105293)),f319(f319(f8(x105291,f932(x105291,x105291),x105292),f75(x105291)),x105294))),x105295)))))),f319(f319(f7(x105292,f932(x105293,a923),f932(x105293,a923)),f319(f319(f8(f932(a923,a923),f932(f932(x105293,a923),f932(x105293,a923)),x105292),f8(a923,a923,x105293)),f319(f319(f8(a923,f932(a923,a923),x105292),a317),f319(f319(f7(x105292,f932(x105292,a923),a923),f321(x105292)),x105296)))),f319(f319(f7(x105293,f932(x105293,a923),a923),f321(x105293)),x105297))))))),f319(f319(f75(x105291),f319(f319(f6(x105292,x105291),x105294),x105296)),f319(f319(f6(x105293,x105291),x105295),x105297)))
% 28.73/28.53 [9755]~P27(x97553,x97552,x97554,x97558,x97557)+~P27(x97551,x97553,x97555,x97556,x97558)+P27(x97551,x97552,f319(f66(x97553,x97552,x97551,x97554),x97555),x97556,x97557)
% 28.73/28.53 [9756]~P27(x97561,x97563,x97565,x97566,x97568)+~P27(x97563,x97562,x97564,x97568,x97567)+P27(x97561,x97562,f319(f66(x97563,x97562,x97561,x97564),x97565),x97566,x97567)
% 28.73/28.53 [9787]P27(x97871,x97872,x97873,x97874,x97875)+~P27(x97876,x97871,x97877,x97878,x97874)+~P27(x97876,x97872,f319(f66(x97871,x97872,x97876,x97873),x97877),x97878,x97875)
% 28.73/28.53 [9921]~P1(f319(f319(x99214,x99216),x99218))+~P1(f319(f319(x99215,x99218),x99217))+P1(f319(f319(f245(x99211,x99212,x99213,x99214,x99215),x99216),x99217))
% 28.73/28.53 [9922]~P1(f319(f319(x99224,x99226),x99228))+~P1(f319(f319(x99225,x99228),x99227))+P1(f319(f319(f245(x99221,x99222,x99223,x99224,x99225),x99226),x99227))
% 28.73/28.53 [9511]~P21(x95118,x95111,x95113,x95115)+~P1(f319(f55(x95118),x95116))+E(f319(f66(x95111,x95111,x95112,f319(x95113,x95114)),f319(f66(x95111,x95111,x95112,f319(x95115,x95116)),x95117)),f319(f66(x95111,x95111,x95112,f319(x95115,x95116)),f319(f66(x95111,x95111,x95112,f319(x95113,x95114)),x95117)))
% 28.73/28.53 [9912]~P24(x99127,x99122,x99125,x99128,x99126,x99121)+~P1(f319(f55(x99122),x99124))+E(f319(x99121,f319(f319(f301(x99122),x99123),x99124)),f319(f319(x99125,f319(x99126,x99123)),f319(x99121,x99124)))
% 28.73/28.53 [10045]~P26(x100452,x100454,x100456,x100458)+~P26(x100451,x100453,x100455,x100457)+P26(f931(x100451,x100452),f931(x100453,x100454),f250(x100451,x100453,x100452,x100454,x100455,x100456),f319(f319(f246(x100451,x100452),x100457),f319(f16(f932(x100452,a923),x100451),x100458)))
% 28.73/28.53 [9700]P1(f319(f319(f321(f931(x97001,x97002)),f319(f319(f244(x97001,x97002),x97003),x97004)),f319(f319(f281(x97001,x97005,x97002),x97006),x97007)))+~P1(f319(f319(f321(f931(x97001,x97005)),f319(f319(f244(x97001,x97005),x97003),x97008)),x97006))+~P1(f319(f319(f321(f931(x97005,x97002)),f319(f319(f244(x97005,x97002),x97008),x97004)),x97007))
% 28.73/28.53 [9891]~P1(f319(f319(f226(f932(f931(x98913,x98912),a923)),x98915),f319(f319(f246(x98913,x98912),x98918),f319(f16(f932(x98912,a923),x98913),x98917))))+~P1(f319(f319(f226(f932(f931(x98911,x98913),a923)),x98914),f319(f319(f246(x98911,x98913),x98916),f319(f16(f932(x98913,a923),x98911),x98918))))+P1(f319(f319(f226(f932(f931(x98911,x98912),a923)),f319(f319(f281(x98911,x98913,x98912),x98914),x98915)),f319(f319(f246(x98911,x98912),x98916),f319(f16(f932(x98912,a923),x98911),x98917))))
% 28.73/28.53 [9949]~E(x99493,x99495)+P1(f319(f319(f321(f931(f931(x99491,x99492),f931(x99491,x99492))),f319(f319(f244(f931(x99491,x99492),f931(x99491,x99492)),f319(f319(f244(x99491,x99492),x99493),x99494)),f319(f319(f244(x99491,x99492),x99495),x99496))),f312(x99491,x99492,x99497,x99498)))+~P1(f319(f319(f321(f931(x99492,x99492)),f319(f319(f244(x99492,x99492),x99494),x99496)),x99498))
% 28.73/28.53 [10065]E(x100651,x100652)+~P1(f319(f319(f321(f931(f931(x100653,x100655),f931(x100653,x100655))),f319(f319(f244(f931(x100653,x100655),f931(x100653,x100655)),f319(f319(f244(x100653,x100655),x100651),x100656)),f319(f319(f244(x100653,x100655),x100652),x100657))),f312(x100653,x100655,x100654,x100658)))+P1(f319(f319(f321(f931(x100653,x100653)),f319(f319(f244(x100653,x100653),x100651),x100652)),x100654))
% 28.73/28.53 [10082]~P1(f319(f319(f321(f931(f931(x100821,x100825),f931(x100821,x100825))),f319(f319(f244(f931(x100821,x100825),f931(x100821,x100825)),f319(f319(f244(x100821,x100825),x100822),x100826)),f319(f319(f244(x100821,x100825),x100823),x100827))),f312(x100821,x100825,x100824,x100828)))+P1(f319(f319(f321(f931(x100821,x100821)),f319(f319(f244(x100821,x100821),x100822),x100823)),x100824))+P1(f319(f319(f321(f931(x100825,x100825)),f319(f319(f244(x100825,x100825),x100826),x100827)),x100828))
% 28.73/28.53 [9991]~P25(x99917,x99915,x99911,x99918,x99912,x99914)+~P1(f319(f55(x99915),x99916))+E(f319(f319(x99911,f319(x99912,x99913)),f319(x99914,f319(f319(f23(f932(x99915,a923)),x99916),f319(f319(f301(x99915),x99913),f180(f932(x99915,a923)))))),f319(x99914,f319(f319(f301(x99915),x99913),x99916)))
% 28.73/28.53 [9463]~P1(f319(f319(f319(x94635,x94638),x94636),x94637))+~P1(f319(f319(f321(x94631),x94638),x94634))+P1(f319(f319(f319(f319(f33(x94631,f932(x94632,f932(x94633,a923))),x94634),x94635),x94636),x94637))
% 28.73/28.53 [9464]~P1(f319(f319(f319(x94645,x94648),x94646),x94647))+~P1(f319(f319(f321(x94641),x94648),x94644))+P1(f319(f319(f319(f319(f33(x94641,f932(x94642,f932(x94643,a923))),x94644),x94645),x94646),x94647))
% 28.73/28.53 [9682]P1(f319(f319(f319(x96821,x96822),x96823),x96824))+~P1(f319(f319(f321(x96825),x96822),x96826))+~P1(f319(f319(f319(f319(f34(x96825,f932(x96827,f932(x96828,a923))),x96826),x96821),x96823),x96824))
% 28.73/28.53 [9683]P1(f319(f319(f319(x96831,x96832),x96833),x96834))+~P1(f319(f319(f321(x96835),x96832),x96836))+~P1(f319(f319(f319(f319(f34(x96835,f932(x96837,f932(x96838,a923))),x96836),x96831),x96833),x96834))
% 28.73/28.53 [9684]P1(f319(f319(f319(x96841,x96842),x96843),x96844))+~P1(f319(f319(f321(x96845),x96842),x96846))+~P1(f319(f319(f319(f319(f34(x96845,f932(x96847,f932(x96848,a923))),x96846),x96841),x96843),x96844))
% 28.73/28.53 [9884]~P23(x98843,x98842,x98844,x98848,x98841)+~P1(f319(f55(x98842),x98847))+E(f319(f319(x98841,f319(f319(f18(x98842,x98843,x98843),f319(f319(f8(x98843,f932(x98843,x98843),x98842),x98844),x98845)),x98846)),x98847),f319(f319(x98844,f319(f319(x98841,x98845),x98847)),f319(f319(x98841,x98846),x98847)))
% 28.73/28.53 [10169]~E(f319(f302(x101692,x101694,x101696),x101698),x1016910)+~E(f319(f302(x101691,x101693,x101695),x101697),x101699)+E(f319(f302(f931(x101691,x101692),f931(x101693,x101694),f250(x101691,x101693,x101692,x101694,x101695,x101696)),f319(f319(f246(x101691,x101692),x101697),f319(f16(f932(x101692,a923),x101691),x101698))),f319(f319(f246(x101693,x101694),x101699),f319(f16(f932(x101694,a923),x101693),x1016910)))
% 28.73/28.53 [5087]~P50(x50871,x50872)+~P54(x50871,x50872)+~P55(x50871,x50872)+P8(x50871,x50872)
% 28.73/28.53 [5088]~P50(x50881,x50882)+~P54(x50881,x50882)+~P55(x50881,x50882)+P8(x50881,x50882)
% 28.73/28.53 [5044]~P4(x50442)+~P14(x50442,x50441)+P14(x50442,f106(x50442,x50441))+E(x50441,f105(x50442))
% 28.73/28.53 [5045]~P4(x50452)+~P14(x50452,x50451)+P14(x50452,f729(x50451,x50452))+E(x50451,f105(x50452))
% 28.73/28.53 [5287]~P6(x52872)+E(f10(x52872,x52871),f32(x52872,x52871))+E(x52871,f180(f932(x52872,a923)))+~P1(f319(f55(x52872),x52871))
% 28.73/28.53 [5288]~P6(x52882)+E(f13(x52882,x52881),f31(x52882,x52881))+E(x52881,f180(f932(x52882,a923)))+~P1(f319(f55(x52882),x52881))
% 28.73/28.53 [5451]~P4(x54512)+~P14(x54512,x54511)+E(x54511,f105(x54512))+E(f319(f319(f143(x54512),f748(x54511,x54512)),f729(x54511,x54512)),x54511)
% 28.73/28.53 [6261]~P102(x62612)+E(x62611,f180(f932(x62612,a923)))+P1(f319(f319(f226(x62612),f10(x62612,x62611)),f13(x62612,x62611)))+~P1(f319(f55(x62612),x62611))
% 28.73/28.53 [6270]~P42(x62702)+~P42(x62701)+E(x62701,x62702)+~E(f319(f302(a1,a925,a96),x62701),f319(f302(a1,a925,a96),x62702))
% 28.73/28.53 [9319]~P126(x93191)+~P1(f319(f319(f321(x93191),x93192),f101(x93191)))+P1(f319(f319(f227(x93191),f319(f319(f74(x93191),f319(f319(f74(x93191),f72(x93191)),x93192)),x93192)),f2(x93191)))+~P1(f319(f319(f227(x93191),x93192),f2(x93191)))
% 28.73/28.53 [9566]~P126(x95661)+~P1(f319(f319(f321(x95661),x95662),f101(x95661)))+~P1(f319(f319(f227(x95661),f319(f319(f74(x95661),f319(f319(f74(x95661),f72(x95661)),x95662)),x95662)),f2(x95661)))+P1(f319(f319(f227(x95661),x95662),f2(x95661)))
% 28.73/28.53 [5103]~P143(x51032)+~P119(x51032)+E(x51031,f2(a925))+E(f319(f319(f236(x51032),f2(x51032)),x51031),f2(x51032))
% 28.73/28.53 [5106]~P143(x51061)+~P119(x51061)+~E(x51062,f2(a925))+E(f319(f319(f236(x51061),f2(x51061)),x51062),f72(x51061))
% 28.73/28.53 [5273]~P144(x52732)+E(x52731,f72(x52732))+E(x52731,f319(f73(x52732),f72(x52732)))+~E(f319(f319(f75(x52732),x52731),x52731),f72(x52732))
% 28.73/28.53 [5525]~P94(x55252)+E(x55251,f2(x55252))+E(f76(x55252,x55251),f319(f73(x55252),f72(x55252)))+P1(f319(f319(f227(x55252),f2(x55252)),x55251))
% 28.73/28.53 [5720]~E(x57202,f72(a1))+~E(x57201,f72(a1))+E(f319(f319(f75(a1),x57201),x57202),f72(a1))+~P1(f319(f319(f227(a1),f2(a1)),x57201))
% 28.73/28.53 [5764]~P94(x57642)+E(f76(x57642,x57641),f72(x57642))+E(x57641,f2(x57642))+~P1(f319(f319(f227(x57642),f2(x57642)),x57641))
% 28.73/28.53 [5773]E(x57731,x57732)+~E(f319(f95(a925),x57731),f319(f95(a925),x57732))+P1(f319(a185,f319(f95(a1),x57732)))+P1(f319(a185,f319(f95(a1),x57731)))
% 28.73/28.53 [5823]~P98(x58231)+~E(x58232,f2(x58231))+E(f319(f319(f74(x58231),x58232),x58232),f2(x58231))+~P1(f319(f319(f321(x58231),x58232),f101(x58231)))
% 28.73/28.53 [5863]E(x58631,f2(a1))+~E(f319(f319(f30(a1),x58632),x58631),f2(a1))+P1(f319(f319(f227(a1),x58631),x58632))+P1(f319(f319(f227(a1),x58632),x58631))
% 28.73/28.53 [5893]E(x58931,f2(a1))+~E(f319(f319(f30(a1),x58932),x58931),f2(a1))+P1(f319(f319(f226(a1),x58932),f2(a1)))+P1(f319(f319(f227(a1),x58932),x58931))
% 28.73/28.53 [5927]E(x59271,f2(a1))+~E(f319(f319(f30(a1),x59272),x59271),f2(a1))+P1(f319(f319(f226(a1),f2(a1)),x59272))+P1(f319(f319(f227(a1),x59271),x59272))
% 28.73/28.53 [5960]E(x59601,f2(a1))+~E(f319(f319(f30(a1),x59602),x59601),f2(a1))+P1(f319(f319(f226(a1),x59602),f2(a1)))+P1(f319(f319(f226(a1),f2(a1)),x59602))
% 28.73/28.53 [5962]~P98(x59622)+E(x59621,f2(x59622))+~E(f319(f319(f74(x59622),x59621),x59621),f2(x59622))+~P1(f319(f319(f321(x59622),x59621),f101(x59622)))
% 28.73/28.53 [6024]E(f319(f95(a925),x60241),f319(f95(a925),x60242))+~E(f319(f95(a1),x60242),f2(a1))+P1(f319(a185,f319(f95(a1),x60242)))+~P1(f319(a185,f319(f95(a1),x60241)))
% 28.73/28.53 [6054]~E(f319(f95(a925),x60542),f319(f95(a925),x60541))+E(f319(f95(a1),x60541),f2(a1))+P1(f319(a185,f319(f95(a1),x60541)))+~P1(f319(a185,f319(f95(a1),x60542)))
% 28.73/28.53 [6064]~P4(x60642)+E(x60641,f180(f932(x60642,a923)))+~P1(f319(f55(x60642),x60641))+P1(f319(f319(f321(x60642),f14(x60642,x60641)),x60641))
% 28.73/28.53 [6065]~P4(x60652)+E(x60651,f180(f932(x60652,a923)))+~P1(f319(f55(x60652),x60651))+P1(f319(f319(f321(x60652),f15(x60652,x60651)),x60651))
% 28.73/28.53 [6238]~P126(x62381)+~P99(x62381)+P1(f319(f319(f226(x62381),f2(x62381)),f319(f95(x62381),x62382)))+~P1(f319(f319(f226(a1),a77),x62382))
% 28.73/28.53 [6239]~P126(x62391)+~P99(x62391)+P1(f319(f319(f227(x62391),f2(x62391)),f319(f95(x62391),x62392)))+~P1(f319(f319(f227(a1),a77),x62392))
% 28.73/28.53 [6260]~P126(x62601)+~P99(x62601)+E(f319(f69(x62601),f319(f95(x62601),x62602)),f319(f95(x62601),x62602))+P1(f319(f319(f227(x62601),f319(f95(x62601),x62602)),f2(x62601)))
% 28.73/28.53 [6293]E(x62931,x62932)+~E(f319(a96,x62931),f319(a96,x62932))+~P1(f319(f319(f226(a1),f2(a1)),x62932))+~P1(f319(f319(f226(a1),f2(a1)),x62931))
% 28.73/28.53 [6294]E(x62941,x62942)+~E(f319(a96,x62941),f319(a96,x62942))+~P1(f319(f319(f226(a1),f2(a1)),x62942))+~P1(f319(f319(f226(a1),f2(a1)),x62941))
% 28.73/28.53 [6324]~E(x63241,f2(a1))+E(f40(x63241,x63242),f319(f319(f244(a1,a1),f2(a1)),f2(a1)))+P1(f319(f319(f226(a1),f2(a1)),x63242))+~P1(f319(f319(f226(a1),f2(a1)),x63241))
% 28.73/28.53 [6487]~P99(x64872)+~P126(x64872)+~P1(f319(f319(f226(x64872),f2(x64872)),f319(f95(x64872),x64871)))+P1(f319(f319(f226(a1),a77),x64871))
% 28.73/28.53 [6488]~P99(x64882)+~P126(x64882)+~P1(f319(f319(f227(x64882),f2(x64882)),f319(f95(x64882),x64881)))+P1(f319(f319(f227(a1),a77),x64881))
% 28.73/28.53 [6493]~P126(x64931)+~P99(x64931)+P1(f319(f319(f226(x64931),f319(f95(x64931),x64932)),f2(x64931)))+~P1(f319(f319(f226(a1),x64932),a77))
% 28.73/28.53 [6494]~P126(x64941)+~P99(x64941)+P1(f319(f319(f227(x64941),f319(f95(x64941),x64942)),f2(x64941)))+~P1(f319(f319(f227(a1),x64942),a77))
% 28.73/28.53 [6816]~P99(x68162)+~P126(x68162)+~P1(f319(f319(f226(x68162),f319(f95(x68162),x68161)),f2(x68162)))+P1(f319(f319(f226(a1),x68161),a77))
% 28.73/28.53 [6817]~P99(x68172)+~P126(x68172)+~P1(f319(f319(f227(x68172),f319(f95(x68172),x68171)),f2(x68172)))+P1(f319(f319(f227(a1),x68171),a77))
% 28.73/28.53 [6910]~P126(x69101)+~P99(x69101)+E(f319(f69(x69101),f319(f95(x69101),x69102)),f319(f73(x69101),f319(f95(x69101),x69102)))+~P1(f319(f319(f227(x69101),f319(f95(x69101),x69102)),f2(x69101)))
% 28.73/28.53 [6930]E(f319(f95(a925),x69301),f319(f95(a925),x69302))+~E(f319(f95(a1),x69302),f2(a1))+~P1(f319(f319(f226(a1),f319(f95(a1),x69301)),f2(a1)))+~P1(f319(a185,f319(f95(a1),x69301)))
% 28.73/28.53 [7099]E(x70991,x70992)+~E(f319(a3,x70991),f319(a3,x70992))+~P1(f319(f319(f321(a925),x70992),f234(f932(a925,a923))))+~P1(f319(f319(f321(a925),x70991),f234(f932(a925,a923))))
% 28.73/28.53 [7324]P1(f319(f319(f226(a925),f319(a96,x73241)),f319(a96,x73242)))+~P1(f319(f319(f226(a1),f2(a1)),x73242))+~P1(f319(f319(f226(a1),f2(a1)),x73241))+~P1(f319(f319(f226(a1),x73241),x73242))
% 28.73/28.53 [7325]P1(f319(f319(f227(a925),f319(a96,x73251)),f319(a96,x73252)))+~P1(f319(f319(f226(a1),f2(a1)),x73252))+~P1(f319(f319(f226(a1),f2(a1)),x73251))+~P1(f319(f319(f227(a1),x73251),x73252))
% 28.73/28.53 [7556]~P7(x75561)+~P42(x75562)+~P1(f319(f319(f321(a1),x75561),x75562))+P1(f319(f319(f321(a925),f319(a96,x75561)),f319(f302(a1,a925,a96),x75562)))
% 28.73/28.53 [7561]~P1(f319(f319(f226(a925),f319(a96,x75611)),f319(a96,x75612)))+~P1(f319(f319(f226(a1),f2(a1)),x75612))+~P1(f319(f319(f226(a1),f2(a1)),x75611))+P1(f319(f319(f226(a1),x75611),x75612))
% 28.73/28.53 [7562]~P1(f319(f319(f227(a925),f319(a96,x75621)),f319(a96,x75622)))+~P1(f319(f319(f226(a1),f2(a1)),x75622))+~P1(f319(f319(f226(a1),f2(a1)),x75621))+P1(f319(f319(f227(a1),x75621),x75622))
% 28.73/28.53 [7804]~P4(x78042)+E(x78041,f180(f932(x78042,a923)))+~P1(f319(f55(x78042),x78041))+P1(f319(f319(f226(x78042),f11(x78042,f224(x78042),x78041)),f12(x78042,f225(x78042),x78041)))
% 28.73/28.53 [8123]~P7(x81231)+~P42(x81232)+P1(f319(f319(f321(a1),x81231),x81232))+~P1(f319(f319(f321(a925),f319(a96,x81231)),f319(f302(a1,a925,a96),x81232)))
% 28.73/28.53 [6060]~P145(x60602)+E(x60601,f2(a1))+E(f319(f73(x60602),f319(f94(x60602),f319(f73(a1),x60601))),f319(f94(x60602),x60601))+~P1(f319(f319(f227(a1),x60601),f2(a1)))
% 28.73/28.53 [6139]~P98(x61391)+~P99(x61391)+~P29(x61391,f319(f95(x61391),x61392))+P29(x61391,f319(f95(x61391),f319(f319(f74(a1),x61392),x61392)))
% 28.73/28.53 [6476]~P84(x64762)+E(x64761,f180(f932(x64762,a923)))+E(f15(x64762,f319(f302(x64762,x64762,f73(x64762)),x64761)),f319(f73(x64762),f14(x64762,x64761)))+~P1(f319(f55(x64762),x64761))
% 28.73/28.53 [6477]~P84(x64772)+E(x64771,f180(f932(x64772,a923)))+E(f14(x64772,f319(f302(x64772,x64772,f73(x64772)),x64771)),f319(f73(x64772),f15(x64772,x64771)))+~P1(f319(f55(x64772),x64771))
% 28.73/28.53 [6510]~P98(x65101)+~P99(x65101)+P29(x65101,f319(f95(x65101),x65102))+~P29(x65101,f319(f95(x65101),f319(f319(f74(a1),x65102),x65102)))
% 28.73/28.53 [6602]E(x66021,f2(a1))+E(f319(a45,f44(f319(f73(a1),x66021),f319(f73(a1),x66022))),f40(x66021,x66022))+P1(f319(f319(f226(a1),f2(a1)),x66022))+~P1(f319(f319(f226(a1),f2(a1)),x66021))
% 28.73/28.53 [7476]~P1(f319(f319(f226(a1),f2(a1)),x74761))+~P1(f319(f319(f227(a1),f2(a1)),x74762))+~P1(f319(f319(f226(a1),x74762),x74761))+P1(f319(f319(f227(a1),f2(a1)),f319(f319(f30(a1),x74761),x74762)))
% 28.73/28.53 [7879]~E(x78792,f2(a1))+E(f207(x78791,x78792),f319(f319(f244(a1,a1),f2(a1)),f72(a1)))+P1(f319(f319(f227(a1),x78792),f2(a1)))+~P1(f319(f307(f931(a1,a1),a213),f319(f319(f244(a1,a1),x78791),x78792)))
% 28.73/28.53 [7880]~E(x78801,f2(a1))+E(f207(x78801,x78802),f319(f319(f244(a1,a1),f2(a1)),f72(a1)))+P1(f319(f319(f227(a1),x78802),f2(a1)))+~P1(f319(f307(f931(a1,a1),a213),f319(f319(f244(a1,a1),x78801),x78802)))
% 28.73/28.53 [8913]~P42(x89132)+~P42(x89131)+P1(f319(f319(f226(f932(a925,a923)),f319(f302(a1,a925,a96),x89131)),f319(f302(a1,a925,a96),x89132)))+~P1(f319(f319(f226(f932(a1,a923)),x89131),x89132))
% 28.73/28.53 [8914]~P42(x89142)+~P42(x89141)+P1(f319(f319(f227(f932(a925,a923)),f319(f302(a1,a925,a96),x89141)),f319(f302(a1,a925,a96),x89142)))+~P1(f319(f319(f227(f932(a1,a923)),x89141),x89142))
% 28.73/28.53 [9149]~E(f750(x91492,x91491),f751(x91492,x91491))+~P1(f319(f129(x91491),f752(x91492,x91491)))+~P1(f319(f129(f926(x91491)),x91492))+P1(f319(f129(x91491),f319(f134(f926(x91491),f926(x91491),f126(x91491),f105(x91491)),x91492)))
% 28.73/28.53 [9238]~P42(x92382)+~P42(x92381)+~P1(f319(f319(f226(f932(a925,a923)),f319(f302(a1,a925,a96),x92381)),f319(f302(a1,a925,a96),x92382)))+P1(f319(f319(f226(f932(a1,a923)),x92381),x92382))
% 28.73/28.53 [9239]~P42(x92392)+~P42(x92391)+~P1(f319(f319(f227(f932(a925,a923)),f319(f302(a1,a925,a96),x92391)),f319(f302(a1,a925,a96),x92392)))+P1(f319(f319(f227(f932(a1,a923)),x92391),x92392))
% 28.73/28.53 [9245]~E(f750(x92452,x92451),f751(x92452,x92451))+~P1(f319(f129(f926(x92451)),x92452))+P1(f319(f129(x92451),f319(f134(f926(x92451),f926(x92451),f126(x92451),f105(x92451)),x92452)))+P1(f319(f319(f321(f926(x92451)),f752(x92452,x92451)),f319(f164(f926(x92451)),x92452)))
% 28.73/28.53 [9287]~P1(f319(f129(x92871),f752(x92872,x92871)))+~P1(f319(f129(f926(x92871)),x92872))+P1(f319(f129(x92871),f319(f134(f926(x92871),f926(x92871),f126(x92871),f105(x92871)),x92872)))+P1(f319(f319(f321(f926(x92871)),f751(x92872,x92871)),f319(f164(f926(x92871)),x92872)))
% 28.73/28.53 [9288]~P1(f319(f129(x92881),f752(x92882,x92881)))+~P1(f319(f129(f926(x92881)),x92882))+P1(f319(f129(x92881),f319(f134(f926(x92881),f926(x92881),f126(x92881),f105(x92881)),x92882)))+P1(f319(f319(f321(f926(x92881)),f750(x92882,x92881)),f319(f164(f926(x92881)),x92882)))
% 28.73/28.53 [9366]~P1(f319(f129(f926(x93661)),x93662))+P1(f319(f129(x93661),f319(f134(f926(x93661),f926(x93661),f126(x93661),f105(x93661)),x93662)))+P1(f319(f319(f321(f926(x93661)),f751(x93662,x93661)),f319(f164(f926(x93661)),x93662)))+P1(f319(f319(f321(f926(x93661)),f752(x93662,x93661)),f319(f164(f926(x93661)),x93662)))
% 28.73/28.53 [9367]~P1(f319(f129(f926(x93671)),x93672))+P1(f319(f129(x93671),f319(f134(f926(x93671),f926(x93671),f126(x93671),f105(x93671)),x93672)))+P1(f319(f319(f321(f926(x93671)),f750(x93672,x93671)),f319(f164(f926(x93671)),x93672)))+P1(f319(f319(f321(f926(x93671)),f752(x93672,x93671)),f319(f164(f926(x93671)),x93672)))
% 28.73/28.53 [9381]~E(f319(f319(f93(f932(x93811,a923)),f319(f164(x93811),f751(x93812,x93811))),f319(f164(x93811),f750(x93812,x93811))),f180(f932(x93811,a923)))+~P1(f319(f129(x93811),f752(x93812,x93811)))+~P1(f319(f129(f926(x93811)),x93812))+P1(f319(f129(x93811),f319(f134(f926(x93811),f926(x93811),f126(x93811),f105(x93811)),x93812)))
% 28.73/28.53 [9446]~E(f319(f319(f93(f932(x94461,a923)),f319(f164(x94461),f751(x94462,x94461))),f319(f164(x94461),f750(x94462,x94461))),f180(f932(x94461,a923)))+~P1(f319(f129(f926(x94461)),x94462))+P1(f319(f129(x94461),f319(f134(f926(x94461),f926(x94461),f126(x94461),f105(x94461)),x94462)))+P1(f319(f319(f321(f926(x94461)),f752(x94462,x94461)),f319(f164(f926(x94461)),x94462)))
% 28.73/28.53 [9725]E(x97251,f2(a1))+E(x97252,f2(a1))+E(f319(f319(f80(a1,f931(a1,a1)),f319(f319(a209,x97252),x97251)),f319(f319(f18(a1,a1,f931(a1,a1)),f319(f319(f8(a1,f932(a1,f931(a1,a1)),a1),f244(a1,a1)),f319(f30(a1),x97252))),f319(f30(a1),x97251))),f207(x97252,x97251))+P1(f319(f319(f227(a1),x97251),f2(a1)))
% 28.73/28.53 [8452]~P99(x84522)+~P126(x84522)+~P1(f319(f319(f226(x84522),f319(f95(x84522),x84521)),f72(x84522)))+P1(f319(f319(f226(a1),x84521),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))
% 28.73/28.53 [8453]~P99(x84532)+~P126(x84532)+~P1(f319(f319(f227(x84532),f319(f95(x84532),x84531)),f72(x84532)))+P1(f319(f319(f227(a1),x84531),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))
% 28.73/28.53 [8730]~P126(x87301)+~P99(x87301)+P1(f319(f319(f226(x87301),f319(f95(x87301),x87302)),f72(x87301)))+~P1(f319(f319(f226(a1),x87302),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))
% 28.73/28.53 [8731]~P126(x87311)+~P99(x87311)+P1(f319(f319(f227(x87311),f319(f95(x87311),x87312)),f72(x87311)))+~P1(f319(f319(f227(a1),x87312),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))
% 28.73/28.53 [8942]~P99(x89422)+~P126(x89422)+~P1(f319(f319(f226(x89422),f72(x89422)),f319(f95(x89422),x89421)))+P1(f319(f319(f226(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),x89421))
% 28.73/28.53 [8943]~P99(x89432)+~P126(x89432)+~P1(f319(f319(f227(x89432),f72(x89432)),f319(f95(x89432),x89431)))+P1(f319(f319(f227(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),x89431))
% 28.73/28.53 [9325]~P126(x93251)+~P99(x93251)+P1(f319(f319(f226(x93251),f72(x93251)),f319(f95(x93251),x93252)))+~P1(f319(f319(f226(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),x93252))
% 28.73/28.53 [9326]~P126(x93261)+~P99(x93261)+P1(f319(f319(f227(x93261),f72(x93261)),f319(f95(x93261),x93262)))+~P1(f319(f319(f227(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),x93262))
% 28.73/28.53 [9857]~P144(x98572)+E(x98571,f72(x98572))+E(x98571,f319(f73(x98572),f72(x98572)))+~E(f319(f319(f236(x98572),x98571),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),f72(x98572))
% 28.73/28.53 [10144]~P74(x101441)+~P99(x101441)+~P1(f319(f319(f227(x101441),f2(x101441)),x101442))+P1(f319(f319(f227(x101441),f2(x101441)),f319(f319(f283(x101441),x101442),f319(f95(x101441),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))))))
% 28.73/28.53 [10145]~P74(x101451)+~P99(x101451)+~P1(f319(f319(f227(x101451),f2(x101451)),x101452))+P1(f319(f319(f227(x101451),f2(x101451)),f319(f319(f283(x101451),x101452),f319(f95(x101451),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))))))
% 28.73/28.53 [10200]~P74(x102001)+~P99(x102001)+P1(f319(f319(f227(x102001),f2(x102001)),x102002))+~P1(f319(f319(f227(x102001),f2(x102001)),f319(f319(f283(x102001),x102002),f319(f95(x102001),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))))))
% 28.73/28.53 [10495]~P145(x104952)+E(x104951,f2(a1))+P1(f319(f319(f227(a1),x104951),f2(a1)))+E(f319(f319(f249(a1,a1,x104952),f319(f319(f7(a1,f932(a1,f932(x104952,x104952)),f932(a1,x104952)),f319(f319(f8(f932(f932(x104952,x104952),x104952),f932(f932(a1,f932(x104952,x104952)),f932(a1,x104952)),a1),f8(f932(x104952,x104952),x104952,a1)),f319(f319(f8(x104952,f932(f932(x104952,x104952),x104952),a1),f80(x104952,x104952)),f94(x104952)))),f319(f319(f7(a1,f932(x104952,x104952),f932(x104952,x104952)),f319(f319(f8(f932(x104952,f932(x104952,x104952)),f932(f932(x104952,x104952),f932(x104952,x104952)),a1),f18(x104952,x104952,x104952)),f319(f319(f7(a1,f932(x104952,x104952),f932(x104952,f932(x104952,x104952))),f319(f319(f8(f932(x104952,f932(x104952,x104952)),f932(f932(x104952,x104952),f932(x104952,f932(x104952,x104952))),a1),f8(x104952,f932(x104952,x104952),x104952)),f319(f319(f8(a923,f932(x104952,f932(x104952,x104952)),a1),f86(x104952)),f319(f319(f7(a1,a1,a923),a316),f2(a1))))),f319(f319(f18(x104952,x104952,x104952),f74(x104952)),f5(x104952))))),f319(f319(f7(x104952,x104952,x104952),f319(f319(f8(x104952,f932(x104952,x104952),x104952),f74(x104952)),f319(f319(f18(x104952,x104952,x104952),f74(x104952)),f5(x104952)))),f72(x104952))))),f40(x104951,f319(f95(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))))),f319(f94(x104952),x104951))
% 28.73/28.53 [10244]P1(f319(f319(f226(a1),x102441),f2(a1)))+P1(f319(f319(f227(a1),x102442),x102441))+~P1(f319(f307(f931(a1,a1),a52),f319(f319(f244(a1,a1),x102442),x102441)))+E(f319(f37(x102441),f41(x102442,f319(f319(f75(a1),f319(f95(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),x102441))),f41(x102442,x102441))
% 28.73/28.53 [10248]P1(f319(f319(f226(a1),x102481),f2(a1)))+~P1(f319(f307(f931(a1,a1),a46),f319(f319(f244(a1,a1),x102482),x102481)))+P1(f319(f319(f226(a1),f2(a1)),f319(f319(f74(a1),x102482),x102481)))+E(f319(f37(x102481),f44(x102482,f319(f319(f75(a1),f319(f95(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),x102481))),f44(x102482,x102481))
% 28.73/28.53 [5406]~P113(x54061)+~P113(x54062)+~P51(x54061,x54062,x54063)+P41(x54061,x54062,x54063)
% 28.73/28.53 [5533]~P39(x55331,x55333)+~P56(x55331,x55333)+~P57(x55331,x55332,x55333)+P9(x55331,x55332,x55333)
% 28.73/28.53 [5534]~P39(x55341,x55343)+~P56(x55341,x55343)+~P57(x55341,x55342,x55343)+P9(x55341,x55342,x55343)
% 28.73/28.53 [5298]~P6(x52983)+~P41(x52983,x52983,x52981)+E(f319(x52981,x52982),x52982)+~E(x52982,f88(x52983,x52981))
% 28.73/28.53 [5299]~P6(x52993)+~P41(x52993,x52993,x52991)+E(f319(x52991,x52992),x52992)+~E(x52992,f87(x52993,x52991))
% 28.73/28.53 [5072]~P98(x50723)+~P99(x50723)+E(x50721,x50722)+~E(f319(f95(x50723),x50721),f319(f95(x50723),x50722))
% 28.73/28.53 [5543]~P54(x55431,x55432)+~P55(x55431,x55432)+P17(x55431,x55432)+~P1(f319(f319(x55432,x55433),x55433))
% 28.73/28.53 [5544]~P54(x55441,x55442)+~P55(x55441,x55442)+P17(x55441,x55442)+~P1(f319(f319(x55442,x55443),x55443))
% 28.73/28.53 [6039]P17(x60392,x60391)+E(f319(x60391,f827(x60391)),f319(x60391,f828(x60391)))+P1(f319(f319(x60391,f827(x60391)),f828(x60391)))+~P1(f319(f319(x60391,x60393),x60393))
% 28.73/28.53 [6072]~P113(x60721)+E(f230(x60721,x60722),x60723)+~P1(f319(x60722,x60723))+P1(f319(x60722,f334(x60723,x60722,x60721)))
% 28.73/28.53 [6248]~P1(f319(x62481,x62482))+~P1(f319(x62481,x62483))+~P1(f319(f319(f226(a925),x62483),f440(x62482,x62481)))+P1(f319(x62481,f2(a925)))
% 28.73/28.53 [6313]P17(x63131,x63132)+P1(f319(f319(x63132,f827(x63132)),f827(x63132)))+P1(f319(f319(x63132,f827(x63132)),f828(x63132)))+~P1(f319(f319(x63132,x63133),x63133))
% 28.73/28.53 [6314]P17(x63141,x63142)+P1(f319(f319(x63142,f827(x63142)),f828(x63142)))+P1(f319(f319(x63142,f828(x63142)),f828(x63142)))+~P1(f319(f319(x63142,x63143),x63143))
% 28.73/28.53 [6668]P152(x66682,x66681,x66683)+E(x66681,f2(a1))+P1(f319(f319(f226(a1),f2(a1)),f868(x66683,x66681,x66682)))+P1(f319(f319(f227(a1),x66681),f2(a1)))
% 28.73/28.53 [6669]P151(x66692,x66691,x66693)+E(x66691,f2(a1))+P1(f319(f319(f226(a1),f2(a1)),f874(x66693,x66691,x66692)))+P1(f319(f319(f227(a1),x66691),f2(a1)))
% 28.73/28.53 [6793]P151(x67931,x67932,x67933)+~P1(f319(x67931,x67933))+P1(f319(f319(f226(a1),f2(a1)),f874(x67933,x67932,x67931)))+P1(f319(f319(f227(a1),x67932),f2(a1)))
% 28.73/28.53 [6822]P152(x68221,x68222,x68223)+P1(f319(f319(f226(a1),f2(a1)),f868(x68223,x68222,x68221)))+~P1(f319(x68221,f2(a1)))+P1(f319(f319(f227(a1),x68222),f2(a1)))
% 28.73/28.53 [6852]P152(x68522,x68521,x68523)+E(x68521,f2(a1))+~P1(f319(x68522,f869(x68523,x68521,x68522)))+P1(f319(f319(f227(a1),x68521),f2(a1)))
% 28.73/28.53 [6853]P151(x68532,x68531,x68533)+E(x68531,f2(a1))+~P1(f319(x68532,f874(x68533,x68531,x68532)))+P1(f319(f319(f227(a1),x68531),f2(a1)))
% 28.73/28.53 [6937]~P113(x69371)+E(f230(x69371,x69372),x69373)+~P1(f319(x69372,x69373))+~P1(f319(f319(f226(x69371),x69373),f334(x69373,x69372,x69371)))
% 28.73/28.53 [6955]~P4(x69551)+~P6(x69551)+~P1(f319(f319(f227(x69551),x69552),f31(x69551,x69553)))+P1(f319(f319(f227(x69551),x69552),f879(x69553,x69552,x69551)))
% 28.73/28.53 [6965]P151(x69651,x69652,x69653)+~P1(f319(x69651,x69653))+~P1(f319(x69651,f874(x69653,x69652,x69651)))+P1(f319(f319(f227(a1),x69652),f2(a1)))
% 28.73/28.53 [6995]P152(x69951,x69952,x69953)+~P1(f319(x69951,f869(x69953,x69952,x69951)))+~P1(f319(x69951,f2(a1)))+P1(f319(f319(f227(a1),x69952),f2(a1)))
% 28.73/28.53 [7244]P152(x72442,x72441,x72443)+E(x72441,f2(a1))+P1(f319(f319(f226(a1),f2(a1)),f868(x72443,x72441,x72442)))+P1(f319(f319(f227(a1),x72441),f867(x72443,x72441,x72442)))
% 28.73/28.53 [7245]P151(x72452,x72451,x72453)+E(x72451,f2(a1))+P1(f319(f319(f226(a1),f2(a1)),f874(x72453,x72451,x72452)))+P1(f319(f319(f227(a1),x72451),f878(x72453,x72451,x72452)))
% 28.73/28.53 [7366]P151(x73661,x73662,x73663)+~P1(f319(x73661,x73663))+P1(f319(f319(f226(a1),f2(a1)),f874(x73663,x73662,x73661)))+P1(f319(f319(f227(a1),x73662),f878(x73663,x73662,x73661)))
% 28.73/28.53 [7387]P152(x73871,x73872,x73873)+P1(f319(f319(f226(a1),f2(a1)),f868(x73873,x73872,x73871)))+P1(f319(f319(f227(a1),x73872),f867(x73873,x73872,x73871)))+~P1(f319(x73871,f2(a1)))
% 28.73/28.53 [7419]P152(x74192,x74191,x74193)+E(x74191,f2(a1))+~P1(f319(x74192,f869(x74193,x74191,x74192)))+P1(f319(f319(f227(a1),x74191),f867(x74193,x74191,x74192)))
% 28.73/28.53 [7420]P151(x74202,x74201,x74203)+E(x74201,f2(a1))+~P1(f319(x74202,f874(x74203,x74201,x74202)))+P1(f319(f319(f227(a1),x74201),f878(x74203,x74201,x74202)))
% 28.73/28.53 [7465]P152(x74652,x74651,x74653)+E(x74651,f2(a1))+P1(f319(f319(f226(a1),f2(a1)),f868(x74653,x74651,x74652)))+~P1(f319(x74652,f873(x74653,x74651,x74652)))
% 28.73/28.53 [7466]P151(x74662,x74661,x74663)+E(x74661,f2(a1))+P1(f319(f319(f226(a1),f2(a1)),f874(x74663,x74661,x74662)))+~P1(f319(x74662,f878(x74663,x74661,x74662)))
% 28.73/28.53 [7560]P151(x75601,x75602,x75603)+~P1(f319(x75601,x75603))+~P1(f319(x75601,f874(x75603,x75602,x75601)))+P1(f319(f319(f227(a1),x75602),f878(x75603,x75602,x75601)))
% 28.73/28.53 [7575]P152(x75751,x75752,x75753)+~P1(f319(x75751,f869(x75753,x75752,x75751)))+P1(f319(f319(f227(a1),x75752),f867(x75753,x75752,x75751)))+~P1(f319(x75751,f2(a1)))
% 28.73/28.53 [7578]P151(x75781,x75782,x75783)+~P1(f319(x75781,x75783))+P1(f319(f319(f226(a1),f2(a1)),f874(x75783,x75782,x75781)))+~P1(f319(x75781,f878(x75783,x75782,x75781)))
% 28.73/28.53 [7594]P152(x75941,x75942,x75943)+P1(f319(f319(f226(a1),f2(a1)),f868(x75943,x75942,x75941)))+~P1(f319(x75941,f873(x75943,x75942,x75941)))+~P1(f319(x75941,f2(a1)))
% 28.73/28.53 [7616]P152(x76162,x76161,x76163)+E(x76161,f2(a1))+~P1(f319(x76162,f869(x76163,x76161,x76162)))+~P1(f319(x76162,f873(x76163,x76161,x76162)))
% 28.73/28.53 [7617]P151(x76172,x76171,x76173)+E(x76171,f2(a1))+~P1(f319(x76172,f874(x76173,x76171,x76172)))+~P1(f319(x76172,f878(x76173,x76171,x76172)))
% 28.73/28.53 [7702]P151(x77021,x77022,x77023)+~P1(f319(x77021,x77023))+~P1(f319(x77021,f874(x77023,x77022,x77021)))+~P1(f319(x77021,f878(x77023,x77022,x77021)))
% 28.73/28.53 [7719]P152(x77191,x77192,x77193)+~P1(f319(x77191,f869(x77193,x77192,x77191)))+~P1(f319(x77191,f873(x77193,x77192,x77191)))+~P1(f319(x77191,f2(a1)))
% 28.73/28.53 [7763]P152(x77632,x77631,x77633)+E(x77631,f2(a1))+P1(f319(f319(f226(a1),f2(a1)),f868(x77633,x77631,x77632)))+P1(f319(f319(f226(a1),f867(x77633,x77631,x77632)),f2(a1)))
% 28.73/28.53 [7764]P151(x77642,x77641,x77643)+E(x77641,f2(a1))+P1(f319(f319(f226(a1),f2(a1)),f874(x77643,x77641,x77642)))+P1(f319(f319(f226(a1),f878(x77643,x77641,x77642)),f2(a1)))
% 28.73/28.53 [7765]~P93(x77651)+~P1(f319(f319(f226(x77651),x77653),f2(x77651)))+~P1(f319(f319(f226(x77651),x77652),f2(x77651)))+P1(f319(f319(f226(x77651),f319(f319(f74(x77651),x77652),x77653)),f2(x77651)))
% 28.73/28.53 [7766]~P145(x77661)+~P1(f319(f319(f321(x77661),x77663),f101(x77661)))+~P1(f319(f319(f321(x77661),x77662),f101(x77661)))+P1(f319(f319(f321(x77661),f319(f319(f23(x77661),x77662),x77663)),f101(x77661)))
% 28.73/28.53 [7767]~P145(x77671)+~P1(f319(f319(f321(x77671),x77673),f101(x77671)))+~P1(f319(f319(f321(x77671),x77672),f101(x77671)))+P1(f319(f319(f321(x77671),f319(f319(f75(x77671),x77672),x77673)),f101(x77671)))
% 28.73/28.53 [7768]~P149(x77681)+~P1(f319(f319(f321(x77681),x77683),f178(x77681)))+~P1(f319(f319(f321(x77681),x77682),f178(x77681)))+P1(f319(f319(f321(x77681),f319(f319(f75(x77681),x77682),x77683)),f178(x77681)))
% 28.73/28.53 [7769]~P145(x77691)+~P1(f319(f319(f321(x77691),x77693),f101(x77691)))+~P1(f319(f319(f321(x77691),x77692),f101(x77691)))+P1(f319(f319(f321(x77691),f319(f319(f74(x77691),x77692),x77693)),f101(x77691)))
% 28.73/28.53 [7770]~P149(x77701)+~P1(f319(f319(f321(x77701),x77703),f178(x77701)))+~P1(f319(f319(f321(x77701),x77702),f178(x77701)))+P1(f319(f319(f321(x77701),f319(f319(f74(x77701),x77702),x77703)),f178(x77701)))
% 28.73/28.53 [7771]~P93(x77711)+~P1(f319(f319(f226(x77711),x77713),f2(x77711)))+~P1(f319(f319(f227(x77711),x77712),f2(x77711)))+P1(f319(f319(f227(x77711),f319(f319(f74(x77711),x77712),x77713)),f2(x77711)))
% 28.73/28.53 [7772]~P93(x77721)+~P1(f319(f319(f226(x77721),x77722),f2(x77721)))+~P1(f319(f319(f227(x77721),x77723),f2(x77721)))+P1(f319(f319(f227(x77721),f319(f319(f74(x77721),x77722),x77723)),f2(x77721)))
% 28.73/28.53 [7773]~P93(x77731)+~P1(f319(f319(f227(x77731),x77733),f2(x77731)))+~P1(f319(f319(f227(x77731),x77732),f2(x77731)))+P1(f319(f319(f227(x77731),f319(f319(f74(x77731),x77732),x77733)),f2(x77731)))
% 28.73/28.53 [7800]P152(x78003,x78001,x78002)+E(x78001,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x78001),f869(x78002,x78001,x78003))),f868(x78002,x78001,x78003)),x78002)+P1(f319(f319(f227(a1),x78001),f2(a1)))
% 28.73/28.53 [7801]P151(x78013,x78011,x78012)+E(x78011,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x78011),f875(x78012,x78011,x78013))),f874(x78012,x78011,x78013)),x78012)+P1(f319(f319(f227(a1),x78011),f2(a1)))
% 28.73/28.53 [7884]P151(x78841,x78842,x78843)+~P1(f319(x78841,x78843))+P1(f319(f319(f226(a1),f2(a1)),f874(x78843,x78842,x78841)))+P1(f319(f319(f226(a1),f878(x78843,x78842,x78841)),f2(a1)))
% 28.73/28.53 [7914]P152(x79141,x79142,x79143)+P1(f319(f319(f226(a1),f2(a1)),f868(x79143,x79142,x79141)))+~P1(f319(x79141,f2(a1)))+P1(f319(f319(f226(a1),f867(x79143,x79142,x79141)),f2(a1)))
% 28.73/28.53 [7923]P151(x79233,x79231,x79232)+~P1(f319(x79233,x79232))+E(f319(f319(f74(a1),f319(f319(f75(a1),x79231),f875(x79232,x79231,x79233))),f874(x79232,x79231,x79233)),x79232)+P1(f319(f319(f227(a1),x79231),f2(a1)))
% 28.73/28.53 [7929]P152(x79292,x79291,x79293)+E(x79291,f2(a1))+~P1(f319(x79292,f869(x79293,x79291,x79292)))+P1(f319(f319(f226(a1),f867(x79293,x79291,x79292)),f2(a1)))
% 28.73/28.53 [7930]P151(x79302,x79301,x79303)+E(x79301,f2(a1))+~P1(f319(x79302,f874(x79303,x79301,x79302)))+P1(f319(f319(f226(a1),f878(x79303,x79301,x79302)),f2(a1)))
% 28.73/28.53 [7935]P152(x79353,x79351,x79352)+E(f319(f319(f74(a1),f319(f319(f75(a1),x79351),f869(x79352,x79351,x79353))),f868(x79352,x79351,x79353)),x79352)+~P1(f319(x79353,f2(a1)))+P1(f319(f319(f227(a1),x79351),f2(a1)))
% 28.73/28.53 [7991]P151(x79911,x79912,x79913)+~P1(f319(x79911,x79913))+~P1(f319(x79911,f874(x79913,x79912,x79911)))+P1(f319(f319(f226(a1),f878(x79913,x79912,x79911)),f2(a1)))
% 28.73/28.53 [7995]P152(x79951,x79952,x79953)+~P1(f319(x79951,f869(x79953,x79952,x79951)))+~P1(f319(x79951,f2(a1)))+P1(f319(f319(f226(a1),f867(x79953,x79952,x79951)),f2(a1)))
% 28.73/28.53 [8064]~P130(x80641)+~P1(f319(f319(f226(x80641),f319(f319(f75(x80641),x80643),x80642)),f2(x80641)))+P1(f319(f319(f226(x80641),x80642),f2(x80641)))+P1(f319(f319(f226(x80641),x80643),f2(x80641)))
% 28.73/28.53 [8065]~P74(x80651)+~P1(f319(f319(f226(x80651),f319(f319(f283(x80651),x80653),x80652)),f2(x80651)))+P1(f319(f319(f226(x80651),x80652),f2(x80651)))+P1(f319(f319(f226(x80651),x80653),f2(x80651)))
% 28.73/28.53 [8066]~P74(x80661)+~P1(f319(f319(f227(x80661),f319(f319(f283(x80661),x80663),x80662)),f2(x80661)))+P1(f319(f319(f227(x80661),x80662),f2(x80661)))+P1(f319(f319(f227(x80661),x80663),f2(x80661)))
% 28.73/28.53 [8180]P152(x81803,x81801,x81802)+E(x81801,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x81801),f869(x81802,x81801,x81803))),f868(x81802,x81801,x81803)),x81802)+P1(f319(f319(f227(a1),x81801),f867(x81802,x81801,x81803)))
% 28.73/28.53 [8181]P151(x81813,x81811,x81812)+E(x81811,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x81811),f875(x81812,x81811,x81813))),f874(x81812,x81811,x81813)),x81812)+P1(f319(f319(f227(a1),x81811),f878(x81812,x81811,x81813)))
% 28.73/28.53 [8194]P152(x81943,x81941,x81942)+E(x81941,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x81941),f873(x81942,x81941,x81943))),f867(x81942,x81941,x81943)),x81942)+P1(f319(f319(f226(a1),f2(a1)),f868(x81942,x81941,x81943)))
% 28.73/28.53 [8195]P151(x81953,x81951,x81952)+E(x81951,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x81951),f876(x81952,x81951,x81953))),f878(x81952,x81951,x81953)),x81952)+P1(f319(f319(f226(a1),f2(a1)),f874(x81952,x81951,x81953)))
% 28.73/28.53 [8238]P151(x82383,x82381,x82382)+~P1(f319(x82383,x82382))+E(f319(f319(f74(a1),f319(f319(f75(a1),x82381),f875(x82382,x82381,x82383))),f874(x82382,x82381,x82383)),x82382)+P1(f319(f319(f227(a1),x82381),f878(x82382,x82381,x82383)))
% 28.73/28.53 [8247]P152(x82473,x82471,x82472)+E(f319(f319(f74(a1),f319(f319(f75(a1),x82471),f869(x82472,x82471,x82473))),f868(x82472,x82471,x82473)),x82472)+P1(f319(f319(f227(a1),x82471),f867(x82472,x82471,x82473)))+~P1(f319(x82473,f2(a1)))
% 28.73/28.53 [8253]P151(x82533,x82531,x82532)+~P1(f319(x82533,x82532))+E(f319(f319(f74(a1),f319(f319(f75(a1),x82531),f876(x82532,x82531,x82533))),f878(x82532,x82531,x82533)),x82532)+P1(f319(f319(f226(a1),f2(a1)),f874(x82532,x82531,x82533)))
% 28.73/28.53 [8259]P152(x82593,x82591,x82592)+E(f319(f319(f74(a1),f319(f319(f75(a1),x82591),f873(x82592,x82591,x82593))),f867(x82592,x82591,x82593)),x82592)+P1(f319(f319(f226(a1),f2(a1)),f868(x82592,x82591,x82593)))+~P1(f319(x82593,f2(a1)))
% 28.73/28.53 [8270]P152(x82703,x82701,x82702)+E(x82701,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x82701),f869(x82702,x82701,x82703))),f868(x82702,x82701,x82703)),x82702)+~P1(f319(x82703,f873(x82702,x82701,x82703)))
% 28.73/28.53 [8271]P151(x82713,x82711,x82712)+E(x82711,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x82711),f875(x82712,x82711,x82713))),f874(x82712,x82711,x82713)),x82712)+~P1(f319(x82713,f878(x82712,x82711,x82713)))
% 28.73/28.53 [8272]P152(x82723,x82721,x82722)+E(x82721,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x82721),f873(x82722,x82721,x82723))),f867(x82722,x82721,x82723)),x82722)+~P1(f319(x82723,f869(x82722,x82721,x82723)))
% 28.73/28.53 [8273]P151(x82733,x82731,x82732)+E(x82731,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x82731),f876(x82732,x82731,x82733))),f878(x82732,x82731,x82733)),x82732)+~P1(f319(x82733,f874(x82732,x82731,x82733)))
% 28.73/28.53 [8332]P151(x83323,x83321,x83322)+~P1(f319(x83323,x83322))+E(f319(f319(f74(a1),f319(f319(f75(a1),x83321),f875(x83322,x83321,x83323))),f874(x83322,x83321,x83323)),x83322)+~P1(f319(x83323,f878(x83322,x83321,x83323)))
% 28.73/28.53 [8333]P151(x83333,x83331,x83332)+~P1(f319(x83333,x83332))+E(f319(f319(f74(a1),f319(f319(f75(a1),x83331),f876(x83332,x83331,x83333))),f878(x83332,x83331,x83333)),x83332)+~P1(f319(x83333,f874(x83332,x83331,x83333)))
% 28.73/28.53 [8346]P152(x83463,x83461,x83462)+E(f319(f319(f74(a1),f319(f319(f75(a1),x83461),f869(x83462,x83461,x83463))),f868(x83462,x83461,x83463)),x83462)+~P1(f319(x83463,f873(x83462,x83461,x83463)))+~P1(f319(x83463,f2(a1)))
% 28.73/28.53 [8347]P152(x83473,x83471,x83472)+E(f319(f319(f74(a1),f319(f319(f75(a1),x83471),f873(x83472,x83471,x83473))),f867(x83472,x83471,x83473)),x83472)+~P1(f319(x83473,f869(x83472,x83471,x83473)))+~P1(f319(x83473,f2(a1)))
% 28.73/28.53 [8445]P152(x84453,x84451,x84452)+E(x84451,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x84451),f869(x84452,x84451,x84453))),f868(x84452,x84451,x84453)),x84452)+P1(f319(f319(f226(a1),f867(x84452,x84451,x84453)),f2(a1)))
% 28.73/28.53 [8446]P151(x84463,x84461,x84462)+E(x84461,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x84461),f875(x84462,x84461,x84463))),f874(x84462,x84461,x84463)),x84462)+P1(f319(f319(f226(a1),f878(x84462,x84461,x84463)),f2(a1)))
% 28.73/28.53 [8486]P151(x84863,x84861,x84862)+~P1(f319(x84863,x84862))+E(f319(f319(f74(a1),f319(f319(f75(a1),x84861),f875(x84862,x84861,x84863))),f874(x84862,x84861,x84863)),x84862)+P1(f319(f319(f226(a1),f878(x84862,x84861,x84863)),f2(a1)))
% 28.73/28.53 [8491]P152(x84913,x84911,x84912)+E(f319(f319(f74(a1),f319(f319(f75(a1),x84911),f869(x84912,x84911,x84913))),f868(x84912,x84911,x84913)),x84912)+~P1(f319(x84913,f2(a1)))+P1(f319(f319(f226(a1),f867(x84912,x84911,x84913)),f2(a1)))
% 28.73/28.53 [8627]P152(x86273,x86271,x86272)+E(x86271,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x86271),f873(x86272,x86271,x86273))),f867(x86272,x86271,x86273)),x86272)+E(f319(f319(f74(a1),f319(f319(f75(a1),x86271),f869(x86272,x86271,x86273))),f868(x86272,x86271,x86273)),x86272)
% 28.73/28.53 [8628]P151(x86283,x86281,x86282)+E(x86281,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x86281),f876(x86282,x86281,x86283))),f878(x86282,x86281,x86283)),x86282)+E(f319(f319(f74(a1),f319(f319(f75(a1),x86281),f875(x86282,x86281,x86283))),f874(x86282,x86281,x86283)),x86282)
% 28.73/28.53 [8648]P151(x86483,x86481,x86482)+~P1(f319(x86483,x86482))+E(f319(f319(f74(a1),f319(f319(f75(a1),x86481),f876(x86482,x86481,x86483))),f878(x86482,x86481,x86483)),x86482)+E(f319(f319(f74(a1),f319(f319(f75(a1),x86481),f875(x86482,x86481,x86483))),f874(x86482,x86481,x86483)),x86482)
% 28.73/28.53 [8659]P152(x86593,x86591,x86592)+E(f319(f319(f74(a1),f319(f319(f75(a1),x86591),f873(x86592,x86591,x86593))),f867(x86592,x86591,x86593)),x86592)+E(f319(f319(f74(a1),f319(f319(f75(a1),x86591),f869(x86592,x86591,x86593))),f868(x86592,x86591,x86593)),x86592)+~P1(f319(x86593,f2(a1)))
% 28.73/28.53 [9334]~P130(x93341)+~E(x93343,f2(x93341))+~E(x93342,f2(x93341))+P1(f319(f319(f226(x93341),f319(f319(f74(x93341),f319(f319(f75(x93341),x93342),x93342)),f319(f319(f75(x93341),x93343),x93343))),f2(x93341)))
% 28.73/28.53 [10433]~P126(x104331)+~E(x104333,f2(x104331))+~E(x104332,f2(x104331))+P1(f319(f319(f226(x104331),f319(f319(f74(x104331),f319(f319(f236(x104331),x104332),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))))),f319(f319(f236(x104331),x104333),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))))),f2(x104331)))
% 28.73/28.53 [5020]~E(x50203,x50201)+~P124(x50202)+E(x50201,f2(x50202))+E(f319(f319(f283(x50202),x50203),x50201),f72(x50202))
% 28.73/28.53 [5073]~P104(x50731)+~E(x50733,f180(x50731))+~E(x50732,f180(x50731))+E(f319(f319(f102(x50731),x50732),x50733),f180(x50731))
% 28.73/28.53 [5074]~P103(x50741)+~E(x50743,f234(x50741))+~E(x50742,f234(x50741))+E(f319(f319(f93(x50741),x50742),x50743),f234(x50741))
% 28.73/28.53 [5168]~P124(x51683)+E(x51681,x51682)+E(x51682,f2(x51683))+~E(f319(f319(f283(x51683),x51681),x51682),f72(x51683))
% 28.73/28.53 [5185]~P147(x51852)+E(x51851,f2(x51852))+E(x51853,f2(x51852))+~E(f319(f319(f75(x51852),x51853),x51851),f2(x51852))
% 28.73/28.53 [5186]~P138(x51862)+E(x51861,f2(x51862))+E(x51863,f2(x51862))+~E(f319(f319(f75(x51862),x51863),x51861),f2(x51862))
% 28.73/28.53 [5187]~P138(x51872)+E(x51871,f2(x51872))+E(x51873,f2(x51872))+~E(f319(f319(f75(x51872),x51873),x51871),f2(x51872))
% 28.73/28.53 [5563]~P117(x55633)+E(x55631,x55632)+E(x55631,f319(f73(x55633),x55632))+~E(f319(f319(f75(x55633),x55631),x55631),f319(f319(f75(x55633),x55632),x55632))
% 28.73/28.53 [5602]~P96(x56021)+E(f319(f73(x56021),x56022),x56023)+~E(f319(f319(f102(x56021),x56022),x56023),f234(x56021))+~E(f319(f319(f93(x56021),x56022),x56023),f180(x56021))
% 28.73/28.53 [5676]~P4(x56763)+E(x56761,x56762)+P1(f319(f319(f227(x56763),x56762),x56761))+P1(f319(f319(f227(x56763),x56761),x56762))
% 28.73/28.53 [5677]~P4(x56773)+E(x56771,x56772)+P1(f319(f319(f227(x56773),x56772),x56771))+P1(f319(f319(f227(x56773),x56771),x56772))
% 28.73/28.53 [5678]~P4(x56783)+E(x56781,x56782)+P1(f319(f319(f227(x56783),x56782),x56781))+P1(f319(f319(f227(x56783),x56781),x56782))
% 28.73/28.53 [5679]~P4(x56793)+E(x56791,x56792)+P1(f319(f319(f227(x56793),x56792),x56791))+P1(f319(f319(f227(x56793),x56791),x56792))
% 28.73/28.53 [5680]~P4(x56803)+E(x56801,x56802)+P1(f319(f319(f227(x56803),x56802),x56801))+P1(f319(f319(f227(x56803),x56801),x56802))
% 28.73/28.53 [5681]~P126(x56813)+E(x56811,x56812)+P1(f319(f319(f227(x56813),x56812),x56811))+P1(f319(f319(f227(x56813),x56811),x56812))
% 28.73/28.53 [5682]~P4(x56823)+E(x56821,x56822)+P1(f319(f319(f227(x56823),x56822),x56821))+P1(f319(f319(f227(x56823),x56821),x56822))
% 28.73/28.53 [5683]~E(x56832,x56833)+~P4(x56831)+P1(f319(f319(f227(x56831),x56832),x56833))+P1(f319(f319(f226(x56831),x56832),x56833))
% 28.73/28.53 [5855]P152(x58552,x58551,x58553)+E(x58551,f2(a1))+P1(f319(f319(f227(a1),x58551),f2(a1)))+P1(f319(f319(f227(a1),f2(a1)),x58551))
% 28.73/28.53 [5856]P151(x58562,x58561,x58563)+E(x58561,f2(a1))+P1(f319(f319(f227(a1),x58561),f2(a1)))+P1(f319(f319(f227(a1),f2(a1)),x58561))
% 28.73/28.53 [5881]E(x58811,x58812)+P1(f319(f319(x58813,x58811),x58812))+P1(f319(f319(f227(a925),x58812),x58811))+P1(f319(f319(f227(a925),x58811),x58812))
% 28.73/28.53 [5943]~P113(x59433)+E(x59431,x59432)+~P1(f319(f319(f226(x59433),x59432),x59431))+P1(f319(f319(f227(x59433),x59432),x59431))
% 28.73/28.53 [5944]~P4(x59443)+E(x59441,x59442)+~P1(f319(f319(f226(x59443),x59441),x59442))+P1(f319(f319(f227(x59443),x59441),x59442))
% 28.73/28.53 [5945]~P4(x59453)+E(x59451,x59452)+~P1(f319(f319(f226(x59453),x59451),x59452))+P1(f319(f319(f227(x59453),x59451),x59452))
% 28.73/28.53 [5946]~P113(x59463)+E(x59461,x59462)+~P1(f319(f319(f226(x59463),x59461),x59462))+P1(f319(f319(f227(x59463),x59461),x59462))
% 28.73/28.53 [5947]~P113(x59473)+E(x59471,x59472)+~P1(f319(f319(f226(x59473),x59471),x59472))+P1(f319(f319(f227(x59473),x59471),x59472))
% 28.73/28.53 [5948]~P113(x59483)+E(x59481,x59482)+~P1(f319(f319(f226(x59483),x59481),x59482))+P1(f319(f319(f227(x59483),x59481),x59482))
% 28.73/28.53 [5949]~P113(x59493)+E(x59491,x59492)+~P1(f319(f319(f226(x59493),x59491),x59492))+P1(f319(f319(f227(x59493),x59491),x59492))
% 28.73/28.53 [5950]~P113(x59503)+E(x59501,x59502)+~P1(f319(f319(f226(x59503),x59501),x59502))+P1(f319(f319(f227(x59503),x59501),x59502))
% 28.73/28.53 [5951]~P113(x59513)+E(x59511,x59512)+~P1(f319(f319(f226(x59513),x59511),x59512))+P1(f319(f319(f227(x59513),x59511),x59512))
% 28.73/28.53 [6057]P151(x60571,x60572,x60573)+~P1(f319(x60571,x60573))+P1(f319(f319(f227(a1),x60572),f2(a1)))+P1(f319(f319(f227(a1),f2(a1)),x60572))
% 28.73/28.53 [6112]P152(x61121,x61122,x61123)+~P1(f319(x61121,f2(a1)))+P1(f319(f319(f227(a1),x61122),f2(a1)))+P1(f319(f319(f227(a1),f2(a1)),x61122))
% 28.73/28.53 [6117]~P102(x61171)+E(f319(f319(f102(x61171),x61172),f10(x61171,x61173)),x61172)+~P1(f319(f55(x61171),x61173))+~P1(f319(f319(f321(x61171),x61172),x61173))
% 28.73/28.53 [6118]~P102(x61181)+E(f319(f319(f93(x61181),x61182),f13(x61181,x61183)),x61182)+~P1(f319(f55(x61181),x61183))+~P1(f319(f319(f321(x61181),x61182),x61183))
% 28.73/28.53 [6156]~P102(x61561)+E(f319(f319(f102(x61561),x61562),f13(x61561,x61563)),f13(x61561,x61563))+~P1(f319(f55(x61561),x61563))+~P1(f319(f319(f321(x61561),x61562),x61563))
% 28.73/28.53 [6157]~P102(x61571)+E(f319(f319(f93(x61571),x61572),f10(x61571,x61573)),f10(x61571,x61573))+~P1(f319(f55(x61571),x61573))+~P1(f319(f319(f321(x61571),x61572),x61573))
% 28.73/28.53 [6158]~P4(x61581)+E(f319(f319(f224(x61581),x61582),f14(x61581,x61583)),f14(x61581,x61583))+~P1(f319(f55(x61581),x61583))+~P1(f319(f319(f321(x61581),x61582),x61583))
% 28.73/28.53 [6159]~P4(x61591)+E(f319(f319(f225(x61591),x61592),f15(x61591,x61593)),f15(x61591,x61593))+~P1(f319(f55(x61591),x61593))+~P1(f319(f319(f321(x61591),x61592),x61593))
% 28.73/28.53 [6195]E(x61951,x61952)+~P113(x61953)+~P1(f319(f319(f226(x61953),x61952),x61951))+~P1(f319(f319(f226(x61953),x61951),x61952))
% 28.73/28.53 [6196]E(x61961,x61962)+~P113(x61963)+~P1(f319(f319(f226(x61963),x61962),x61961))+~P1(f319(f319(f226(x61963),x61961),x61962))
% 28.73/28.53 [6197]E(x61971,x61972)+~P113(x61973)+~P1(f319(f319(f226(x61973),x61972),x61971))+~P1(f319(f319(f226(x61973),x61971),x61972))
% 28.73/28.53 [6198]E(x61981,x61982)+~P113(x61983)+~P1(f319(f319(f226(x61983),x61982),x61981))+~P1(f319(f319(f226(x61983),x61981),x61982))
% 28.73/28.53 [6200]~E(x62001,x62002)+~P4(x62003)+~P1(f319(f319(f226(x62003),x62001),x62002))+~P1(f319(f319(f227(x62003),x62001),x62002))
% 28.73/28.53 [6341]~P2(x63411)+P1(f319(f319(f227(x63411),x63413),x63412))+~P1(f319(f319(f226(x63411),x63413),x63412))+P1(f319(f319(f226(x63411),x63412),x63413))
% 28.73/28.53 [6367]~P4(x63671)+~P1(f319(f55(x63671),x63673))+P1(f319(f319(f226(x63671),x63672),f15(x63671,x63673)))+~P1(f319(f319(f321(x63671),x63672),x63673))
% 28.73/28.53 [6412]~P4(x64121)+E(f319(f319(f224(x64121),x64122),f12(x64121,f225(x64121),x64123)),x64122)+~P1(f319(f55(x64121),x64123))+~P1(f319(f319(f321(x64121),x64122),x64123))
% 28.73/28.53 [6413]~P4(x64131)+E(f319(f319(f225(x64131),x64132),f11(x64131,f224(x64131),x64133)),x64132)+~P1(f319(f55(x64131),x64133))+~P1(f319(f319(f321(x64131),x64132),x64133))
% 28.73/28.53 [6554]E(x65541,x65542)+~E(f319(f319(f23(a925),x65541),x65543),f319(f319(f23(a925),x65542),x65543))+~P1(f319(f319(f226(a925),x65543),x65541))+~P1(f319(f319(f226(a925),x65543),x65542))
% 28.73/28.53 [6581]~P4(x65811)+~P1(f319(f55(x65811),x65812))+~P1(f319(f319(f321(x65811),x65813),x65812))+P1(f319(f319(f226(x65811),f14(x65811,x65812)),x65813))
% 28.73/28.53 [6622]E(x66221,f2(a925))+~P1(f319(f42(x66223,x66221),x66222))+P1(f319(f319(f227(a925),f2(a925)),x66221))+P1(f319(f319(f227(a925),x66221),f319(f248(a925,a925),x66222)))
% 28.73/28.53 [6647]P152(x66472,x66471,x66473)+E(x66471,f2(a1))+P1(f319(f319(f227(a1),x66471),f867(x66473,x66471,x66472)))+P1(f319(f319(f227(a1),f2(a1)),x66471))
% 28.73/28.53 [6648]P151(x66482,x66481,x66483)+E(x66481,f2(a1))+P1(f319(f319(f227(a1),x66481),f878(x66483,x66481,x66482)))+P1(f319(f319(f227(a1),f2(a1)),x66481))
% 28.73/28.53 [6649]~P4(x66491)+E(f319(f319(f224(x66491),x66492),f11(x66491,f224(x66491),x66493)),f11(x66491,f224(x66491),x66493))+~P1(f319(f55(x66491),x66493))+~P1(f319(f319(f321(x66491),x66492),x66493))
% 28.73/28.53 [6650]~P4(x66501)+E(f319(f319(f225(x66501),x66502),f12(x66501,f225(x66501),x66503)),f12(x66501,f225(x66501),x66503))+~P1(f319(f55(x66501),x66503))+~P1(f319(f319(f321(x66501),x66502),x66503))
% 28.73/28.53 [6655]~P1(f319(x66551,x66552))+P1(f319(x66551,f523(x66552,x66551,x66553)))+P1(f319(x66551,f2(a925)))+~P1(f319(f319(f227(a925),x66552),x66553))
% 28.73/28.53 [6713]~P1(f319(x67131,x67132))+~P1(f319(f55(x67133),x67132))+P1(f319(x67131,f335(x67131,x67132,x67133)))+P1(f319(x67131,f180(f932(x67133,a923))))
% 28.73/28.53 [6726]~P126(x67261)+~P99(x67261)+P1(f319(f319(f226(x67261),f319(f95(x67261),x67262)),f319(f95(x67261),x67263)))+~P1(f319(f319(f226(a1),x67262),x67263))
% 28.73/28.53 [6727]~P126(x67271)+~P99(x67271)+P1(f319(f319(f227(x67271),f319(f95(x67271),x67272)),f319(f95(x67271),x67273)))+~P1(f319(f319(f227(a1),x67272),x67273))
% 28.73/28.53 [6730]~P1(f319(x67301,x67303))+~P1(f319(f55(x67302),x67303))+P1(f319(f55(x67302),f335(x67301,x67303,x67302)))+P1(f319(x67301,f180(f932(x67302,a923))))
% 28.73/28.53 [6763]P151(x67631,x67632,x67633)+~P1(f319(x67631,x67633))+P1(f319(f319(f227(a1),x67632),f878(x67633,x67632,x67631)))+P1(f319(f319(f227(a1),f2(a1)),x67632))
% 28.73/28.53 [6799]P152(x67991,x67992,x67993)+P1(f319(f319(f227(a1),x67992),f867(x67993,x67992,x67991)))+~P1(f319(x67991,f2(a1)))+P1(f319(f319(f227(a1),f2(a1)),x67992))
% 28.73/28.53 [6833]~P3(x68331)+~P100(x68331)+E(f319(f319(f224(x68331),f319(f95(x68331),x68332)),f319(f95(x68331),x68333)),f319(f95(x68331),x68333))+P1(f319(f319(f226(x68331),f319(f95(x68331),x68332)),f319(f95(x68331),x68333)))
% 28.73/28.53 [6834]~P3(x68341)+~P100(x68341)+E(f319(f319(f225(x68341),f319(f95(x68341),x68342)),f319(f95(x68341),x68343)),f319(f95(x68341),x68342))+P1(f319(f319(f226(x68341),f319(f95(x68341),x68342)),f319(f95(x68341),x68343)))
% 28.73/28.53 [6840]E(x68401,f2(a925))+~P1(f319(f42(x68403,x68401),x68402))+~P1(f319(f319(f227(a925),f2(a925)),x68401))+P1(f319(f319(f226(a925),f2(a925)),f319(f248(a925,a925),x68402)))
% 28.73/28.53 [6893]P152(x68932,x68931,x68933)+E(x68931,f2(a1))+~P1(f319(x68932,f873(x68933,x68931,x68932)))+P1(f319(f319(f227(a1),f2(a1)),x68931))
% 28.73/28.53 [6894]P151(x68942,x68941,x68943)+E(x68941,f2(a1))+~P1(f319(x68942,f878(x68943,x68941,x68942)))+P1(f319(f319(f227(a1),f2(a1)),x68941))
% 28.73/28.53 [6898]P1(f319(x68981,x68982))+~P1(f319(f55(x68983),x68982))+P1(f319(x68981,f777(x68981,x68982,x68983)))+~P1(f319(x68981,f180(f932(x68983,a923))))
% 28.73/28.53 [6921]P1(f319(x69211,x69212))+P1(f319(f55(x69213),f777(x69211,x69212,x69213)))+~P1(f319(f55(x69213),x69212))+~P1(f319(x69211,f180(f932(x69213,a923))))
% 28.73/28.53 [6984]P151(x69841,x69842,x69843)+~P1(f319(x69841,x69843))+~P1(f319(x69841,f878(x69843,x69842,x69841)))+P1(f319(f319(f227(a1),f2(a1)),x69842))
% 28.73/28.53 [7014]P152(x70141,x70142,x70143)+~P1(f319(x70141,f873(x70143,x70142,x70141)))+~P1(f319(x70141,f2(a1)))+P1(f319(f319(f227(a1),f2(a1)),x70142))
% 28.73/28.53 [7025]E(x70251,f2(a925))+~P1(f319(f42(x70253,x70251),x70252))+P1(f319(f319(f226(a925),f319(f248(a925,a925),x70252)),f2(a925)))+P1(f319(f319(f227(a925),f2(a925)),x70251))
% 28.73/28.53 [7123]~P99(x71233)+~P126(x71233)+~P1(f319(f319(f226(x71233),f319(f95(x71233),x71231)),f319(f95(x71233),x71232)))+P1(f319(f319(f226(a1),x71231),x71232))
% 28.73/28.53 [7124]~P99(x71243)+~P126(x71243)+~P1(f319(f319(f227(x71243),f319(f95(x71243),x71241)),f319(f95(x71243),x71242)))+P1(f319(f319(f227(a1),x71241),x71242))
% 28.73/28.53 [7152]~P4(x71521)+~P14(x71521,x71523)+P14(x71521,f319(f319(f143(x71521),x71522),x71523))+~P1(f319(f319(f226(x71521),x71522),f732(x71523,x71522,x71521)))
% 28.73/28.53 [7153]~P4(x71531)+~P14(x71531,x71533)+P14(x71531,f319(f319(f143(x71531),x71532),x71533))+~P1(f319(f319(f226(x71531),x71532),f734(x71533,x71532,x71531)))
% 28.73/28.53 [7154]~P4(x71541)+~P14(x71541,x71543)+P14(x71541,f319(f319(f143(x71541),x71542),x71543))+~P1(f319(f319(f226(x71541),x71542),f759(x71542,x71543,x71541)))
% 28.73/28.53 [7238]P152(x72382,x72381,x72383)+E(x72381,f2(a1))+P1(f319(f319(f227(a1),x72381),f2(a1)))+P1(f319(f319(f227(a1),f868(x72383,x72381,x72382)),x72381))
% 28.73/28.53 [7239]P151(x72392,x72391,x72393)+E(x72391,f2(a1))+P1(f319(f319(f227(a1),x72391),f2(a1)))+P1(f319(f319(f227(a1),f874(x72393,x72391,x72392)),x72391))
% 28.73/28.53 [7243]~P4(x72431)+~P100(x72431)+P1(f319(f319(f226(x72431),f319(f95(x72431),x72432)),f319(f95(x72431),x72433)))+P1(f319(f319(f227(x72431),f319(f95(x72431),x72433)),f319(f95(x72431),x72432)))
% 28.73/28.53 [7275]P152(x72752,x72751,x72753)+E(x72751,f2(a1))+P1(f319(f319(f226(a1),f867(x72753,x72751,x72752)),f2(a1)))+P1(f319(f319(f227(a1),f2(a1)),x72751))
% 28.73/28.53 [7276]P151(x72762,x72761,x72763)+E(x72761,f2(a1))+P1(f319(f319(f226(a1),f878(x72763,x72761,x72762)),f2(a1)))+P1(f319(f319(f227(a1),f2(a1)),x72761))
% 28.73/28.53 [7302]~P4(x73021)+~P14(x73021,x73023)+E(f319(f319(f140(x73021,x73021,f5(x73021)),x73022),f162(x73021,x73022,x73023)),x73023)+~P1(f319(f319(f321(x73021),x73022),f319(f164(x73021),x73023)))
% 28.73/28.53 [7349]P151(x73491,x73492,x73493)+~P1(f319(x73491,x73493))+P1(f319(f319(f227(a1),x73492),f2(a1)))+P1(f319(f319(f227(a1),f874(x73493,x73492,x73491)),x73492))
% 28.73/28.53 [7355]~P3(x73551)+~P100(x73551)+E(f319(f319(f224(x73551),f319(f95(x73551),x73552)),f319(f95(x73551),x73553)),f319(f95(x73551),x73552))+~P1(f319(f319(f226(x73551),f319(f95(x73551),x73552)),f319(f95(x73551),x73553)))
% 28.73/28.53 [7356]~P3(x73561)+~P100(x73561)+E(f319(f319(f225(x73561),f319(f95(x73561),x73562)),f319(f95(x73561),x73563)),f319(f95(x73561),x73563))+~P1(f319(f319(f226(x73561),f319(f95(x73561),x73562)),f319(f95(x73561),x73563)))
% 28.73/28.53 [7370]P152(x73701,x73702,x73703)+~P1(f319(x73701,f2(a1)))+P1(f319(f319(f227(a1),x73702),f2(a1)))+P1(f319(f319(f227(a1),f868(x73703,x73702,x73701)),x73702))
% 28.73/28.53 [7380]P151(x73801,x73802,x73803)+~P1(f319(x73801,x73803))+P1(f319(f319(f226(a1),f878(x73803,x73802,x73801)),f2(a1)))+P1(f319(f319(f227(a1),f2(a1)),x73802))
% 28.73/28.53 [7404]P152(x74041,x74042,x74043)+~P1(f319(x74041,f2(a1)))+P1(f319(f319(f226(a1),f867(x74043,x74042,x74041)),f2(a1)))+P1(f319(f319(f227(a1),f2(a1)),x74042))
% 28.73/28.53 [7432]~P1(f319(x74321,x74322))+P1(f319(x74321,f2(a925)))+~P1(f319(f319(f227(a925),x74322),x74323))+P1(f319(f319(f227(a925),f523(x74322,x74321,x74323)),x74323))
% 28.73/28.53 [7449]~P4(x74491)+~P14(x74491,x74493)+P14(x74491,f319(f319(f143(x74491),x74492),x74493))+P1(f319(f319(f321(x74491),f732(x74493,x74492,x74491)),f319(f164(x74491),x74493)))
% 28.73/28.53 [7450]~P4(x74501)+~P14(x74501,x74503)+P14(x74501,f319(f319(f143(x74501),x74502),x74503))+P1(f319(f319(f321(x74501),f734(x74503,x74502,x74501)),f319(f164(x74501),x74503)))
% 28.73/28.53 [7451]~P4(x74511)+~P14(x74511,x74513)+P14(x74511,f319(f319(f143(x74511),x74512),x74513))+P1(f319(f319(f321(x74511),f759(x74512,x74513,x74511)),f319(f164(x74511),x74513)))
% 28.73/28.53 [7564]~P4(x75641)+~P6(x75641)+~P1(f319(f319(f227(x75641),x75643),f31(x75641,x75642)))+P1(f319(f319(f321(x75641),f879(x75642,x75643,x75641)),x75642))
% 28.73/28.53 [7717]~P4(x77171)+~P6(x77171)+~P1(f319(f319(f227(x77171),f32(x77171,x77173)),x77172))+P1(f319(f319(f321(x77171),f885(x77172,x77173,x77171)),x77173))
% 28.73/28.53 [7718]~P4(x77181)+~P6(x77181)+~P1(f319(f319(f227(x77181),f32(x77181,x77183)),x77182))+P1(f319(f319(f227(x77181),f885(x77182,x77183,x77181)),x77182))
% 28.73/28.53 [7729]P152(x77292,x77291,x77293)+E(x77291,f2(a1))+P1(f319(f319(f227(a1),x77291),f867(x77293,x77291,x77292)))+P1(f319(f319(f227(a1),f868(x77293,x77291,x77292)),x77291))
% 28.73/28.53 [7730]P151(x77302,x77301,x77303)+E(x77301,f2(a1))+P1(f319(f319(f227(a1),x77301),f878(x77303,x77301,x77302)))+P1(f319(f319(f227(a1),f874(x77303,x77301,x77302)),x77301))
% 28.73/28.53 [7823]P152(x78233,x78231,x78232)+E(x78231,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x78231),f873(x78232,x78231,x78233))),f867(x78232,x78231,x78233)),x78232)+P1(f319(f319(f227(a1),f2(a1)),x78231))
% 28.73/28.53 [7824]P151(x78243,x78241,x78242)+E(x78241,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x78241),f876(x78242,x78241,x78243))),f878(x78242,x78241,x78243)),x78242)+P1(f319(f319(f227(a1),f2(a1)),x78241))
% 28.73/28.53 [7825]~P139(x78251)+~P1(f319(f319(f226(x78251),x78252),f2(x78251)))+P1(f319(f319(f226(x78251),f319(f319(f75(x78251),x78252),x78253)),f2(x78251)))+~P1(f319(f319(f226(x78251),f2(x78251)),x78253))
% 28.73/28.53 [7826]~P139(x78261)+~P1(f319(f319(f226(x78261),x78263),f2(x78261)))+P1(f319(f319(f226(x78261),f319(f319(f75(x78261),x78262),x78263)),f2(x78261)))+~P1(f319(f319(f226(x78261),f2(x78261)),x78262))
% 28.73/28.53 [7827]~P139(x78271)+~P1(f319(f319(f226(x78271),x78273),f2(x78271)))+P1(f319(f319(f226(x78271),f319(f319(f75(x78271),x78272),x78273)),f2(x78271)))+~P1(f319(f319(f226(x78271),f2(x78271)),x78272))
% 28.73/28.53 [7828]~P139(x78281)+~P1(f319(f319(f226(x78281),x78282),f2(x78281)))+P1(f319(f319(f226(x78281),f319(f319(f75(x78281),x78282),x78283)),f2(x78281)))+~P1(f319(f319(f226(x78281),f2(x78281)),x78283))
% 28.73/28.53 [7829]~P139(x78291)+~P1(f319(f319(f226(x78291),x78292),f2(x78291)))+P1(f319(f319(f226(x78291),f319(f319(f75(x78291),x78292),x78293)),f2(x78291)))+~P1(f319(f319(f226(x78291),f2(x78291)),x78293))
% 28.73/28.53 [7830]~P130(x78301)+~P1(f319(f319(f226(x78301),x78303),f2(x78301)))+P1(f319(f319(f226(x78301),f319(f319(f75(x78301),x78302),x78303)),f2(x78301)))+~P1(f319(f319(f226(x78301),f2(x78301)),x78302))
% 28.73/28.53 [7831]~P130(x78311)+~P1(f319(f319(f226(x78311),x78312),f2(x78311)))+P1(f319(f319(f226(x78311),f319(f319(f75(x78311),x78312),x78313)),f2(x78311)))+~P1(f319(f319(f226(x78311),f2(x78311)),x78313))
% 28.73/28.53 [7832]~P75(x78321)+~P1(f319(f319(f226(x78321),x78322),f2(x78321)))+P1(f319(f319(f226(x78321),f319(f319(f283(x78321),x78322),x78323)),f2(x78321)))+~P1(f319(f319(f227(x78321),f2(x78321)),x78323))
% 28.73/28.53 [7833]~P75(x78331)+~P1(f319(f319(f227(x78331),x78333),f2(x78331)))+P1(f319(f319(f226(x78331),f319(f319(f283(x78331),x78332),x78333)),f2(x78331)))+~P1(f319(f319(f226(x78331),f2(x78331)),x78332))
% 28.73/28.53 [7834]~P74(x78341)+~P1(f319(f319(f226(x78341),x78343),f2(x78341)))+P1(f319(f319(f226(x78341),f319(f319(f283(x78341),x78342),x78343)),f2(x78341)))+~P1(f319(f319(f226(x78341),f2(x78341)),x78342))
% 28.73/28.53 [7835]~P74(x78351)+~P1(f319(f319(f226(x78351),x78352),f2(x78351)))+P1(f319(f319(f226(x78351),f319(f319(f283(x78351),x78352),x78353)),f2(x78351)))+~P1(f319(f319(f226(x78351),f2(x78351)),x78353))
% 28.73/28.53 [7836]~P134(x78361)+~P1(f319(f319(f227(x78361),x78362),f2(x78361)))+P1(f319(f319(f227(x78361),f319(f319(f75(x78361),x78362),x78363)),f2(x78361)))+~P1(f319(f319(f227(x78361),f2(x78361)),x78363))
% 28.73/28.53 [7837]~P134(x78371)+~P1(f319(f319(f227(x78371),x78373),f2(x78371)))+P1(f319(f319(f227(x78371),f319(f319(f75(x78371),x78372),x78373)),f2(x78371)))+~P1(f319(f319(f227(x78371),f2(x78371)),x78372))
% 28.73/28.53 [7838]~P134(x78381)+~P1(f319(f319(f227(x78381),x78382),f2(x78381)))+P1(f319(f319(f227(x78381),f319(f319(f75(x78381),x78382),x78383)),f2(x78381)))+~P1(f319(f319(f227(x78381),f2(x78381)),x78383))
% 28.73/28.53 [7839]~P75(x78391)+~P1(f319(f319(f227(x78391),x78393),f2(x78391)))+P1(f319(f319(f227(x78391),f319(f319(f283(x78391),x78392),x78393)),f2(x78391)))+~P1(f319(f319(f227(x78391),f2(x78391)),x78392))
% 28.73/28.53 [7840]~P75(x78401)+~P1(f319(f319(f227(x78401),x78402),f2(x78401)))+P1(f319(f319(f227(x78401),f319(f319(f283(x78401),x78402),x78403)),f2(x78401)))+~P1(f319(f319(f227(x78401),f2(x78401)),x78403))
% 28.73/28.53 [7841]~P74(x78411)+~P1(f319(f319(f227(x78411),x78413),f2(x78411)))+P1(f319(f319(f227(x78411),f319(f319(f283(x78411),x78412),x78413)),f2(x78411)))+~P1(f319(f319(f227(x78411),f2(x78411)),x78412))
% 28.73/28.53 [7842]~P74(x78421)+~P1(f319(f319(f227(x78421),x78422),f2(x78421)))+P1(f319(f319(f227(x78421),f319(f319(f283(x78421),x78422),x78423)),f2(x78421)))+~P1(f319(f319(f227(x78421),f2(x78421)),x78423))
% 28.73/28.53 [7857]P151(x78571,x78572,x78573)+~P1(f319(x78571,x78573))+P1(f319(f319(f227(a1),x78572),f878(x78573,x78572,x78571)))+P1(f319(f319(f227(a1),f874(x78573,x78572,x78571)),x78572))
% 28.73/28.53 [7870]P152(x78701,x78702,x78703)+P1(f319(f319(f227(a1),x78702),f867(x78703,x78702,x78701)))+~P1(f319(x78701,f2(a1)))+P1(f319(f319(f227(a1),f868(x78703,x78702,x78701)),x78702))
% 28.73/28.53 [7921]P152(x79212,x79211,x79213)+E(x79211,f2(a1))+~P1(f319(x79212,f873(x79213,x79211,x79212)))+P1(f319(f319(f227(a1),f868(x79213,x79211,x79212)),x79211))
% 28.73/28.53 [7922]P151(x79222,x79221,x79223)+E(x79221,f2(a1))+~P1(f319(x79222,f878(x79223,x79221,x79222)))+P1(f319(f319(f227(a1),f874(x79223,x79221,x79222)),x79221))
% 28.73/28.53 [7932]P151(x79323,x79321,x79322)+~P1(f319(x79323,x79322))+E(f319(f319(f74(a1),f319(f319(f75(a1),x79321),f876(x79322,x79321,x79323))),f878(x79322,x79321,x79323)),x79322)+P1(f319(f319(f227(a1),f2(a1)),x79321))
% 28.73/28.53 [7947]P152(x79473,x79471,x79472)+E(f319(f319(f74(a1),f319(f319(f75(a1),x79471),f873(x79472,x79471,x79473))),f867(x79472,x79471,x79473)),x79472)+~P1(f319(x79473,f2(a1)))+P1(f319(f319(f227(a1),f2(a1)),x79471))
% 28.73/28.53 [7975]~P1(f319(x79751,x79753))+~P1(f319(f55(x79752),x79753))+P1(f319(f319(f321(x79752),f336(x79751,x79753,x79752)),f335(x79751,x79753,x79752)))+P1(f319(x79751,f180(f932(x79752,a923))))
% 28.73/28.53 [7986]P151(x79861,x79862,x79863)+~P1(f319(x79861,x79863))+~P1(f319(x79861,f878(x79863,x79862,x79861)))+P1(f319(f319(f227(a1),f874(x79863,x79862,x79861)),x79862))
% 28.73/28.53 [7992]P152(x79921,x79922,x79923)+~P1(f319(x79921,f873(x79923,x79922,x79921)))+~P1(f319(x79921,f2(a1)))+P1(f319(f319(f227(a1),f868(x79923,x79922,x79921)),x79922))
% 28.73/28.53 [8059]~P100(x80591)+~P4(x80591)+~P1(f319(f319(f226(x80591),f319(f95(x80591),x80592)),f319(f95(x80591),x80593)))+~P1(f319(f319(f227(x80591),f319(f95(x80591),x80593)),f319(f95(x80591),x80592)))
% 28.73/28.53 [8095]~P130(x80951)+~P1(f319(f319(f226(x80951),f319(f319(f75(x80951),x80953),x80952)),f2(x80951)))+P1(f319(f319(f226(x80951),x80952),f2(x80951)))+P1(f319(f319(f226(x80951),f2(x80951)),x80952))
% 28.73/28.53 [8096]~P130(x80961)+~P1(f319(f319(f226(x80961),f319(f319(f75(x80961),x80962),x80963)),f2(x80961)))+P1(f319(f319(f226(x80961),x80962),f2(x80961)))+P1(f319(f319(f226(x80961),f2(x80961)),x80962))
% 28.73/28.53 [8097]~P74(x80971)+~P1(f319(f319(f226(x80971),f319(f319(f283(x80971),x80973),x80972)),f2(x80971)))+P1(f319(f319(f226(x80971),x80972),f2(x80971)))+P1(f319(f319(f226(x80971),f2(x80971)),x80972))
% 28.73/28.53 [8098]~P74(x80981)+~P1(f319(f319(f226(x80981),f319(f319(f283(x80981),x80982),x80983)),f2(x80981)))+P1(f319(f319(f226(x80981),x80982),f2(x80981)))+P1(f319(f319(f226(x80981),f2(x80981)),x80982))
% 28.73/28.53 [8099]~P74(x80991)+~P1(f319(f319(f227(x80991),f319(f319(f283(x80991),x80993),x80992)),f2(x80991)))+P1(f319(f319(f227(x80991),x80992),f2(x80991)))+P1(f319(f319(f227(x80991),f2(x80991)),x80992))
% 28.73/28.53 [8100]~P74(x81001)+~P1(f319(f319(f227(x81001),f319(f319(f283(x81001),x81002),x81003)),f2(x81001)))+P1(f319(f319(f227(x81001),x81002),f2(x81001)))+P1(f319(f319(f227(x81001),f2(x81001)),x81002))
% 28.73/28.53 [8124]~P130(x81241)+~P1(f319(f319(f226(x81241),f319(f319(f75(x81241),x81242),x81243)),f2(x81241)))+P1(f319(f319(f226(x81241),f2(x81241)),x81242))+P1(f319(f319(f226(x81241),f2(x81241)),x81243))
% 28.73/28.53 [8125]~P74(x81251)+~P1(f319(f319(f226(x81251),f319(f319(f283(x81251),x81252),x81253)),f2(x81251)))+P1(f319(f319(f226(x81251),f2(x81251)),x81252))+P1(f319(f319(f226(x81251),f2(x81251)),x81253))
% 28.73/28.53 [8126]~P74(x81261)+~P1(f319(f319(f227(x81261),f319(f319(f283(x81261),x81262),x81263)),f2(x81261)))+P1(f319(f319(f227(x81261),f2(x81261)),x81262))+P1(f319(f319(f227(x81261),f2(x81261)),x81263))
% 28.73/28.53 [8148]P152(x81482,x81481,x81483)+E(x81481,f2(a1))+P1(f319(f319(f226(a1),f867(x81483,x81481,x81482)),f2(a1)))+P1(f319(f319(f227(a1),f868(x81483,x81481,x81482)),x81481))
% 28.73/28.53 [8149]P151(x81492,x81491,x81493)+E(x81491,f2(a1))+P1(f319(f319(f226(a1),f878(x81493,x81491,x81492)),f2(a1)))+P1(f319(f319(f227(a1),f874(x81493,x81491,x81492)),x81491))
% 28.73/28.53 [8156]~P129(x81561)+~P1(f319(f319(f227(x81561),x81562),f72(x81561)))+P1(f319(f319(f227(x81561),f319(f319(f236(x81561),x81562),f319(a104,x81563))),f72(x81561)))+~P1(f319(f319(f227(x81561),f2(x81561)),x81562))
% 28.73/28.53 [8211]~P4(x82111)+~E(x82113,f105(x82111))+~P14(x82111,f319(f160(x82111),x82113))+E(f319(f134(x82111,x82111,f319(f7(x82111,x82111,x82111),f225(x82111)),x82112),f319(f160(x82111),x82113)),x82112)
% 28.73/28.53 [8215]P151(x82151,x82152,x82153)+~P1(f319(x82151,x82153))+P1(f319(f319(f226(a1),f878(x82153,x82152,x82151)),f2(a1)))+P1(f319(f319(f227(a1),f874(x82153,x82152,x82151)),x82152))
% 28.73/28.53 [8222]P152(x82221,x82222,x82223)+~P1(f319(x82221,f2(a1)))+P1(f319(f319(f226(a1),f867(x82223,x82222,x82221)),f2(a1)))+P1(f319(f319(f227(a1),f868(x82223,x82222,x82221)),x82222))
% 28.73/28.53 [8440]P152(x84403,x84401,x84402)+E(x84401,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x84401),f873(x84402,x84401,x84403))),f867(x84402,x84401,x84403)),x84402)+P1(f319(f319(f227(a1),f868(x84402,x84401,x84403)),x84401))
% 28.73/28.53 [8441]P151(x84413,x84411,x84412)+E(x84411,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x84411),f876(x84412,x84411,x84413))),f878(x84412,x84411,x84413)),x84412)+P1(f319(f319(f227(a1),f874(x84412,x84411,x84413)),x84411))
% 28.73/28.53 [8477]P151(x84773,x84771,x84772)+~P1(f319(x84773,x84772))+E(f319(f319(f74(a1),f319(f319(f75(a1),x84771),f876(x84772,x84771,x84773))),f878(x84772,x84771,x84773)),x84772)+P1(f319(f319(f227(a1),f874(x84772,x84771,x84773)),x84771))
% 28.73/28.53 [8478]~P78(x84781)+~P79(x84781)+~P42(x84783)+E(f319(f319(f6(a925,x84781),f319(f319(f8(a1,x84781,a925),x84782),f92(a1))),f319(f302(a1,a925,a96),x84783)),f319(f319(f6(a1,x84781),x84782),x84783))
% 28.73/28.53 [8479]~P78(x84791)+~P79(x84791)+~P42(x84793)+E(f319(f319(f9(a925,x84791),f319(f319(f8(a1,x84791,a925),x84792),f92(a1))),f319(f302(a1,a925,a96),x84793)),f319(f319(f9(a1,x84791),x84792),x84793))
% 28.73/28.53 [8488]P152(x84883,x84881,x84882)+E(f319(f319(f74(a1),f319(f319(f75(a1),x84881),f873(x84882,x84881,x84883))),f867(x84882,x84881,x84883)),x84882)+~P1(f319(x84883,f2(a1)))+P1(f319(f319(f227(a1),f868(x84882,x84881,x84883)),x84881))
% 28.73/28.53 [8511]~E(x85112,f2(a925))+~E(f319(f243(a925,a925),x85113),f2(a925))+~E(x85111,f319(f319(f74(a925),f319(f319(f75(a925),f319(f243(a925,a925),x85113)),x85112)),f319(f248(a925,a925),x85113)))+P1(f319(f42(x85111,x85112),x85113))
% 28.73/28.53 [8568]P1(f319(x85681,x85682))+~P1(f319(f319(f321(x85683),f784(x85681,x85682,x85683)),f777(x85681,x85682,x85683)))+~P1(f319(f55(x85683),x85682))+~P1(f319(x85681,f180(f932(x85683,a923))))
% 28.73/28.53 [9203]P1(f319(x92031,x92032))+~P1(f319(f55(x92033),x92032))+~P1(f319(x92031,f319(f319(f301(x92033),f784(x92031,x92032,x92033)),f777(x92031,x92032,x92033))))+~P1(f319(x92031,f180(f932(x92033,a923))))
% 28.73/28.53 [9439]P1(f319(f319(f226(a1),x94391),f2(a1)))+~P1(f319(f319(f227(a1),f319(f319(f74(a1),f319(f319(f75(a1),x94393),x94391)),x94392)),f2(a1)))+~P1(f319(f319(f226(a1),f2(a1)),x94392))+~P1(f319(f319(f227(a1),f2(a1)),x94393))
% 28.73/28.53 [6013]~P102(x60132)+E(x60131,f180(f932(x60132,a923)))+~P1(f319(f55(x60132),x60131))+E(f10(x60132,f319(f319(f301(x60132),x60133),x60131)),f319(f319(f93(x60132),x60133),f10(x60132,x60131)))
% 28.73/28.53 [6014]~P102(x60142)+E(x60141,f180(f932(x60142,a923)))+~P1(f319(f55(x60142),x60141))+E(f13(x60142,f319(f319(f301(x60142),x60143),x60141)),f319(f319(f102(x60142),x60143),f13(x60142,x60141)))
% 28.73/28.53 [6015]~P4(x60152)+E(x60151,f180(f932(x60152,a923)))+~P1(f319(f55(x60152),x60151))+E(f14(x60152,f319(f319(f301(x60152),x60153),x60151)),f319(f319(f224(x60152),x60153),f14(x60152,x60151)))
% 28.73/28.53 [6016]~P4(x60162)+E(x60161,f180(f932(x60162,a923)))+~P1(f319(f55(x60162),x60161))+E(f15(x60162,f319(f319(f301(x60162),x60163),x60161)),f319(f319(f225(x60162),x60163),f15(x60162,x60161)))
% 28.73/28.53 [6338]~P130(x63381)+~E(x63383,f2(x63381))+~E(x63382,f2(x63381))+E(f319(f319(f74(x63381),f319(f319(f75(x63381),x63382),x63382)),f319(f319(f75(x63381),x63383),x63383)),f2(x63381))
% 28.73/28.53 [6405]~P101(x64052)+E(x64051,f180(f932(x64052,a923)))+~P1(f319(f55(x64052),x64051))+E(f319(f57(x64052,f75(x64052)),f319(f319(f301(x64052),x64053),x64051)),f319(f319(f75(x64052),x64053),f319(f57(x64052,f75(x64052)),x64051)))
% 28.73/28.53 [6531]~P4(x65312)+E(x65311,f180(f932(x65312,a923)))+~P1(f319(f55(x65312),x65311))+E(f11(x65312,f224(x65312),f319(f319(f301(x65312),x65313),x65311)),f319(f319(f224(x65312),x65313),f11(x65312,f224(x65312),x65311)))
% 28.73/28.53 [6532]~P4(x65322)+E(x65321,f180(f932(x65322,a923)))+~P1(f319(f55(x65322),x65321))+E(f12(x65322,f225(x65322),f319(f319(f301(x65322),x65323),x65321)),f319(f319(f225(x65322),x65323),f12(x65322,f225(x65322),x65321)))
% 28.73/28.53 [6939]~P102(x69391)+~P1(f319(f55(x69391),x69393))+E(f319(f319(f58(x69391,x69391,f93(x69391)),x69392),x69393),f10(x69391,f319(f319(f301(x69391),x69392),x69393)))+P1(f319(f319(f321(x69391),x69392),x69393))
% 28.73/28.53 [6940]~P102(x69401)+~P1(f319(f55(x69401),x69403))+E(f319(f319(f58(x69401,x69401,f102(x69401)),x69402),x69403),f13(x69401,f319(f319(f301(x69401),x69402),x69403)))+P1(f319(f319(f321(x69401),x69402),x69403))
% 28.73/28.53 [6941]~P4(x69411)+~P1(f319(f55(x69411),x69413))+E(f319(f319(f58(x69411,x69411,f224(x69411)),x69412),x69413),f14(x69411,f319(f319(f301(x69411),x69412),x69413)))+P1(f319(f319(f321(x69411),x69412),x69413))
% 28.73/28.53 [6942]~P4(x69421)+~P1(f319(f55(x69421),x69423))+E(f319(f319(f58(x69421,x69421,f225(x69421)),x69422),x69423),f15(x69421,f319(f319(f301(x69421),x69422),x69423)))+P1(f319(f319(f321(x69421),x69422),x69423))
% 28.73/28.53 [7048]~P76(x70481)+~P1(f319(f55(x70481),x70483))+E(f319(f57(x70481,f75(x70481)),f319(f319(f301(x70481),x70482),x70483)),f319(f319(f58(x70481,x70481,f75(x70481)),x70482),x70483))+P1(f319(f319(f321(x70481),x70482),x70483))
% 28.73/28.53 [7065]~P4(x70651)+~P1(f319(f55(x70651),x70653))+E(f11(x70651,f224(x70651),f319(f319(f301(x70651),x70652),x70653)),f319(f319(f58(x70651,x70651,f224(x70651)),x70652),x70653))+P1(f319(f319(f321(x70651),x70652),x70653))
% 28.73/28.53 [7066]~P4(x70661)+~P1(f319(f55(x70661),x70663))+E(f12(x70661,f225(x70661),f319(f319(f301(x70661),x70662),x70663)),f319(f319(f58(x70661,x70661,f225(x70661)),x70662),x70663))+P1(f319(f319(f321(x70661),x70662),x70663))
% 28.73/28.53 [7130]~E(f319(f319(f74(a1),x71302),f319(f319(f75(a1),x71303),x71301)),x71303)+~P1(f319(f319(f227(a1),f2(a1)),x71303))+P1(f319(f319(f226(a1),f72(a1)),x71301))+~P1(f319(f319(f227(a1),x71302),x71303))
% 28.73/28.53 [7159]~E(f319(f319(f74(a1),x71592),f319(f319(f75(a1),x71593),x71591)),x71593)+P1(f319(f319(f226(a1),x71591),f72(a1)))+~P1(f319(f319(f226(a1),f2(a1)),x71592))+~P1(f319(f319(f227(a1),f2(a1)),x71593))
% 28.73/28.53 [7175]E(x71751,f2(a925))+~P1(f319(f42(x71753,x71751),x71752))+~P1(f319(f319(f227(a925),f2(a925)),x71751))+P1(f319(f319(f227(a925),f319(f248(a925,a925),x71752)),x71751))
% 28.73/28.53 [7206]~P142(x72061)+~P1(f319(f319(f226(x72061),x72062),f2(x72061)))+~P1(f319(f319(f226(x72061),x72063),f2(x72061)))+E(f319(f319(f75(x72061),f319(f69(x72061),x72062)),f319(f69(x72061),x72063)),f319(f69(x72061),f319(f319(f75(x72061),x72062),x72063)))
% 28.73/28.53 [7252]~P142(x72521)+~P1(f319(f319(f226(x72521),x72522),f2(x72521)))+E(f319(f319(f75(x72521),f319(f69(x72521),x72522)),f319(f69(x72521),x72523)),f319(f69(x72521),f319(f319(f75(x72521),x72522),x72523)))+~P1(f319(f319(f226(x72521),f2(x72521)),x72523))
% 28.73/28.53 [7253]~P142(x72531)+~P1(f319(f319(f226(x72531),x72533),f2(x72531)))+E(f319(f319(f75(x72531),f319(f69(x72531),x72532)),f319(f69(x72531),x72533)),f319(f69(x72531),f319(f319(f75(x72531),x72532),x72533)))+~P1(f319(f319(f226(x72531),f2(x72531)),x72532))
% 28.73/28.53 [7310]~P142(x73101)+E(f319(f319(f75(x73101),f319(f69(x73101),x73102)),f319(f69(x73101),x73103)),f319(f69(x73101),f319(f319(f75(x73101),x73102),x73103)))+~P1(f319(f319(f226(x73101),f2(x73101)),x73102))+~P1(f319(f319(f226(x73101),f2(x73101)),x73103))
% 28.73/28.53 [7326]~P132(x73261)+~P1(f319(f319(f226(x73261),x73263),f2(x73261)))+~P1(f319(f319(f226(x73261),x73262),f2(x73261)))+P1(f319(f319(f226(x73261),f2(x73261)),f319(f319(f75(x73261),x73262),x73263)))
% 28.73/28.53 [7327]~P132(x73271)+~P1(f319(f319(f226(x73271),x73273),f2(x73271)))+~P1(f319(f319(f226(x73271),x73272),f2(x73271)))+P1(f319(f319(f226(x73271),f2(x73271)),f319(f319(f75(x73271),x73272),x73273)))
% 28.73/28.53 [7328]~P130(x73281)+~P1(f319(f319(f226(x73281),x73283),f2(x73281)))+~P1(f319(f319(f226(x73281),x73282),f2(x73281)))+P1(f319(f319(f226(x73281),f2(x73281)),f319(f319(f75(x73281),x73282),x73283)))
% 28.73/28.53 [7329]~P75(x73291)+~P1(f319(f319(f227(x73291),x73293),f2(x73291)))+~P1(f319(f319(f226(x73291),x73292),f2(x73291)))+P1(f319(f319(f226(x73291),f2(x73291)),f319(f319(f283(x73291),x73292),x73293)))
% 28.73/28.53 [7330]~P74(x73301)+~P1(f319(f319(f226(x73301),x73303),f2(x73301)))+~P1(f319(f319(f226(x73301),x73302),f2(x73301)))+P1(f319(f319(f226(x73301),f2(x73301)),f319(f319(f283(x73301),x73302),x73303)))
% 28.73/28.53 [7331]~P130(x73311)+~P1(f319(f319(f227(x73311),x73313),f2(x73311)))+~P1(f319(f319(f227(x73311),x73312),f2(x73311)))+P1(f319(f319(f227(x73311),f2(x73311)),f319(f319(f75(x73311),x73312),x73313)))
% 28.73/28.53 [7332]~P75(x73321)+~P1(f319(f319(f227(x73321),x73323),f2(x73321)))+~P1(f319(f319(f227(x73321),x73322),f2(x73321)))+P1(f319(f319(f227(x73321),f2(x73321)),f319(f319(f283(x73321),x73322),x73323)))
% 28.73/28.53 [7333]~P74(x73331)+~P1(f319(f319(f227(x73331),x73333),f2(x73331)))+~P1(f319(f319(f227(x73331),x73332),f2(x73331)))+P1(f319(f319(f227(x73331),f2(x73331)),f319(f319(f283(x73331),x73332),x73333)))
% 28.73/28.53 [7334]~P129(x73341)+~P1(f319(f319(f227(a925),f2(a925)),x73343))+~P1(f319(f319(f227(x73341),f72(x73341)),x73342))+P1(f319(f319(f227(x73341),f72(x73341)),f319(f319(f236(x73341),x73342),x73343)))
% 28.73/28.53 [7433]~P132(x74331)+~P1(f319(f319(f226(x74331),f2(x74331)),x74333))+~P1(f319(f319(f226(x74331),f2(x74331)),x74332))+P1(f319(f319(f226(x74331),f2(x74331)),f319(f319(f75(x74331),x74332),x74333)))
% 28.73/28.53 [7434]~P139(x74341)+~P1(f319(f319(f226(x74341),f2(x74341)),x74343))+~P1(f319(f319(f226(x74341),f2(x74341)),x74342))+P1(f319(f319(f226(x74341),f2(x74341)),f319(f319(f75(x74341),x74342),x74343)))
% 28.73/28.53 [7435]~P130(x74351)+~P1(f319(f319(f226(x74351),f2(x74351)),x74353))+~P1(f319(f319(f226(x74351),f2(x74351)),x74352))+P1(f319(f319(f226(x74351),f2(x74351)),f319(f319(f75(x74351),x74352),x74353)))
% 28.73/28.53 [7436]~P93(x74361)+~P1(f319(f319(f226(x74361),f2(x74361)),x74363))+~P1(f319(f319(f226(x74361),f2(x74361)),x74362))+P1(f319(f319(f226(x74361),f2(x74361)),f319(f319(f74(x74361),x74362),x74363)))
% 28.73/28.53 [7437]~P75(x74371)+~P1(f319(f319(f227(x74371),f2(x74371)),x74373))+~P1(f319(f319(f226(x74371),f2(x74371)),x74372))+P1(f319(f319(f226(x74371),f2(x74371)),f319(f319(f283(x74371),x74372),x74373)))
% 28.73/28.53 [7438]~P74(x74381)+~P1(f319(f319(f226(x74381),f2(x74381)),x74383))+~P1(f319(f319(f226(x74381),f2(x74381)),x74382))+P1(f319(f319(f226(x74381),f2(x74381)),f319(f319(f283(x74381),x74382),x74383)))
% 28.73/28.53 [7439]~P129(x74391)+~P1(f319(f319(f227(x74391),f72(x74391)),x74393))+~P1(f319(f319(f227(x74391),f72(x74391)),x74392))+P1(f319(f319(f227(x74391),f72(x74391)),f319(f319(f75(x74391),x74392),x74393)))
% 28.73/28.53 [7440]~P134(x74401)+~P1(f319(f319(f227(x74401),f2(x74401)),x74403))+~P1(f319(f319(f227(x74401),f2(x74401)),x74402))+P1(f319(f319(f227(x74401),f2(x74401)),f319(f319(f75(x74401),x74402),x74403)))
% 28.73/28.53 [7441]~P93(x74411)+~P1(f319(f319(f226(x74411),f2(x74411)),x74413))+~P1(f319(f319(f227(x74411),f2(x74411)),x74412))+P1(f319(f319(f227(x74411),f2(x74411)),f319(f319(f74(x74411),x74412),x74413)))
% 28.73/28.53 [7442]~P93(x74421)+~P1(f319(f319(f226(x74421),f2(x74421)),x74422))+~P1(f319(f319(f227(x74421),f2(x74421)),x74423))+P1(f319(f319(f227(x74421),f2(x74421)),f319(f319(f74(x74421),x74422),x74423)))
% 28.73/28.53 [7443]~P93(x74431)+~P1(f319(f319(f227(x74431),f2(x74431)),x74433))+~P1(f319(f319(f227(x74431),f2(x74431)),x74432))+P1(f319(f319(f227(x74431),f2(x74431)),f319(f319(f74(x74431),x74432),x74433)))
% 28.73/28.53 [7444]~P75(x74441)+~P1(f319(f319(f227(x74441),f2(x74441)),x74443))+~P1(f319(f319(f227(x74441),f2(x74441)),x74442))+P1(f319(f319(f227(x74441),f2(x74441)),f319(f319(f283(x74441),x74442),x74443)))
% 28.73/28.53 [7445]~P74(x74451)+~P1(f319(f319(f227(x74451),f2(x74451)),x74453))+~P1(f319(f319(f227(x74451),f2(x74451)),x74452))+P1(f319(f319(f227(x74451),f2(x74451)),f319(f319(f283(x74451),x74452),x74453)))
% 28.73/28.53 [7524]~P102(x75241)+~P1(f319(f55(x75241),x75243))+E(f10(x75241,f319(f319(f301(x75241),x75242),x75243)),x75242)+~E(f319(f319(f23(f932(x75241,a923)),x75243),f319(f319(f301(x75241),x75242),f180(f932(x75241,a923)))),f180(f932(x75241,a923)))
% 28.73/28.53 [7525]~P102(x75251)+~P1(f319(f55(x75251),x75253))+E(f13(x75251,f319(f319(f301(x75251),x75252),x75253)),x75252)+~E(f319(f319(f23(f932(x75251,a923)),x75253),f319(f319(f301(x75251),x75252),f180(f932(x75251,a923)))),f180(f932(x75251,a923)))
% 28.73/28.53 [7526]~P4(x75261)+~P1(f319(f55(x75261),x75263))+E(f14(x75261,f319(f319(f301(x75261),x75262),x75263)),x75262)+~E(f319(f319(f23(f932(x75261,a923)),x75263),f319(f319(f301(x75261),x75262),f180(f932(x75261,a923)))),f180(f932(x75261,a923)))
% 28.73/28.53 [7527]~P4(x75271)+~P1(f319(f55(x75271),x75273))+E(f15(x75271,f319(f319(f301(x75271),x75272),x75273)),x75272)+~E(f319(f319(f23(f932(x75271,a923)),x75273),f319(f319(f301(x75271),x75272),f180(f932(x75271,a923)))),f180(f932(x75271,a923)))
% 28.73/28.53 [7529]~P130(x75291)+P1(f319(f319(f226(x75291),x75292),f2(x75291)))+P1(f319(f319(f226(x75291),f2(x75291)),x75293))+~P1(f319(f319(f226(x75291),f2(x75291)),f319(f319(f75(x75291),x75293),x75292)))
% 28.73/28.53 [7530]~P130(x75301)+P1(f319(f319(f226(x75301),x75302),f2(x75301)))+P1(f319(f319(f226(x75301),f2(x75301)),x75303))+~P1(f319(f319(f226(x75301),f2(x75301)),f319(f319(f75(x75301),x75302),x75303)))
% 28.73/28.53 [7531]~P74(x75311)+P1(f319(f319(f226(x75311),x75312),f2(x75311)))+P1(f319(f319(f226(x75311),f2(x75311)),x75313))+~P1(f319(f319(f226(x75311),f2(x75311)),f319(f319(f283(x75311),x75313),x75312)))
% 28.73/28.53 [7532]~P74(x75321)+P1(f319(f319(f226(x75321),x75322),f2(x75321)))+P1(f319(f319(f226(x75321),f2(x75321)),x75323))+~P1(f319(f319(f226(x75321),f2(x75321)),f319(f319(f283(x75321),x75322),x75323)))
% 28.73/28.53 [7533]~P130(x75331)+P1(f319(f319(f226(x75331),x75332),f2(x75331)))+P1(f319(f319(f226(x75331),f2(x75331)),x75332))+~P1(f319(f319(f226(x75331),f2(x75331)),f319(f319(f75(x75331),x75333),x75332)))
% 28.73/28.53 [7534]~P130(x75341)+P1(f319(f319(f226(x75341),x75342),f2(x75341)))+P1(f319(f319(f226(x75341),f2(x75341)),x75342))+~P1(f319(f319(f226(x75341),f2(x75341)),f319(f319(f75(x75341),x75342),x75343)))
% 28.73/28.53 [7535]~P74(x75351)+P1(f319(f319(f226(x75351),x75352),f2(x75351)))+P1(f319(f319(f226(x75351),f2(x75351)),x75352))+~P1(f319(f319(f226(x75351),f2(x75351)),f319(f319(f283(x75351),x75353),x75352)))
% 28.73/28.53 [7536]~P74(x75361)+P1(f319(f319(f226(x75361),x75362),f2(x75361)))+P1(f319(f319(f226(x75361),f2(x75361)),x75362))+~P1(f319(f319(f226(x75361),f2(x75361)),f319(f319(f283(x75361),x75362),x75363)))
% 28.73/28.53 [7537]~P74(x75371)+P1(f319(f319(f227(x75371),x75372),f2(x75371)))+P1(f319(f319(f227(x75371),f2(x75371)),x75373))+~P1(f319(f319(f227(x75371),f2(x75371)),f319(f319(f283(x75371),x75373),x75372)))
% 28.73/28.53 [7538]~P74(x75381)+P1(f319(f319(f227(x75381),x75382),f2(x75381)))+P1(f319(f319(f227(x75381),f2(x75381)),x75383))+~P1(f319(f319(f227(x75381),f2(x75381)),f319(f319(f283(x75381),x75382),x75383)))
% 28.73/28.53 [7539]~P74(x75391)+P1(f319(f319(f227(x75391),x75392),f2(x75391)))+P1(f319(f319(f227(x75391),f2(x75391)),x75392))+~P1(f319(f319(f227(x75391),f2(x75391)),f319(f319(f283(x75391),x75393),x75392)))
% 28.73/28.53 [7540]~P74(x75401)+P1(f319(f319(f227(x75401),x75402),f2(x75401)))+P1(f319(f319(f227(x75401),f2(x75401)),x75402))+~P1(f319(f319(f227(x75401),f2(x75401)),f319(f319(f283(x75401),x75402),x75403)))
% 28.73/28.53 [7624]~E(f319(f319(f93(f932(x76241,a923)),f319(f164(x76241),x76242)),f319(f164(x76241),x76243)),f180(f932(x76241,a923)))+~P1(f319(f129(x76241),x76243))+~P1(f319(f129(x76241),x76242))+P1(f319(f129(x76241),f319(f319(f126(x76241),x76242),x76243)))
% 28.73/28.53 [7625]~P4(x76251)+~P1(f319(f55(x76251),x76253))+E(f11(x76251,f224(x76251),f319(f319(f301(x76251),x76252),x76253)),x76252)+~E(f319(f319(f23(f932(x76251,a923)),x76253),f319(f319(f301(x76251),x76252),f180(f932(x76251,a923)))),f180(f932(x76251,a923)))
% 28.73/28.53 [7626]~P4(x76261)+~P1(f319(f55(x76261),x76263))+E(f12(x76261,f225(x76261),f319(f319(f301(x76261),x76262),x76263)),x76262)+~E(f319(f319(f23(f932(x76261,a923)),x76263),f319(f319(f301(x76261),x76262),f180(f932(x76261,a923)))),f180(f932(x76261,a923)))
% 28.73/28.53 [7638]~P92(x76381)+~P1(f319(f319(f226(x76381),x76382),x76383))+~P1(f319(f319(f226(x76381),f319(f73(x76381),x76382)),x76383))+P1(f319(f319(f226(x76381),f319(f69(x76381),x76382)),x76383))
% 28.73/28.53 [7639]~P92(x76391)+~P1(f319(f319(f226(x76391),x76392),x76393))+~P1(f319(f319(f226(x76391),f319(f73(x76391),x76392)),x76393))+P1(f319(f319(f226(x76391),f319(f69(x76391),x76392)),x76393))
% 28.73/28.53 [7640]~P126(x76401)+~P1(f319(f319(f227(x76401),x76402),x76403))+~P1(f319(f319(f227(x76401),f319(f73(x76401),x76402)),x76403))+P1(f319(f319(f227(x76401),f319(f69(x76401),x76402)),x76403))
% 28.73/28.53 [7707]~P134(x77071)+P1(f319(f319(f227(x77071),f2(x77071)),x77072))+~P1(f319(f319(f227(x77071),f2(x77071)),x77073))+~P1(f319(f319(f227(x77071),f2(x77071)),f319(f319(f75(x77071),x77073),x77072)))
% 28.73/28.53 [7708]~P134(x77081)+P1(f319(f319(f227(x77081),f2(x77081)),x77082))+~P1(f319(f319(f227(x77081),f2(x77081)),x77083))+~P1(f319(f319(f227(x77081),f2(x77081)),f319(f319(f75(x77081),x77082),x77083)))
% 28.73/28.53 [8006]E(x80061,x80062)+~P1(f319(f55(x80063),x80061))+~P1(f319(f319(f226(a925),f319(f29(x80063),x80061)),f319(f29(x80063),x80062)))+~P1(f319(f319(f226(f932(x80063,a923)),x80062),x80061))
% 28.73/28.53 [8075]~P1(f319(f319(f226(a925),x80752),x80751))+~P1(f319(f319(f226(a925),x80752),x80753))+~P1(f319(f319(f226(a925),x80751),x80753))+P1(f319(f319(f226(a925),f319(f319(f23(a925),x80751),x80752)),f319(f319(f23(a925),x80753),x80752)))
% 28.73/28.53 [8076]~P1(f319(f319(f226(a925),x80762),x80761))+~P1(f319(f319(f226(a925),x80762),x80763))+~P1(f319(f319(f227(a925),x80761),x80763))+P1(f319(f319(f227(a925),f319(f319(f23(a925),x80761),x80762)),f319(f319(f23(a925),x80763),x80762)))
% 28.73/28.53 [8153]~P1(f319(f319(f227(a1),x81531),f2(a1)))+~P1(f319(f319(f227(a1),f2(a1)),x81532))+~P1(f319(f319(f226(a1),x81532),x81533))+P1(f319(f319(f226(a1),f319(f319(f30(a1),x81531),x81532)),f319(f319(f30(a1),x81531),x81533)))
% 28.73/28.53 [8164]~P1(f319(f319(f226(a1),f2(a1)),x81641))+~P1(f319(f319(f227(a1),f2(a1)),x81643))+~P1(f319(f319(f226(a1),x81643),x81642))+P1(f319(f319(f226(a1),f319(f319(f30(a1),x81641),x81642)),f319(f319(f30(a1),x81641),x81643)))
% 28.73/28.53 [8300]E(f319(x83001,f443(x83002,x83001,x83003)),x83002)+~P1(f319(f319(f226(a1),x83002),f319(x83001,x83003)))+P1(f319(f319(f227(a925),f444(x83002,x83001,x83003)),x83003))+~P1(f319(f319(f226(a1),f319(x83001,f2(a925))),x83002))
% 28.73/28.53 [8301]E(f319(x83011,f448(x83012,x83011,x83013)),x83012)+~P1(f319(f319(f226(a1),x83012),f319(x83011,x83013)))+P1(f319(f319(f227(a925),f449(x83012,x83011,x83013)),x83013))+~P1(f319(f319(f226(a1),f319(x83011,f2(a925))),x83012))
% 28.73/28.53 [8403]~P1(f319(f55(x84031),x84033))+~P1(f319(f319(f227(a925),f319(f29(x84031),x84032)),f319(f29(x84031),x84033)))+~P1(f319(f319(f226(f932(x84031,a923)),x84032),x84033))+P1(f319(f319(f227(f932(x84031,a923)),x84032),x84033))
% 28.73/28.53 [8430]E(f319(f319(f74(a1),f375(x84303,x84301,x84302)),f376(x84303,x84301,x84302)),x84301)+E(f319(f319(f23(a1),x84301),x84302),x84301)+~P1(f319(f319(f227(a1),f2(a1)),x84302))+~P1(f319(f319(f321(a1),f319(f319(f23(a1),x84301),f72(a1))),x84303))
% 28.73/28.53 [8431]E(f319(f319(f23(a1),f377(x84313,x84311,x84312)),f378(x84313,x84311,x84312)),x84311)+E(f319(f319(f74(a1),x84311),x84312),x84311)+~P1(f319(f319(f227(a1),f2(a1)),x84312))+~P1(f319(f319(f321(a1),f319(f319(f74(a1),x84311),f72(a1))),x84313))
% 28.73/28.53 [8483]~P1(f319(f319(f226(a925),x84833),x84831))+P1(f319(f319(f226(a925),x84831),x84832))+~P1(f319(f319(f226(a925),x84833),x84832))+~P1(f319(f319(f226(a925),f319(f319(f23(a925),x84831),x84833)),f319(f319(f23(a925),x84832),x84833)))
% 28.73/28.53 [8484]~P1(f319(f319(f226(a925),x84843),x84841))+P1(f319(f319(f227(a925),x84841),x84842))+~P1(f319(f319(f226(a925),x84843),x84842))+~P1(f319(f319(f227(a925),f319(f319(f23(a925),x84841),x84843)),f319(f319(f23(a925),x84842),x84843)))
% 28.73/28.53 [8503]~P4(x85032)+E(x85031,f105(x85032))+~P14(x85032,f319(f160(x85032),x85031))+E(f319(f134(x85032,x85032,f319(f7(x85032,x85032,x85032),f225(x85032)),x85033),f319(f160(x85032),x85031)),f319(f319(f225(x85032),f319(f319(f156(x85032),x85031),f2(a925))),x85033))
% 28.73/28.53 [8551]~P6(x85511)+~P41(x85511,x85511,x85513)+P1(f319(f319(f226(x85511),x85512),f88(x85511,x85513)))+~P1(f319(f319(f226(x85511),x85512),f319(x85513,f319(f319(f102(x85511),x85512),f88(x85511,x85513)))))
% 28.73/28.53 [8573]E(f319(f319(f23(a1),x85731),x85732),x85731)+~P1(f319(f319(f227(a1),f2(a1)),x85732))+P1(f319(f319(f321(a1),f375(x85733,x85731,x85732)),x85733))+~P1(f319(f319(f321(a1),f319(f319(f23(a1),x85731),f72(a1))),x85733))
% 28.73/28.53 [8574]E(f319(f319(f74(a1),x85741),x85742),x85741)+~P1(f319(f319(f227(a1),f2(a1)),x85742))+P1(f319(f319(f321(a1),f377(x85743,x85741,x85742)),x85743))+~P1(f319(f319(f321(a1),f319(f319(f74(a1),x85741),f72(a1))),x85743))
% 28.73/28.53 [8646]~P1(f319(f319(f226(a1),x86461),f319(x86462,x86463)))+P1(f319(f319(f227(a925),f444(x86461,x86462,x86463)),x86463))+P1(f319(f319(f226(a925),f443(x86461,x86462,x86463)),x86463))+~P1(f319(f319(f226(a1),f319(x86462,f2(a925))),x86461))
% 28.73/28.53 [8647]~P1(f319(f319(f226(a1),x86471),f319(x86472,x86473)))+P1(f319(f319(f227(a925),f449(x86471,x86472,x86473)),x86473))+P1(f319(f319(f226(a925),f448(x86471,x86472,x86473)),x86473))+~P1(f319(f319(f226(a1),f319(x86472,f2(a925))),x86471))
% 28.73/28.53 [8724]E(f319(f319(f23(a1),x87241),x87242),x87241)+~P1(f319(f319(f227(a1),f2(a1)),x87242))+P1(f319(f319(f321(a1),f376(x87243,x87241,x87242)),f295(a1,f72(a1),x87242)))+~P1(f319(f319(f321(a1),f319(f319(f23(a1),x87241),f72(a1))),x87243))
% 28.73/28.53 [8725]E(f319(f319(f74(a1),x87251),x87252),x87251)+~P1(f319(f319(f227(a1),f2(a1)),x87252))+P1(f319(f319(f321(a1),f378(x87253,x87251,x87252)),f295(a1,f72(a1),x87252)))+~P1(f319(f319(f321(a1),f319(f319(f74(a1),x87251),f72(a1))),x87253))
% 28.73/28.53 [8858]~P129(x88581)+~P1(f319(f319(f227(x88581),x88582),f72(x88581)))+~P1(f319(f319(f227(x88581),f2(x88581)),x88582))+P1(f319(f319(f227(x88581),f319(f319(f75(x88581),x88582),f319(f319(f236(x88581),x88582),x88583))),f319(f319(f236(x88581),x88582),x88583)))
% 28.73/28.53 [8951]~P1(f319(x89511,x89512))+P1(f319(x89511,f2(a925)))+~P1(f319(f319(f227(a925),x89512),x89513))+~P1(f319(x89511,f39(a925,f319(a104,f523(x89512,x89511,x89513)),x89513)))
% 28.73/28.53 [9105]E(f544(x91051,x91052,x91053),f2(a925))+P1(f319(f319(x91051,x91053),x91052))+P1(f319(f319(x91051,f544(x91051,x91052,x91053)),f39(a925,f543(x91051,x91052,x91053),f544(x91051,x91052,x91053))))+~P1(f319(f307(f931(a925,a925),a211),f319(f319(f244(a925,a925),x91053),x91052)))
% 28.73/28.53 [9143]~P26(x91431,x91431,x91432,x91433)+E(f319(f302(x91431,x91431,x91432),x91433),x91433)+~P1(f319(f55(x91431),x91433))+~P1(f319(f319(f226(f932(x91431,a923)),f319(f302(x91431,x91431,x91432),x91433)),x91433))
% 28.73/28.53 [9216]~P6(x92161)+~P41(x92161,x92161,x92163)+P1(f319(f319(f226(x92161),f319(f319(f102(x92161),x92162),f88(x92161,x92163))),f319(x92163,f319(f319(f102(x92161),x92162),f88(x92161,x92163)))))+~P1(f319(f319(f226(x92161),x92162),f319(x92163,f319(f319(f102(x92161),x92162),f88(x92161,x92163)))))
% 28.73/28.53 [9363]P1(f319(f319(x93631,x93632),x93633))+P1(f319(f319(f227(a1),f795(x93631,x93633,x93632)),f796(x93631,x93633,x93632)))+P1(f319(f319(x93631,f795(x93631,x93633,x93632)),f319(f319(f74(a1),f796(x93631,x93633,x93632)),f72(a1))))+~P1(f319(f307(f931(a1,a1),a125),f319(f319(f244(a1,a1),x93632),x93633)))
% 28.73/28.53 [9380]P1(f319(f319(x93801,x93802),x93803))+~P1(f319(f319(f227(a1),f542(x93801,x93803,x93802)),f2(a1)))+P1(f319(f319(x93801,f319(f73(a1),f541(x93801,x93803,x93802))),f319(f73(a1),f542(x93801,x93803,x93802))))+~P1(f319(f307(f931(a1,a1),a213),f319(f319(f244(a1,a1),x93802),x93803)))
% 28.73/28.53 [9572]P1(f319(f319(x95721,x95722),x95723))+P1(f319(f319(x95721,f319(f319(f74(a1),f698(x95721,x95723,x95722)),f72(a1))),f699(x95721,x95723,x95722)))+~P1(f319(f319(f226(a1),f698(x95721,x95723,x95722)),f699(x95721,x95723,x95722)))+~P1(f319(f307(f931(a1,a1),a174),f319(f319(f244(a1,a1),x95722),x95723)))
% 28.73/28.53 [10025]~P5(x100252)+~P5(x100251)+~P1(f319(f51(f931(x100251,x100252)),x100253))+P1(f319(f51(x100251),f319(f319(f8(f932(x100252,a923),a923,x100251),f51(x100252)),f319(f319(f8(f932(x100252,f931(x100251,x100252)),f932(x100252,a923),x100251),f319(f8(f931(x100251,x100252),a923,x100252),x100253)),f244(x100251,x100252)))))
% 28.73/28.53 [10026]~P5(x100262)+~P5(x100261)+~P1(f319(f50(f931(x100261,x100262)),x100263))+P1(f319(f50(x100261),f319(f319(f8(f932(x100262,a923),a923,x100261),f50(x100262)),f319(f319(f8(f932(x100262,f931(x100261,x100262)),f932(x100262,a923),x100261),f319(f8(f931(x100261,x100262),a923,x100262),x100263)),f244(x100261,x100262)))))
% 28.73/28.53 [10126]~P5(x101262)+~P5(x101261)+P1(f319(f51(f931(x101261,x101262)),x101263))+~P1(f319(f51(x101261),f319(f319(f8(f932(x101262,a923),a923,x101261),f51(x101262)),f319(f319(f8(f932(x101262,f931(x101261,x101262)),f932(x101262,a923),x101261),f319(f8(f931(x101261,x101262),a923,x101262),x101263)),f244(x101261,x101262)))))
% 28.73/28.53 [10127]~P5(x101272)+~P5(x101271)+P1(f319(f50(f931(x101271,x101272)),x101273))+~P1(f319(f50(x101271),f319(f319(f8(f932(x101272,a923),a923,x101271),f50(x101272)),f319(f319(f8(f932(x101272,f931(x101271,x101272)),f932(x101272,a923),x101271),f319(f8(f931(x101271,x101272),a923,x101272),x101273)),f244(x101271,x101272)))))
% 28.73/28.53 [10304]E(f319(x103041,f443(x103042,x103041,x103043)),x103042)+~P1(f319(f319(f226(a1),x103042),f319(x103041,x103043)))+~P1(f319(f319(f226(a1),f319(f69(a1),f319(f319(f23(a1),f319(x103041,f319(f319(f74(a925),f444(x103042,x103041,x103043)),f72(a925)))),f319(x103041,f444(x103042,x103041,x103043))))),f72(a1)))+~P1(f319(f319(f226(a1),f319(x103041,f2(a925))),x103042))
% 28.73/28.53 [10305]E(f319(x103051,f448(x103052,x103051,x103053)),x103052)+~P1(f319(f319(f226(a1),x103052),f319(x103051,x103053)))+~P1(f319(f319(f226(a1),f319(f69(a1),f319(f319(f23(a1),f319(x103051,f319(f319(f74(a925),f449(x103052,x103051,x103053)),f72(a925)))),f319(x103051,f449(x103052,x103051,x103053))))),f72(a1)))+~P1(f319(f319(f226(a1),f319(x103051,f2(a925))),x103052))
% 28.73/28.53 [10308]~P1(f319(f319(f226(a1),x103081),f319(x103082,x103083)))+~P1(f319(f319(f226(a1),f319(f69(a1),f319(f319(f23(a1),f319(x103082,f319(f319(f74(a925),f444(x103081,x103082,x103083)),f72(a925)))),f319(x103082,f444(x103081,x103082,x103083))))),f72(a1)))+P1(f319(f319(f226(a925),f443(x103081,x103082,x103083)),x103083))+~P1(f319(f319(f226(a1),f319(x103082,f2(a925))),x103081))
% 28.73/28.53 [10309]~P1(f319(f319(f226(a1),x103091),f319(x103092,x103093)))+~P1(f319(f319(f226(a1),f319(f69(a1),f319(f319(f23(a1),f319(x103092,f319(f319(f74(a925),f449(x103091,x103092,x103093)),f72(a925)))),f319(x103092,f449(x103091,x103092,x103093))))),f72(a1)))+P1(f319(f319(f226(a925),f448(x103091,x103092,x103093)),x103093))+~P1(f319(f319(f226(a1),f319(x103092,f2(a925))),x103091))
% 28.73/28.53 [10367]E(x103671,x103672)+~E(f319(f134(f926(x103673),f926(x103673),f126(x103673),f105(x103673)),x103671),f319(f134(f926(x103673),f926(x103673),f126(x103673),f105(x103673)),x103672))+~E(f319(f181(f926(f926(x103673))),x103671),f319(f181(f926(f926(x103673))),x103672))+~P1(f319(f319(f249(f926(x103673),f926(x103673),a923),f319(f319(f7(f926(x103673),f932(f926(x103673),a925),f932(f926(x103673),a923)),f319(f319(f8(f932(a925,a923),f932(f932(f926(x103673),a925),f932(f926(x103673),a923)),f926(x103673)),f8(a925,a923,f926(x103673))),f319(f319(f8(a925,f932(a925,a923),f926(x103673)),a316),f181(f926(x103673))))),f181(f926(x103673)))),f724(x103672,x103671,x103673)))
% 28.73/28.53 [10368]E(x103681,x103682)+~E(f319(f134(f926(x103683),f926(x103683),f126(x103683),f105(x103683)),x103681),f319(f134(f926(x103683),f926(x103683),f126(x103683),f105(x103683)),x103682))+~E(f319(f181(f926(f926(x103683))),x103681),f319(f181(f926(f926(x103683))),x103682))+~P1(f319(f319(f249(f926(x103683),f926(x103683),a923),f319(f319(f7(f926(x103683),f932(f926(x103683),a925),f932(f926(x103683),a923)),f319(f319(f8(f932(a925,a923),f932(f932(f926(x103683),a925),f932(f926(x103683),a923)),f926(x103683)),f8(a925,a923,f926(x103683))),f319(f319(f8(a925,f932(a925,a923),f926(x103683)),a316),f181(f926(x103683))))),f181(f926(x103683)))),f725(x103681,x103682,x103683)))
% 28.73/28.53 [7036]~E(f72(a925),f2(a925))+~P1(f319(f55(x70361),x70363))+~P1(f319(f55(x70361),x70362))+E(f319(f319(f74(a925),f319(f29(x70361),x70362)),f319(f29(x70361),x70363)),f319(f29(x70361),f319(f319(f102(f932(x70361,a923)),x70362),x70363)))
% 28.73/28.53 [7452]~P108(x74521)+~P1(f319(f55(x74521),x74522))+~P1(f319(f319(f321(x74521),x74523),x74522))+P1(f319(f319(f226(x74521),f319(f57(x74521,f93(x74521)),x74522)),x74523))
% 28.73/28.53 [7453]~P4(x74531)+~P1(f319(f55(x74531),x74532))+~P1(f319(f319(f321(x74531),x74533),x74532))+P1(f319(f319(f226(x74531),f319(f57(x74531,f224(x74531)),x74532)),x74533))
% 28.73/28.53 [7701]~P1(f319(f55(x77011),x77013))+~P1(f319(f55(x77011),x77012))+~E(f319(f319(f93(f932(x77011,a923)),x77012),x77013),f180(f932(x77011,a923)))+E(f319(f319(f74(a925),f319(f29(x77011),x77012)),f319(f29(x77011),x77013)),f319(f29(x77011),f319(f319(f102(f932(x77011,a923)),x77012),x77013)))
% 28.73/28.53 [8489]~P38(x84891,x84893)+~P38(x84891,x84892)+~E(f319(f319(f93(f932(x84891,a923)),f319(f256(x84891,x84891),x84892)),f319(f276(x84891,x84891),x84893)),f180(f932(x84891,a923)))+P38(x84891,f319(f319(f102(f932(f931(x84891,x84891),a923)),x84892),x84893))
% 28.73/28.53 [8585]E(x85851,f319(f319(f30(a925),x85852),x85853))+~P1(f319(f319(f227(a925),f2(a925)),x85853))+~P1(f319(f319(f227(a925),x85852),f319(f319(f75(a925),x85853),f319(a104,x85851))))+~P1(f319(f319(f226(a925),f319(f319(f75(a925),x85853),x85851)),x85852))
% 28.73/28.53 [8722]~P1(f319(f55(x87221),x87222))+~P1(f319(f55(x87221),x87223))+E(f319(f319(f74(a925),f319(f29(x87221),x87222)),f319(f29(x87221),x87223)),f319(f29(x87221),f319(f319(f102(f932(x87221,a923)),x87222),x87223)))+P1(f319(f319(f321(x87221),f423(x87223,x87222,x87221)),f319(f319(f93(f932(x87221,a923)),x87222),x87223)))
% 28.73/28.53 [9117]~P130(x91172)+~E(x91171,f2(x91172))+~E(x91173,f2(x91172))+~P1(f319(f319(f227(x91172),f2(x91172)),f319(f319(f74(x91172),f319(f319(f75(x91172),x91173),x91173)),f319(f319(f75(x91172),x91171),x91171))))
% 28.73/28.53 [9654]~P38(x96541,x96543)+~P38(x96541,x96542)+P38(x96541,f319(f319(f102(f932(f931(x96541,x96541),a923)),x96542),x96543))+~P1(f319(f319(f226(f932(f931(x96541,x96541),a923)),f319(f319(f281(x96541,x96541,x96541),x96542),x96543)),x96542))
% 28.73/28.53 [9785]~P1(f319(x97851,x97853))+~P1(f319(f55(x97852),x97853))+P1(f319(x97851,f180(f932(x97852,a923))))+~P1(f319(x97851,f319(f319(f23(f932(x97852,a923)),f335(x97851,x97853,x97852)),f319(f319(f301(x97852),f336(x97851,x97853,x97852)),f180(f932(x97852,a923))))))
% 28.73/28.53 [8898]~P1(f319(f319(f227(a1),f2(a1)),x88983))+P1(f319(f319(f226(a1),f2(a1)),x88981))+~P1(f319(f319(f227(a1),x88982),x88983))+~P1(f319(f319(f226(a1),f2(a1)),f319(f319(f74(a1),f319(f319(f75(a1),x88983),x88981)),x88982)))
% 28.73/28.53 [8922]~P102(x89221)+~P1(f319(f55(x89221),x89222))+E(f319(f319(f23(f932(x89221,a923)),x89222),f319(f319(f301(x89221),x89223),f180(f932(x89221,a923)))),f180(f932(x89221,a923)))+E(f319(f319(f93(x89221),x89223),f10(x89221,f319(f319(f23(f932(x89221,a923)),x89222),f319(f319(f301(x89221),x89223),f180(f932(x89221,a923)))))),f10(x89221,f319(f319(f301(x89221),x89223),x89222)))
% 28.73/28.53 [8923]~P102(x89231)+~P1(f319(f55(x89231),x89232))+E(f319(f319(f23(f932(x89231,a923)),x89232),f319(f319(f301(x89231),x89233),f180(f932(x89231,a923)))),f180(f932(x89231,a923)))+E(f319(f319(f102(x89231),x89233),f13(x89231,f319(f319(f23(f932(x89231,a923)),x89232),f319(f319(f301(x89231),x89233),f180(f932(x89231,a923)))))),f13(x89231,f319(f319(f301(x89231),x89233),x89232)))
% 28.73/28.53 [8924]~P4(x89241)+~P1(f319(f55(x89241),x89242))+E(f319(f319(f23(f932(x89241,a923)),x89242),f319(f319(f301(x89241),x89243),f180(f932(x89241,a923)))),f180(f932(x89241,a923)))+E(f319(f319(f224(x89241),x89243),f14(x89241,f319(f319(f23(f932(x89241,a923)),x89242),f319(f319(f301(x89241),x89243),f180(f932(x89241,a923)))))),f14(x89241,f319(f319(f301(x89241),x89243),x89242)))
% 28.73/28.53 [8925]~P4(x89251)+~P1(f319(f55(x89251),x89252))+E(f319(f319(f23(f932(x89251,a923)),x89252),f319(f319(f301(x89251),x89253),f180(f932(x89251,a923)))),f180(f932(x89251,a923)))+E(f319(f319(f225(x89251),x89253),f15(x89251,f319(f319(f23(f932(x89251,a923)),x89252),f319(f319(f301(x89251),x89253),f180(f932(x89251,a923)))))),f15(x89251,f319(f319(f301(x89251),x89253),x89252)))
% 28.73/28.53 [8998]~P4(x89981)+~P1(f319(f55(x89981),x89982))+E(f319(f319(f23(f932(x89981,a923)),x89982),f319(f319(f301(x89981),x89983),f180(f932(x89981,a923)))),f180(f932(x89981,a923)))+E(f319(f319(f224(x89981),x89983),f11(x89981,f224(x89981),f319(f319(f23(f932(x89981,a923)),x89982),f319(f319(f301(x89981),x89983),f180(f932(x89981,a923)))))),f11(x89981,f224(x89981),f319(f319(f301(x89981),x89983),x89982)))
% 28.73/28.53 [8999]~P4(x89991)+~P1(f319(f55(x89991),x89992))+E(f319(f319(f23(f932(x89991,a923)),x89992),f319(f319(f301(x89991),x89993),f180(f932(x89991,a923)))),f180(f932(x89991,a923)))+E(f319(f319(f225(x89991),x89993),f12(x89991,f225(x89991),f319(f319(f23(f932(x89991,a923)),x89992),f319(f319(f301(x89991),x89993),f180(f932(x89991,a923)))))),f12(x89991,f225(x89991),f319(f319(f301(x89991),x89993),x89992)))
% 28.73/28.53 [9385]~P6(x93851)+~P41(x93851,x93851,x93852)+P1(f319(f319(f226(x93851),f87(x93851,x93852)),x93853))+~P1(f319(f319(f226(x93851),f319(x93852,f319(f319(f93(x93851),f87(x93851,x93852)),x93853))),x93853))
% 28.73/28.53 [9591]E(x95911,x95912)+~E(f319(f134(f926(x95913),f926(x95913),f126(x95913),f105(x95913)),x95911),f319(f134(f926(x95913),f926(x95913),f126(x95913),f105(x95913)),x95912))+~E(f319(f181(f926(f926(x95913))),x95911),f319(f181(f926(f926(x95913))),x95912))+P1(f319(f319(f321(f931(f926(x95913),f926(x95913))),f724(x95912,x95911,x95913)),f319(f164(f931(f926(x95913),f926(x95913))),f319(f319(f173(f926(x95913),f926(x95913)),x95911),x95912))))
% 28.73/28.53 [9592]E(x95921,x95922)+~E(f319(f134(f926(x95923),f926(x95923),f126(x95923),f105(x95923)),x95921),f319(f134(f926(x95923),f926(x95923),f126(x95923),f105(x95923)),x95922))+~E(f319(f181(f926(f926(x95923))),x95921),f319(f181(f926(f926(x95923))),x95922))+P1(f319(f319(f321(f931(f926(x95923),f926(x95923))),f725(x95921,x95922,x95923)),f319(f164(f931(f926(x95923),f926(x95923))),f319(f319(f173(f926(x95923),f926(x95923)),x95922),x95921))))
% 28.73/28.53 [10473]~P106(x104732)+E(x104731,f180(f932(x104732,a923)))+~P1(f319(f55(x104732),x104731))+E(f10(x104732,f319(f254(x104732),f319(f319(f8(f932(x104732,a923),a923,x104732),f81(x104732)),f319(f319(f7(x104732,f932(x104732,a923),f932(x104732,a923)),f319(f319(f8(f932(x104732,f932(a923,a923)),f932(f932(x104732,a923),f932(x104732,a923)),x104732),f18(x104732,a923,a923)),f319(f319(f8(f932(x104732,a923),f932(x104732,f932(a923,a923)),x104732),f319(f8(a923,f932(a923,a923),x104732),a317)),f319(f319(f7(x104732,f932(x104732,x104732),f932(x104732,a923)),f319(f319(f8(f932(x104732,a923),f932(f932(x104732,x104732),f932(x104732,a923)),x104732),f8(x104732,a923,x104732)),a316)),f319(f102(x104732),x104733))))),f319(f319(f7(x104732,f932(x104732,a923),a923),f321(x104732)),x104731))))),f319(f319(f102(x104732),x104733),f10(x104732,x104731)))
% 28.73/28.53 [10474]~P106(x104742)+E(x104741,f180(f932(x104742,a923)))+~P1(f319(f55(x104742),x104741))+E(f13(x104742,f319(f254(x104742),f319(f319(f8(f932(x104742,a923),a923,x104742),f81(x104742)),f319(f319(f7(x104742,f932(x104742,a923),f932(x104742,a923)),f319(f319(f8(f932(x104742,f932(a923,a923)),f932(f932(x104742,a923),f932(x104742,a923)),x104742),f18(x104742,a923,a923)),f319(f319(f8(f932(x104742,a923),f932(x104742,f932(a923,a923)),x104742),f319(f8(a923,f932(a923,a923),x104742),a317)),f319(f319(f7(x104742,f932(x104742,x104742),f932(x104742,a923)),f319(f319(f8(f932(x104742,a923),f932(f932(x104742,x104742),f932(x104742,a923)),x104742),f8(x104742,a923,x104742)),a316)),f319(f93(x104742),x104743))))),f319(f319(f7(x104742,f932(x104742,a923),a923),f321(x104742)),x104741))))),f319(f319(f93(x104742),x104743),f13(x104742,x104741)))
% 28.73/28.53 [10475]~P85(x104752)+E(x104751,f180(f932(x104752,a923)))+~P1(f319(f55(x104752),x104751))+E(f14(x104752,f319(f254(x104752),f319(f319(f8(f932(x104752,a923),a923,x104752),f81(x104752)),f319(f319(f7(x104752,f932(x104752,a923),f932(x104752,a923)),f319(f319(f8(f932(x104752,f932(a923,a923)),f932(f932(x104752,a923),f932(x104752,a923)),x104752),f18(x104752,a923,a923)),f319(f319(f8(f932(x104752,a923),f932(x104752,f932(a923,a923)),x104752),f319(f8(a923,f932(a923,a923),x104752),a317)),f319(f319(f7(x104752,f932(x104752,x104752),f932(x104752,a923)),f319(f319(f8(f932(x104752,a923),f932(f932(x104752,x104752),f932(x104752,a923)),x104752),f8(x104752,a923,x104752)),a316)),f319(f74(x104752),x104753))))),f319(f319(f7(x104752,f932(x104752,a923),a923),f321(x104752)),x104751))))),f319(f319(f74(x104752),x104753),f14(x104752,x104751)))
% 28.73/28.53 [10476]~P85(x104762)+E(x104761,f180(f932(x104762,a923)))+~P1(f319(f55(x104762),x104761))+E(f15(x104762,f319(f254(x104762),f319(f319(f8(f932(x104762,a923),a923,x104762),f81(x104762)),f319(f319(f7(x104762,f932(x104762,a923),f932(x104762,a923)),f319(f319(f8(f932(x104762,f932(a923,a923)),f932(f932(x104762,a923),f932(x104762,a923)),x104762),f18(x104762,a923,a923)),f319(f319(f8(f932(x104762,a923),f932(x104762,f932(a923,a923)),x104762),f319(f8(a923,f932(a923,a923),x104762),a317)),f319(f319(f7(x104762,f932(x104762,x104762),f932(x104762,a923)),f319(f319(f8(f932(x104762,a923),f932(f932(x104762,x104762),f932(x104762,a923)),x104762),f8(x104762,a923,x104762)),a316)),f319(f74(x104762),x104763))))),f319(f319(f7(x104762,f932(x104762,a923),a923),f321(x104762)),x104761))))),f319(f319(f74(x104762),x104763),f15(x104762,x104761)))
% 28.73/28.53 [10477]~P4(x104772)+E(x104771,f180(f932(x104772,a923)))+~P1(f319(f55(x104772),x104771))+E(f12(x104772,f225(x104772),f319(f254(x104772),f319(f319(f8(f932(x104772,a923),a923,x104772),f81(x104772)),f319(f319(f7(x104772,f932(x104772,a923),f932(x104772,a923)),f319(f319(f8(f932(x104772,f932(a923,a923)),f932(f932(x104772,a923),f932(x104772,a923)),x104772),f18(x104772,a923,a923)),f319(f319(f8(f932(x104772,a923),f932(x104772,f932(a923,a923)),x104772),f319(f8(a923,f932(a923,a923),x104772),a317)),f319(f319(f7(x104772,f932(x104772,x104772),f932(x104772,a923)),f319(f319(f8(f932(x104772,a923),f932(f932(x104772,x104772),f932(x104772,a923)),x104772),f8(x104772,a923,x104772)),a316)),f319(f224(x104772),x104773))))),f319(f319(f7(x104772,f932(x104772,a923),a923),f321(x104772)),x104771))))),f319(f319(f224(x104772),x104773),f12(x104772,f225(x104772),x104771)))
% 28.73/28.53 [10478]~P4(x104782)+E(x104781,f180(f932(x104782,a923)))+~P1(f319(f55(x104782),x104781))+E(f11(x104782,f224(x104782),f319(f254(x104782),f319(f319(f8(f932(x104782,a923),a923,x104782),f81(x104782)),f319(f319(f7(x104782,f932(x104782,a923),f932(x104782,a923)),f319(f319(f8(f932(x104782,f932(a923,a923)),f932(f932(x104782,a923),f932(x104782,a923)),x104782),f18(x104782,a923,a923)),f319(f319(f8(f932(x104782,a923),f932(x104782,f932(a923,a923)),x104782),f319(f8(a923,f932(a923,a923),x104782),a317)),f319(f319(f7(x104782,f932(x104782,x104782),f932(x104782,a923)),f319(f319(f8(f932(x104782,a923),f932(f932(x104782,x104782),f932(x104782,a923)),x104782),f8(x104782,a923,x104782)),a316)),f319(f225(x104782),x104783))))),f319(f319(f7(x104782,f932(x104782,a923),a923),f321(x104782)),x104781))))),f319(f319(f225(x104782),x104783),f11(x104782,f224(x104782),x104781)))
% 28.73/28.53 [10190]~P126(x101901)+~E(x101903,f2(x101901))+~E(x101902,f2(x101901))+E(f319(f319(f74(x101901),f319(f319(f236(x101901),x101902),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))))),f319(f319(f236(x101901),x101903),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))))),f2(x101901))
% 28.73/28.53 [10348]~P129(x103481)+~P1(f319(f319(f226(x103481),f2(x103481)),x103483))+P1(f319(f319(f226(x103481),x103482),x103483))+~P1(f319(f319(f226(x103481),f319(f319(f236(x103481),x103482),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))))),f319(f319(f236(x103481),x103483),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))))))
% 28.73/28.53 [10349]~P129(x103491)+~P1(f319(f319(f226(x103491),f2(x103491)),x103493))+P1(f319(f319(f227(x103491),x103492),x103493))+~P1(f319(f319(f227(x103491),f319(f319(f236(x103491),x103492),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))))),f319(f319(f236(x103491),x103493),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))))))
% 28.73/28.53 [10404]~P126(x104042)+~E(x104041,f2(x104042))+~E(x104043,f2(x104042))+~P1(f319(f319(f227(x104042),f2(x104042)),f319(f319(f74(x104042),f319(f319(f236(x104042),x104043),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))))),f319(f319(f236(x104042),x104041),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))))))
% 28.73/28.53 [6214]~P4(x62141)+~P113(x62142)+~P51(x62141,x62142,x62143)+P26(x62141,x62142,x62143,x62144)
% 28.73/28.53 [6919]~P8(x69193,x69192)+~P1(f319(x69191,x69194))+~P1(f319(f319(f321(x69193),x69194),f262(x69193,x69192)))+P1(f319(x69191,f840(x69191,x69192,x69193)))
% 28.73/28.53 [8833]P27(x88331,x88332,f415(x88333,x88332,x88334,x88331),x88334,x88333)+~E(f319(f29(x88331),x88334),f319(f29(x88332),x88333))+~P1(f319(f55(x88332),x88333))+~P1(f319(f55(x88331),x88334))
% 28.73/28.53 [9554]E(x95541,x95542)+~E(f680(x95541,x95542,x95544,x95543),f683(x95541,x95542,x95544,x95543))+P1(f319(f319(f321(f931(f926(x95543),f926(x95543))),f319(f319(f244(f926(x95543),f926(x95543)),x95542),x95541)),f139(x95543,x95544)))+P1(f319(f319(f321(f931(f926(x95543),f926(x95543))),f319(f319(f244(f926(x95543),f926(x95543)),x95541),x95542)),f139(x95543,x95544)))
% 28.73/28.53 [5058]~P72(x50582)+~E(x50584,f2(x50582))+~E(x50581,f2(x50582))+E(x50581,f319(f319(f283(x50582),x50583),x50584))
% 28.73/28.53 [5059]~P72(x50591)+~E(x50593,f2(x50591))+~E(x50594,f2(x50591))+E(f319(f319(f283(x50591),x50592),x50593),x50594)
% 28.73/28.53 [5176]~P72(x51762)+E(x51761,f2(x51762))+~E(x51763,f2(x51762))+~E(x51761,f319(f319(f283(x51762),x51764),x51763))
% 28.73/28.53 [5177]~P72(x51772)+E(x51771,f2(x51772))+~E(x51773,f2(x51772))+~E(f319(f319(f283(x51772),x51774),x51773),x51771)
% 28.73/28.53 [5364]~P124(x53642)+E(x53641,f2(x53642))+~E(f319(f319(f283(x53642),x53643),x53641),x53644)+E(x53643,f319(f319(f75(x53642),x53644),x53641))
% 28.73/28.53 [5365]~P124(x53652)+E(x53651,f2(x53652))+~E(f319(f319(f75(x53652),x53653),x53651),x53654)+E(x53653,f319(f319(f283(x53652),x53654),x53651))
% 28.73/28.53 [5366]~P124(x53662)+E(x53661,f2(x53662))+~E(f319(f319(f75(x53662),x53663),x53661),x53664)+E(x53663,f319(f319(f283(x53662),x53664),x53661))
% 28.73/28.53 [5367]~P72(x53672)+E(x53671,f2(x53672))+~E(f319(f319(f283(x53672),x53673),x53671),x53674)+E(x53673,f319(f319(f75(x53672),x53674),x53671))
% 28.73/28.53 [5368]~P72(x53682)+E(x53681,f2(x53682))+~E(f319(f319(f75(x53682),x53683),x53681),x53684)+E(x53683,f319(f319(f283(x53682),x53684),x53681))
% 28.73/28.53 [5369]~P124(x53692)+E(x53691,f2(x53692))+~E(x53693,f319(f319(f283(x53692),x53694),x53691))+E(f319(f319(f75(x53692),x53693),x53691),x53694)
% 28.73/28.53 [5370]~P124(x53702)+E(x53701,f2(x53702))+~E(x53703,f319(f319(f75(x53702),x53704),x53701))+E(f319(f319(f283(x53702),x53703),x53701),x53704)
% 28.73/28.53 [5371]~P124(x53712)+E(x53711,f2(x53712))+~E(x53713,f319(f319(f75(x53712),x53714),x53711))+E(f319(f319(f283(x53712),x53713),x53711),x53714)
% 28.73/28.53 [5372]~P72(x53722)+E(x53721,f2(x53722))+~E(x53723,f319(f319(f283(x53722),x53724),x53721))+E(f319(f319(f75(x53722),x53723),x53721),x53724)
% 28.73/28.53 [5373]~P72(x53732)+E(x53731,f2(x53732))+~E(x53733,f319(f319(f75(x53732),x53734),x53731))+E(f319(f319(f283(x53732),x53733),x53731),x53734)
% 28.73/28.53 [5397]~P72(x53972)+~E(x53971,f2(x53972))+~E(f319(f319(f75(x53972),x53971),x53974),x53973)+E(x53971,f319(f319(f283(x53972),x53973),x53974))
% 28.73/28.53 [5398]~P72(x53981)+~E(x53984,f2(x53981))+~E(x53982,f319(f319(f75(x53981),x53984),x53983))+E(f319(f319(f283(x53981),x53982),x53983),x53984)
% 28.73/28.53 [5472]~E(x54723,x54724)+~E(x54722,x54723)+~P113(x54721)+E(f295(x54721,x54722,x54723),f319(f319(f301(x54721),x54724),f180(f932(x54721,a923))))
% 28.73/28.53 [5671]~E(f106(x56712,x56711),x56713)+~E(f136(x56712,x56711),x56714)+E(x56711,f105(x56712))+E(f319(f319(f126(x56712),x56713),f319(f319(f143(x56712),x56714),f105(x56712))),x56711)
% 28.73/28.53 [6304]~P129(x63043)+E(x63041,x63042)+~E(f319(f319(f236(x63043),x63044),x63041),f319(f319(f236(x63043),x63044),x63042))+~P1(f319(f319(f227(x63043),f72(x63043)),x63044))
% 28.73/28.53 [6305]E(x63051,x63052)+~E(f319(f319(f301(x63053),x63054),x63051),f319(f319(f301(x63053),x63054),x63052))+P1(f319(f319(f321(x63053),x63054),x63052))+P1(f319(f319(f321(x63053),x63054),x63051))
% 28.73/28.53 [6347]E(f319(x63471,x63472),f72(a925))+~E(f319(f319(f9(x63473,a925),x63471),x63474),f72(a925))+~P1(f319(f55(x63473),x63474))+~P1(f319(f319(f321(x63473),x63472),x63474))
% 28.73/28.53 [6348]E(f319(x63481,x63482),f2(a925))+~E(f319(f319(f6(x63483,a925),x63481),x63484),f2(a925))+~P1(f319(f55(x63483),x63484))+~P1(f319(f319(f321(x63483),x63482),x63484))
% 28.73/28.53 [6566]~P113(x65661)+~P1(f319(f319(f226(x65661),x65664),x65663))+P1(f319(f319(f226(x65661),x65662),x65663))+~P1(f319(f319(f226(x65661),x65662),x65664))
% 28.73/28.53 [6567]~P2(x65671)+~P1(f319(f319(f226(x65671),x65672),x65674))+P1(f319(f319(f226(x65671),x65672),x65673))+~P1(f319(f319(f226(x65671),x65674),x65673))
% 28.73/28.53 [6568]~P113(x65681)+~P1(f319(f319(f227(x65681),x65684),x65683))+P1(f319(f319(f227(x65681),x65682),x65683))+~P1(f319(f319(f226(x65681),x65682),x65684))
% 28.73/28.53 [6569]~P113(x65691)+~P1(f319(f319(f227(x65691),x65692),x65694))+P1(f319(f319(f227(x65691),x65692),x65693))+~P1(f319(f319(f226(x65691),x65694),x65693))
% 28.73/28.53 [6570]~P113(x65701)+~P1(f319(f319(f227(x65701),x65704),x65703))+P1(f319(f319(f227(x65701),x65702),x65703))+~P1(f319(f319(f227(x65701),x65702),x65704))
% 28.73/28.53 [6571]~P2(x65711)+~P1(f319(f319(f227(x65711),x65712),x65714))+P1(f319(f319(f227(x65711),x65712),x65713))+~P1(f319(f319(f226(x65711),x65714),x65713))
% 28.73/28.53 [6572]~P2(x65721)+~P1(f319(f319(f227(x65721),x65724),x65723))+P1(f319(f319(f227(x65721),x65722),x65723))+~P1(f319(f319(f226(x65721),x65722),x65724))
% 28.73/28.53 [6573]~P2(x65731)+~P1(f319(f319(f227(x65731),x65732),x65734))+P1(f319(f319(f227(x65731),x65732),x65733))+~P1(f319(f319(f227(x65731),x65734),x65733))
% 28.73/28.53 [6656]~P36(x66564,x66563,x66562)+E(x66561,f775(x66562,x66563,x66564))+~P1(f319(x66563,x66561))+~P1(f319(f319(f321(x66564),x66561),f319(f164(x66564),x66562)))
% 28.73/28.53 [6657]~P36(x66574,x66573,x66572)+E(x66571,f787(x66572,x66573,x66574))+~P1(f319(x66573,x66571))+~P1(f319(f319(f321(x66574),x66571),f319(f164(x66574),x66572)))
% 28.73/28.53 [6809]~P6(x68091)+~P1(f319(f319(f226(x68091),x68092),f32(x68091,x68094)))+P1(f319(f319(f226(x68091),x68092),x68093))+~P1(f319(f319(f321(x68091),x68093),x68094))
% 28.73/28.53 [6957]~P4(x69571)+~P14(x69571,f319(f319(f143(x69571),x69572),x69574))+~P1(f319(f319(f321(x69571),x69573),f319(f164(x69571),x69574)))+P1(f319(f319(f226(x69571),x69572),x69573))
% 28.73/28.53 [6958]~P4(x69581)+~P14(x69581,f319(f319(f143(x69581),x69582),x69584))+~P1(f319(f319(f321(x69581),x69583),f319(f164(x69581),x69584)))+P1(f319(f319(f226(x69581),x69582),x69583))
% 28.73/28.53 [7046]~P6(x70461)+~P1(f319(f319(f226(x70461),f31(x70461,x70464)),x70463))+P1(f319(f319(f226(x70461),x70462),x70463))+~P1(f319(f319(f321(x70461),x70462),x70464))
% 28.73/28.53 [7455]~P4(x74551)+E(f319(f319(f102(f932(x74551,a923)),f319(f294(x74551,x74552),x74553)),f319(f294(x74551,x74553),x74554)),f319(f294(x74551,x74552),x74554))+~P1(f319(f319(f226(x74551),x74553),x74554))+~P1(f319(f319(f226(x74551),x74552),x74553))
% 28.73/28.53 [7499]P36(x74991,x74992,x74993)+~E(f789(x74993,x74992,x74991,x74994),x74994)+~P1(f319(x74992,x74994))+~P1(f319(f319(f321(x74991),x74994),f319(f164(x74991),x74993)))
% 28.73/28.53 [7500]P36(x75001,x75002,x75003)+~E(f799(x75003,x75002,x75001,x75004),x75004)+~P1(f319(x75002,x75004))+~P1(f319(f319(f321(x75001),x75004),f319(f164(x75001),x75003)))
% 28.73/28.53 [7574]~P4(x75741)+E(f319(f319(f102(f932(x75741,a923)),f319(f294(x75741,x75742),x75743)),f295(x75741,x75743,x75744)),f295(x75741,x75742,x75744))+~P1(f319(f319(f226(x75741),x75743),x75744))+~P1(f319(f319(f226(x75741),x75742),x75743))
% 28.73/28.53 [7634]~P4(x76341)+E(f319(f319(f102(f932(x76341,a923)),f298(x76341,x76342,x76343)),f319(f294(x76341,x76343),x76344)),f298(x76341,x76342,x76344))+~P1(f319(f319(f226(x76341),x76343),x76344))+~P1(f319(f319(f227(x76341),x76342),x76343))
% 28.73/28.53 [7651]~P4(x76511)+E(f319(f319(f102(f932(x76511,a923)),f295(x76511,x76512,x76513)),f298(x76511,x76513,x76514)),f319(f294(x76511,x76512),x76514))+~P1(f319(f319(f226(x76511),x76512),x76513))+~P1(f319(f319(f227(x76511),x76513),x76514))
% 28.73/28.53 [7682]~P4(x76821)+E(f319(f319(f102(f932(x76821,a923)),f295(x76821,x76822,x76823)),f297(x76821,x76823,x76824)),f295(x76821,x76822,x76824))+~P1(f319(f319(f226(x76821),x76823),x76824))+~P1(f319(f319(f226(x76821),x76822),x76823))
% 28.73/28.53 [7683]~P4(x76831)+E(f319(f319(f102(f932(x76831,a923)),f297(x76831,x76832,x76833)),f297(x76831,x76833,x76834)),f297(x76831,x76832,x76834))+~P1(f319(f319(f226(x76831),x76833),x76834))+~P1(f319(f319(f226(x76831),x76832),x76833))
% 28.73/28.53 [7684]~P4(x76841)+E(f319(f319(f102(f932(x76841,a923)),f297(x76841,x76842,x76843)),f298(x76841,x76843,x76844)),f298(x76841,x76842,x76844))+~P1(f319(f319(f226(x76841),x76842),x76843))+~P1(f319(f319(f227(x76841),x76843),x76844))
% 28.73/28.53 [7685]~P4(x76851)+E(f319(f319(f102(f932(x76851,a923)),f298(x76851,x76852,x76853)),f295(x76851,x76853,x76854)),f297(x76851,x76852,x76854))+~P1(f319(f319(f226(x76851),x76853),x76854))+~P1(f319(f319(f227(x76851),x76852),x76853))
% 28.73/28.53 [8473]P26(x84731,x84732,f422(x84733,x84732,x84734,x84731),x84734)+~P1(f319(f55(x84732),x84733))+~P1(f319(f55(x84731),x84734))+~P1(f319(f319(f226(a925),f319(f29(x84731),x84734)),f319(f29(x84732),x84733)))
% 28.73/28.53 [8494]P36(x84941,x84942,x84943)+~P1(f319(x84942,x84944))+P1(f319(x84942,f789(x84943,x84942,x84941,x84944)))+~P1(f319(f319(f321(x84941),x84944),f319(f164(x84941),x84943)))
% 28.73/28.53 [8495]P36(x84951,x84952,x84953)+~P1(f319(x84952,x84954))+P1(f319(x84952,f799(x84953,x84952,x84951,x84954)))+~P1(f319(f319(f321(x84951),x84954),f319(f164(x84951),x84953)))
% 28.73/28.53 [8550]~P78(x85501)+~E(f319(x85503,f521(x85503,x85504,x85502,x85501)),f72(x85501))+E(f319(f319(f319(f59(x85501,x85502,f75(x85501)),x85503),f72(x85501)),x85504),f72(x85501))+~P1(f319(f55(x85502),x85504))
% 28.73/28.53 [8822]~P129(x88221)+~P1(f319(f319(f226(x88221),f2(x88221)),x88223))+P1(f319(f319(f226(x88221),x88222),x88223))+~P1(f319(f319(f226(x88221),f319(f319(f236(x88221),x88222),f319(a104,x88224))),f319(f319(f236(x88221),x88223),f319(a104,x88224))))
% 28.73/28.53 [8997]~P41(f932(x89974,a923),f932(x89974,a923),x89973)+P1(f319(x89971,x89972))+~P1(f319(x89971,f460(x89971,x89973,x89972,x89974)))+~P1(f319(f319(f321(x89974),x89972),f87(f932(x89974,a923),x89973)))
% 28.73/28.53 [9144]P36(x91441,x91442,x91443)+~P1(f319(x91442,x91444))+~P1(f319(f319(f321(x91441),x91444),f319(f164(x91441),x91443)))+P1(f319(f319(f321(x91441),f789(x91443,x91442,x91441,x91444)),f319(f164(x91441),x91443)))
% 28.73/28.53 [9145]P36(x91451,x91452,x91453)+~P1(f319(x91452,x91454))+~P1(f319(f319(f321(x91451),x91454),f319(f164(x91451),x91453)))+P1(f319(f319(f321(x91451),f799(x91453,x91452,x91451,x91454)),f319(f164(x91451),x91453)))
% 28.73/28.53 [9224]~P78(x92241)+E(f319(f319(f319(f59(x92241,x92242,f75(x92241)),x92243),f72(x92241)),x92244),f72(x92241))+~P1(f319(f55(x92242),x92244))+P1(f319(f319(f321(x92242),f521(x92243,x92244,x92242,x92241)),x92244))
% 28.73/28.53 [9726]~P1(f319(f319(f226(a1),x97264),f2(a1)))+P1(f319(f319(f226(a1),f319(f319(f74(a1),f319(f319(f75(a1),x97261),f39(a1,x97262,x97263))),x97264)),f2(a1)))+~P1(f319(f319(f227(a1),f2(a1)),x97263))+~P1(f319(f319(f227(a1),x97261),x97264))
% 28.73/28.53 [10183]~P1(f319(f55(x101831),x101832))+~P1(f319(f319(f321(x101831),x101834),x101832))+~P1(f319(f319(f321(x101831),x101833),x101832))+P1(f319(f319(f227(a925),f319(f29(x101831),f319(f319(f23(f932(x101831,a923)),f319(f319(f23(f932(x101831,a923)),x101832),f319(f319(f301(x101831),x101833),f180(f932(x101831,a923))))),f319(f319(f301(x101831),x101834),f180(f932(x101831,a923)))))),f319(f29(x101831),x101832)))
% 28.73/28.53 [7106]~P143(x71063)+~P123(x71063)+P1(f319(x71061,f871(x71062,x71061,x71063)))+~P1(f319(x71061,f319(f319(f75(x71063),x71062),x71064)))
% 28.73/28.53 [7161]~P108(x71611)+~P1(f319(f319(f226(x71611),x71612),x71614))+~P1(f319(f319(f226(x71611),x71612),x71613))+P1(f319(f319(f226(x71611),x71612),f319(f319(f93(x71611),x71613),x71614)))
% 28.73/28.53 [7162]~P108(x71621)+~P1(f319(f319(f226(x71621),x71622),x71624))+~P1(f319(f319(f226(x71621),x71622),x71623))+P1(f319(f319(f226(x71621),x71622),f319(f319(f93(x71621),x71623),x71624)))
% 28.73/28.53 [7163]~P108(x71631)+~P1(f319(f319(f226(x71631),x71632),x71634))+~P1(f319(f319(f226(x71631),x71632),x71633))+P1(f319(f319(f226(x71631),x71632),f319(f319(f93(x71631),x71633),x71634)))
% 28.73/28.53 [7164]~P4(x71641)+~P1(f319(f319(f226(x71641),x71642),x71644))+~P1(f319(f319(f226(x71641),x71642),x71643))+P1(f319(f319(f226(x71641),x71642),f319(f319(f224(x71641),x71643),x71644)))
% 28.73/28.53 [7165]~P4(x71651)+~P1(f319(f319(f226(x71651),x71652),x71654))+~P1(f319(f319(f226(x71651),x71652),x71653))+P1(f319(f319(f226(x71651),x71652),f319(f319(f224(x71651),x71653),x71654)))
% 28.73/28.53 [7166]~P4(x71661)+~P1(f319(f319(f226(x71661),x71662),x71664))+~P1(f319(f319(f226(x71661),x71662),x71663))+P1(f319(f319(f226(x71661),x71662),f319(f319(f224(x71661),x71663),x71664)))
% 28.73/28.53 [7167]~P4(x71671)+~P1(f319(f319(f227(x71671),x71672),x71674))+~P1(f319(f319(f227(x71671),x71672),x71673))+P1(f319(f319(f227(x71671),x71672),f319(f319(f224(x71671),x71673),x71674)))
% 28.73/28.53 [7187]~P73(x71872)+E(x71871,f2(x71872))+E(f319(f319(f283(x71872),f319(f319(f236(x71872),x71871),x71873)),f319(f319(f236(x71872),x71871),x71874)),f319(f319(f236(x71872),x71871),f319(f319(f23(a925),x71873),x71874)))+~P1(f319(f319(f226(a925),x71874),x71873))
% 28.73/28.53 [7231]~P4(x72311)+~P14(x72311,f319(f319(f143(x72311),x72313),x72314))+P14(x72311,f319(f319(f143(x72311),x72312),f319(f319(f143(x72311),x72313),x72314)))+~P1(f319(f319(f226(x72311),x72312),x72313))
% 28.73/28.53 [7232]~P4(x72321)+~P14(x72321,f319(f319(f143(x72321),x72323),x72324))+P14(x72321,f319(f319(f143(x72321),x72322),f319(f319(f143(x72321),x72323),x72324)))+~P1(f319(f319(f226(x72321),x72322),x72323))
% 28.73/28.53 [7268]~P93(x72681)+~P1(f319(f319(f226(x72681),f2(x72681)),x72684))+~P1(f319(f319(f226(x72681),x72682),x72683))+P1(f319(f319(f226(x72681),x72682),f319(f319(f74(x72681),x72683),x72684)))
% 28.73/28.53 [7269]~P93(x72691)+~P1(f319(f319(f226(x72691),f2(x72691)),x72693))+~P1(f319(f319(f226(x72691),x72692),x72694))+P1(f319(f319(f226(x72691),x72692),f319(f319(f74(x72691),x72693),x72694)))
% 28.73/28.53 [7270]~P129(x72701)+~P1(f319(f319(f227(x72701),f2(x72701)),x72703))+~P1(f319(f319(f227(x72701),x72702),x72704))+P1(f319(f319(f227(x72701),x72702),f319(f319(f74(x72701),x72703),x72704)))
% 28.73/28.53 [7271]~P93(x72711)+~P1(f319(f319(f226(x72711),x72712),x72714))+~P1(f319(f319(f227(x72711),f2(x72711)),x72713))+P1(f319(f319(f227(x72711),x72712),f319(f319(f74(x72711),x72713),x72714)))
% 28.73/28.53 [7272]~P93(x72721)+~P1(f319(f319(f226(x72721),f2(x72721)),x72723))+~P1(f319(f319(f227(x72721),x72722),x72724))+P1(f319(f319(f227(x72721),x72722),f319(f319(f74(x72721),x72723),x72724)))
% 28.73/28.53 [7314]~P4(x73141)+P1(f319(f319(f226(x73141),x73142),x73143))+P1(f319(f319(f226(x73141),x73142),x73144))+~P1(f319(f319(f226(x73141),x73142),f319(f319(f225(x73141),x73144),x73143)))
% 28.73/28.53 [7315]~P4(x73151)+P1(f319(f319(f227(x73151),x73152),x73153))+P1(f319(f319(f227(x73151),x73152),x73154))+~P1(f319(f319(f227(x73151),x73152),f319(f319(f225(x73151),x73154),x73153)))
% 28.73/28.53 [7607]~P113(x76072)+~P5(x76071)+~P1(f319(f319(f227(f932(x76071,x76072)),x76073),x76074))+P1(f319(f319(f226(f932(x76071,x76072)),x76073),x76074))
% 28.73/28.53 [7968]~P75(x79681)+~P1(f319(f319(f227(x79681),x79684),f2(x79681)))+~P1(f319(f319(f226(x79681),x79683),f319(f319(f283(x79681),x79682),x79684)))+P1(f319(f319(f226(x79681),x79682),f319(f319(f75(x79681),x79683),x79684)))
% 28.73/28.53 [7969]~P75(x79691)+~P1(f319(f319(f227(x79691),x79694),f2(x79691)))+~P1(f319(f319(f226(x79691),x79693),f319(f319(f75(x79691),x79692),x79694)))+P1(f319(f319(f226(x79691),x79692),f319(f319(f283(x79691),x79693),x79694)))
% 28.73/28.53 [7970]~P75(x79701)+~P1(f319(f319(f227(x79701),x79704),f2(x79701)))+~P1(f319(f319(f227(x79701),x79703),f319(f319(f283(x79701),x79702),x79704)))+P1(f319(f319(f227(x79701),x79702),f319(f319(f75(x79701),x79703),x79704)))
% 28.73/28.53 [7971]~P75(x79711)+~P1(f319(f319(f227(x79711),x79714),f2(x79711)))+~P1(f319(f319(f227(x79711),x79713),f319(f319(f75(x79711),x79712),x79714)))+P1(f319(f319(f227(x79711),x79712),f319(f319(f283(x79711),x79713),x79714)))
% 28.73/28.53 [8078]~P132(x80781)+~P1(f319(f319(f226(x80781),x80782),f2(x80781)))+~P1(f319(f319(f226(x80781),x80784),x80783))+P1(f319(f319(f226(x80781),f319(f319(f75(x80781),x80782),x80783)),f319(f319(f75(x80781),x80782),x80784)))
% 28.73/28.53 [8079]~P130(x80791)+~P1(f319(f319(f227(x80791),x80792),f2(x80791)))+~P1(f319(f319(f226(x80791),x80794),x80793))+P1(f319(f319(f226(x80791),f319(f319(f75(x80791),x80792),x80793)),f319(f319(f75(x80791),x80792),x80794)))
% 28.73/28.53 [8080]~P132(x80801)+~P1(f319(f319(f226(x80801),x80803),f2(x80801)))+~P1(f319(f319(f226(x80801),x80804),x80802))+P1(f319(f319(f226(x80801),f319(f319(f75(x80801),x80802),x80803)),f319(f319(f75(x80801),x80804),x80803)))
% 28.73/28.53 [8081]~P74(x80811)+~P1(f319(f319(f226(x80811),x80813),f2(x80811)))+~P1(f319(f319(f226(x80811),x80814),x80812))+P1(f319(f319(f226(x80811),f319(f319(f283(x80811),x80812),x80813)),f319(f319(f283(x80811),x80814),x80813)))
% 28.73/28.53 [8082]~P130(x80821)+~P1(f319(f319(f227(x80821),x80822),f2(x80821)))+~P1(f319(f319(f227(x80821),x80824),x80823))+P1(f319(f319(f227(x80821),f319(f319(f75(x80821),x80822),x80823)),f319(f319(f75(x80821),x80822),x80824)))
% 28.73/28.53 [8083]~P130(x80831)+~P1(f319(f319(f227(x80831),x80832),f2(x80831)))+~P1(f319(f319(f227(x80831),x80834),x80833))+P1(f319(f319(f227(x80831),f319(f319(f75(x80831),x80832),x80833)),f319(f319(f75(x80831),x80832),x80834)))
% 28.73/28.53 [8084]~P130(x80841)+~P1(f319(f319(f227(x80841),x80843),f2(x80841)))+~P1(f319(f319(f227(x80841),x80844),x80842))+P1(f319(f319(f227(x80841),f319(f319(f75(x80841),x80842),x80843)),f319(f319(f75(x80841),x80844),x80843)))
% 28.73/28.53 [8085]~P130(x80851)+~P1(f319(f319(f227(x80851),x80853),f2(x80851)))+~P1(f319(f319(f227(x80851),x80854),x80852))+P1(f319(f319(f227(x80851),f319(f319(f75(x80851),x80852),x80853)),f319(f319(f75(x80851),x80854),x80853)))
% 28.73/28.53 [8086]~P130(x80861)+~P1(f319(f319(f227(x80861),x80862),f2(x80861)))+~P1(f319(f319(f227(x80861),x80864),x80863))+P1(f319(f319(f227(x80861),f319(f319(f75(x80861),x80862),x80863)),f319(f319(f75(x80861),x80862),x80864)))
% 28.73/28.53 [8087]~P75(x80871)+~P1(f319(f319(f227(x80871),x80873),f2(x80871)))+~P1(f319(f319(f227(x80871),x80874),x80872))+P1(f319(f319(f227(x80871),f319(f319(f283(x80871),x80872),x80873)),f319(f319(f283(x80871),x80874),x80873)))
% 28.73/28.53 [8088]~P129(x80881)+~P1(f319(f319(f227(x80881),f72(x80881)),x80882))+~P1(f319(f319(f226(a925),x80883),x80884))+P1(f319(f319(f226(x80881),f319(f319(f236(x80881),x80882),x80883)),f319(f319(f236(x80881),x80882),x80884)))
% 28.73/28.53 [8089]~P129(x80891)+~P1(f319(f319(f226(x80891),f72(x80891)),x80892))+~P1(f319(f319(f226(a925),x80893),x80894))+P1(f319(f319(f226(x80891),f319(f319(f236(x80891),x80892),x80893)),f319(f319(f236(x80891),x80892),x80894)))
% 28.73/28.53 [8090]~P129(x80901)+~P1(f319(f319(f227(x80901),f72(x80901)),x80902))+~P1(f319(f319(f227(a925),x80903),x80904))+P1(f319(f319(f227(x80901),f319(f319(f236(x80901),x80902),x80903)),f319(f319(f236(x80901),x80902),x80904)))
% 28.73/28.53 [8091]~P129(x80911)+~P1(f319(f319(f227(x80911),f72(x80911)),x80912))+~P1(f319(f319(f227(a925),x80913),x80914))+P1(f319(f319(f227(x80911),f319(f319(f236(x80911),x80912),x80913)),f319(f319(f236(x80911),x80912),x80914)))
% 28.73/28.53 [8118]P1(f319(f319(f227(a925),f2(a925)),f319(x81181,x81182)))+~P1(f319(f55(x81183),x81184))+~P1(f319(f319(f321(x81183),x81182),x81184))+~P1(f319(f319(f227(a925),f2(a925)),f319(f319(f9(x81183,a925),x81181),x81184)))
% 28.73/28.53 [8127]~P141(x81271)+~P1(f319(f319(f226(x81271),x81273),x81274))+~P1(f319(f319(f226(x81271),f2(x81271)),x81272))+P1(f319(f319(f226(x81271),f319(f319(f75(x81271),x81272),x81273)),f319(f319(f75(x81271),x81272),x81274)))
% 28.73/28.53 [8128]~P140(x81281)+~P1(f319(f319(f226(x81281),x81283),x81284))+~P1(f319(f319(f226(x81281),f2(x81281)),x81282))+P1(f319(f319(f226(x81281),f319(f319(f75(x81281),x81282),x81283)),f319(f319(f75(x81281),x81282),x81284)))
% 28.73/28.53 [8129]~P130(x81291)+~P1(f319(f319(f227(x81291),f2(x81291)),x81292))+~P1(f319(f319(f226(x81291),x81293),x81294))+P1(f319(f319(f226(x81291),f319(f319(f75(x81291),x81292),x81293)),f319(f319(f75(x81291),x81292),x81294)))
% 28.73/28.53 [8130]~P141(x81301)+~P1(f319(f319(f226(x81301),x81302),x81304))+~P1(f319(f319(f226(x81301),f2(x81301)),x81303))+P1(f319(f319(f226(x81301),f319(f319(f75(x81301),x81302),x81303)),f319(f319(f75(x81301),x81304),x81303)))
% 28.73/28.53 [8131]~P129(x81311)+~P1(f319(f319(f226(x81311),x81312),x81314))+~P1(f319(f319(f226(x81311),f2(x81311)),x81312))+P1(f319(f319(f226(x81311),f319(f319(f236(x81311),x81312),x81313)),f319(f319(f236(x81311),x81314),x81313)))
% 28.73/28.53 [8132]~P74(x81321)+~P1(f319(f319(f226(x81321),x81322),x81324))+~P1(f319(f319(f226(x81321),f2(x81321)),x81323))+P1(f319(f319(f226(x81321),f319(f319(f283(x81321),x81322),x81323)),f319(f319(f283(x81321),x81324),x81323)))
% 28.73/28.53 [8133]~P130(x81331)+~P1(f319(f319(f227(x81331),x81333),x81334))+~P1(f319(f319(f227(x81331),f2(x81331)),x81332))+P1(f319(f319(f227(x81331),f319(f319(f75(x81331),x81332),x81333)),f319(f319(f75(x81331),x81332),x81334)))
% 28.73/28.53 [8134]~P127(x81341)+~P1(f319(f319(f227(x81341),x81343),x81344))+~P1(f319(f319(f227(x81341),f2(x81341)),x81342))+P1(f319(f319(f227(x81341),f319(f319(f75(x81341),x81342),x81343)),f319(f319(f75(x81341),x81342),x81344)))
% 28.73/28.53 [8135]~P134(x81351)+~P1(f319(f319(f227(x81351),x81353),x81354))+~P1(f319(f319(f227(x81351),f2(x81351)),x81352))+P1(f319(f319(f227(x81351),f319(f319(f75(x81351),x81352),x81353)),f319(f319(f75(x81351),x81352),x81354)))
% 28.73/28.53 [8136]~P130(x81361)+~P1(f319(f319(f227(x81361),x81362),x81364))+~P1(f319(f319(f227(x81361),f2(x81361)),x81363))+P1(f319(f319(f227(x81361),f319(f319(f75(x81361),x81362),x81363)),f319(f319(f75(x81361),x81364),x81363)))
% 28.73/28.53 [8137]~P134(x81371)+~P1(f319(f319(f227(x81371),x81372),x81374))+~P1(f319(f319(f227(x81371),f2(x81371)),x81373))+P1(f319(f319(f227(x81371),f319(f319(f75(x81371),x81372),x81373)),f319(f319(f75(x81371),x81374),x81373)))
% 28.73/28.53 [8138]~P130(x81381)+~P1(f319(f319(f227(x81381),x81383),x81384))+~P1(f319(f319(f227(x81381),f2(x81381)),x81382))+P1(f319(f319(f227(x81381),f319(f319(f75(x81381),x81382),x81383)),f319(f319(f75(x81381),x81382),x81384)))
% 28.73/28.53 [8139]~P75(x81391)+~P1(f319(f319(f227(x81391),x81392),x81394))+~P1(f319(f319(f227(x81391),f2(x81391)),x81393))+P1(f319(f319(f227(x81391),f319(f319(f283(x81391),x81392),x81393)),f319(f319(f283(x81391),x81394),x81393)))
% 28.73/28.53 [8183]~P3(x81832)+P1(f319(f319(f227(f932(x81831,x81832)),x81834),x81833))+~P1(f319(f319(f226(f932(x81831,x81832)),x81834),x81833))+P1(f319(f319(f226(f932(x81831,x81832)),x81833),x81834))
% 28.73/28.53 [8224]P1(f319(f319(f321(x82241),x82242),x82243))+P1(f319(f319(f321(x82241),x82242),x82244))+~P1(f319(f319(f226(f932(x82241,a923)),x82244),x82243))+P1(f319(f319(f227(f932(x82241,a923)),x82244),f319(f319(f301(x82241),x82242),x82243)))
% 28.73/28.53 [8335]~P117(x83352)+E(x83351,f2(x83352))+P1(f319(f319(f279(x83352),x83353),x83354))+~P1(f319(f319(f279(x83352),f319(f319(f75(x83352),x83353),x83351)),f319(f319(f75(x83352),x83354),x83351)))
% 28.73/28.53 [8336]~P117(x83362)+E(x83361,f2(x83362))+P1(f319(f319(f279(x83362),x83363),x83364))+~P1(f319(f319(f279(x83362),f319(f319(f75(x83362),x83361),x83363)),f319(f319(f75(x83362),x83361),x83364)))
% 28.73/28.53 [8384]P1(f319(f319(f321(x83841),x83842),x83843))+P1(f319(f319(f321(x83841),x83842),x83844))+~P1(f319(f319(f227(f932(x83841,a923)),x83844),f319(f319(f301(x83841),x83842),x83843)))+P1(f319(f319(f226(f932(x83841,a923)),x83844),x83843))
% 28.73/28.53 [8450]~P130(x84501)+P1(f319(f319(f227(x84501),x84503),x84502))+P1(f319(f319(f227(x84501),x84502),x84503))+~P1(f319(f319(f227(x84501),f319(f319(f75(x84501),x84504),x84502)),f319(f319(f75(x84501),x84504),x84503)))
% 28.73/28.53 [8451]~P130(x84511)+P1(f319(f319(f227(x84511),x84513),x84512))+P1(f319(f319(f227(x84511),x84512),x84513))+~P1(f319(f319(f227(x84511),f319(f319(f75(x84511),x84512),x84514)),f319(f319(f75(x84511),x84513),x84514)))
% 28.73/28.53 [8462]~P130(x84621)+P1(f319(f319(f227(x84621),x84624),f2(x84621)))+P1(f319(f319(f227(x84621),x84622),x84623))+~P1(f319(f319(f227(x84621),f319(f319(f75(x84621),x84622),x84624)),f319(f319(f75(x84621),x84623),x84624)))
% 28.73/28.53 [8463]~P130(x84631)+P1(f319(f319(f227(x84631),x84634),f2(x84631)))+P1(f319(f319(f227(x84631),x84632),x84633))+~P1(f319(f319(f227(x84631),f319(f319(f75(x84631),x84634),x84632)),f319(f319(f75(x84631),x84634),x84633)))
% 28.73/28.53 [8467]~P130(x84671)+P1(f319(f319(f227(x84671),x84672),x84673))+P1(f319(f319(f227(x84671),f2(x84671)),x84674))+~P1(f319(f319(f227(x84671),f319(f319(f75(x84671),x84674),x84673)),f319(f319(f75(x84671),x84674),x84672)))
% 28.73/28.53 [8468]~P130(x84681)+P1(f319(f319(f227(x84681),x84682),x84683))+P1(f319(f319(f227(x84681),f2(x84681)),x84684))+~P1(f319(f319(f227(x84681),f319(f319(f75(x84681),x84683),x84684)),f319(f319(f75(x84681),x84682),x84684)))
% 28.73/28.53 [8481]~P130(x84811)+P1(f319(f319(f227(x84811),x84812),f2(x84811)))+P1(f319(f319(f227(x84811),f2(x84811)),x84812))+~P1(f319(f319(f227(x84811),f319(f319(f75(x84811),x84813),x84812)),f319(f319(f75(x84811),x84814),x84812)))
% 28.73/28.53 [8482]~P130(x84821)+P1(f319(f319(f227(x84821),x84822),f2(x84821)))+P1(f319(f319(f227(x84821),f2(x84821)),x84822))+~P1(f319(f319(f227(x84821),f319(f319(f75(x84821),x84822),x84823)),f319(f319(f75(x84821),x84822),x84824)))
% 28.73/28.53 [8512]~P130(x85121)+~P1(f319(f319(f227(x85121),x85124),f2(x85121)))+P1(f319(f319(f226(x85121),x85122),x85123))+~P1(f319(f319(f226(x85121),f319(f319(f75(x85121),x85124),x85123)),f319(f319(f75(x85121),x85124),x85122)))
% 28.73/28.53 [8513]~P130(x85131)+~P1(f319(f319(f227(x85131),x85134),f2(x85131)))+P1(f319(f319(f227(x85131),x85132),x85133))+~P1(f319(f319(f227(x85131),f319(f319(f75(x85131),x85134),x85133)),f319(f319(f75(x85131),x85134),x85132)))
% 28.73/28.53 [8523]~P129(x85233)+~P1(f319(f319(f227(x85233),f72(x85233)),x85234))+P1(f319(f319(f226(a925),x85231),x85232))+~P1(f319(f319(f226(x85233),f319(f319(f236(x85233),x85234),x85231)),f319(f319(f236(x85233),x85234),x85232)))
% 28.73/28.53 [8524]~P129(x85243)+~P1(f319(f319(f227(x85243),f72(x85243)),x85244))+P1(f319(f319(f226(a925),x85241),x85242))+~P1(f319(f319(f226(x85243),f319(f319(f236(x85243),x85244),x85241)),f319(f319(f236(x85243),x85244),x85242)))
% 28.73/28.53 [8525]~P129(x85253)+~P1(f319(f319(f227(x85253),f72(x85253)),x85254))+P1(f319(f319(f227(a925),x85251),x85252))+~P1(f319(f319(f227(x85253),f319(f319(f236(x85253),x85254),x85251)),f319(f319(f236(x85253),x85254),x85252)))
% 28.73/28.53 [8526]~P129(x85263)+~P1(f319(f319(f227(x85263),f72(x85263)),x85264))+P1(f319(f319(f227(a925),x85261),x85262))+~P1(f319(f319(f227(x85263),f319(f319(f236(x85263),x85264),x85261)),f319(f319(f236(x85263),x85264),x85262)))
% 28.73/28.53 [8536]~P130(x85361)+P1(f319(f319(f226(x85361),x85362),x85363))+~P1(f319(f319(f227(x85361),f2(x85361)),x85364))+~P1(f319(f319(f226(x85361),f319(f319(f75(x85361),x85364),x85362)),f319(f319(f75(x85361),x85364),x85363)))
% 28.73/28.53 [8537]~P134(x85371)+P1(f319(f319(f226(x85371),x85372),x85373))+~P1(f319(f319(f227(x85371),f2(x85371)),x85374))+~P1(f319(f319(f226(x85371),f319(f319(f75(x85371),x85374),x85372)),f319(f319(f75(x85371),x85374),x85373)))
% 28.73/28.53 [8538]~P134(x85381)+P1(f319(f319(f226(x85381),x85382),x85383))+~P1(f319(f319(f227(x85381),f2(x85381)),x85384))+~P1(f319(f319(f226(x85381),f319(f319(f75(x85381),x85382),x85384)),f319(f319(f75(x85381),x85383),x85384)))
% 28.73/28.53 [8539]~P130(x85391)+P1(f319(f319(f227(x85391),x85392),x85393))+~P1(f319(f319(f227(x85391),f2(x85391)),x85394))+~P1(f319(f319(f227(x85391),f319(f319(f75(x85391),x85394),x85392)),f319(f319(f75(x85391),x85394),x85393)))
% 28.73/28.53 [8540]~P134(x85401)+P1(f319(f319(f227(x85401),x85402),x85403))+~P1(f319(f319(f226(x85401),f2(x85401)),x85404))+~P1(f319(f319(f227(x85401),f319(f319(f75(x85401),x85404),x85402)),f319(f319(f75(x85401),x85404),x85403)))
% 28.73/28.53 [8541]~P135(x85411)+P1(f319(f319(f227(x85411),x85412),x85413))+~P1(f319(f319(f226(x85411),f2(x85411)),x85414))+~P1(f319(f319(f227(x85411),f319(f319(f75(x85411),x85414),x85412)),f319(f319(f75(x85411),x85414),x85413)))
% 28.73/28.53 [8542]~P129(x85421)+~P1(f319(f319(f226(x85421),f2(x85421)),x85423))+P1(f319(f319(f227(x85421),x85422),x85423))+~P1(f319(f319(f227(x85421),f319(f319(f236(x85421),x85422),x85424)),f319(f319(f236(x85421),x85423),x85424)))
% 28.73/28.53 [8543]~P134(x85431)+P1(f319(f319(f227(x85431),x85432),x85433))+~P1(f319(f319(f226(x85431),f2(x85431)),x85434))+~P1(f319(f319(f227(x85431),f319(f319(f75(x85431),x85432),x85434)),f319(f319(f75(x85431),x85433),x85434)))
% 28.73/28.53 [8544]~P135(x85441)+P1(f319(f319(f227(x85441),x85442),x85443))+~P1(f319(f319(f226(x85441),f2(x85441)),x85444))+~P1(f319(f319(f227(x85441),f319(f319(f75(x85441),x85442),x85444)),f319(f319(f75(x85441),x85443),x85444)))
% 28.73/28.53 [8588]P1(f319(f319(f321(x85881),x85882),x85883))+~P1(f319(f319(f226(f932(x85881,a923)),x85883),x85884))+~P1(f319(f319(f227(f932(x85881,a923)),x85883),x85884))+P1(f319(f319(f227(f932(x85881,a923)),x85883),f319(f319(f301(x85881),x85882),x85884)))
% 28.73/28.53 [8621]~P143(x86211)+~P123(x86211)+P1(f319(f319(f279(x86211),x86212),f319(f319(f74(x86211),f871(x86212,x86213,x86211)),f2(x86211))))+~P1(f319(x86213,f319(f319(f75(x86211),x86212),x86214)))
% 28.73/28.53 [8972]E(f319(f319(f23(a1),f380(x89721,x89722,x89723,x89724)),f381(x89721,x89722,x89723,x89724)),x89724)+~P1(f319(f319(f227(a1),f2(a1)),x89723))+~P1(f319(f319(f226(a1),x89721),x89724))+P1(f319(f319(f226(a1),x89721),f319(f319(f74(a1),x89724),x89723)))
% 28.73/28.53 [8973]E(f319(f319(f23(a1),f403(x89731,x89732,x89733,x89734)),f404(x89731,x89732,x89733,x89734)),x89734)+~P1(f319(f319(f227(a1),f2(a1)),x89733))+~P1(f319(f319(f227(a1),x89731),x89734))+P1(f319(f319(f227(a1),x89731),f319(f319(f74(a1),x89734),x89733)))
% 28.73/28.53 [9125]~E(f319(f319(f156(x91251),x91253),f689(x91254,x91253,x91251,x91252)),f319(f319(f156(x91251),x91254),f689(x91254,x91253,x91251,x91252)))+E(f319(f319(f167(x91251),x91252),x91253),f319(f319(f167(x91251),x91252),x91254))+~P1(f319(f319(f226(a925),x91252),f319(f181(f926(x91251)),x91253)))+~P1(f319(f319(f226(a925),x91252),f319(f181(f926(x91251)),x91254)))
% 28.73/28.53 [9191]~P1(f319(f319(f227(a1),f2(a1)),x91913))+~P1(f319(f319(f226(a1),x91911),x91914))+P1(f319(f319(f321(a1),f380(x91911,x91912,x91913,x91914)),x91912))+P1(f319(f319(f226(a1),x91911),f319(f319(f74(a1),x91914),x91913)))
% 28.73/28.53 [9192]~P1(f319(f319(f227(a1),f2(a1)),x91923))+~P1(f319(f319(f227(a1),x91921),x91924))+P1(f319(f319(f321(a1),f403(x91921,x91922,x91923,x91924)),x91922))+P1(f319(f319(f227(a1),x91921),f319(f319(f74(a1),x91924),x91923)))
% 28.73/28.53 [9233]~P108(x92331)+~P1(f319(f55(x92331),x92333))+~P1(f319(f319(f321(x92331),x92334),x92333))+P1(f319(f319(f226(x92331),f319(f319(f58(x92331,x92331,f93(x92331)),x92332),x92333)),f319(f319(f93(x92331),x92334),x92332)))
% 28.73/28.53 [9234]~P4(x92341)+~P1(f319(f55(x92341),x92343))+~P1(f319(f319(f321(x92341),x92344),x92343))+P1(f319(f319(f226(x92341),f319(f319(f58(x92341,x92341,f224(x92341)),x92342),x92343)),f319(f319(f224(x92341),x92344),x92342)))
% 28.73/28.53 [9279]E(f319(f319(f167(x92791),x92792),x92793),f319(f319(f167(x92791),x92792),x92794))+P1(f319(f319(f227(a925),f689(x92793,x92794,x92791,x92792)),x92792))+~P1(f319(f319(f226(a925),x92792),f319(f181(f926(x92791)),x92793)))+~P1(f319(f319(f226(a925),x92792),f319(f181(f926(x92791)),x92794)))
% 28.73/28.53 [9284]~P1(f319(f319(f227(a1),f2(a1)),x92843))+~P1(f319(f319(f226(a1),x92841),x92842))+P1(f319(f319(f321(a1),f381(x92841,x92844,x92843,x92842)),f295(a1,f72(a1),x92843)))+P1(f319(f319(f226(a1),x92841),f319(f319(f74(a1),x92842),x92843)))
% 28.73/28.53 [9285]~P1(f319(f319(f227(a1),f2(a1)),x92853))+~P1(f319(f319(f227(a1),x92851),x92852))+P1(f319(f319(f321(a1),f404(x92851,x92854,x92853,x92852)),f295(a1,f72(a1),x92853)))+P1(f319(f319(f227(a1),x92851),f319(f319(f74(a1),x92852),x92853)))
% 28.73/28.53 [9612]~P4(x96121)+~P1(f319(f55(x96121),x96124))+P1(f319(f319(f321(x96121),f652(x96122,x96123,x96124,x96121)),x96124))+P1(f319(f319(f226(x96121),f319(f319(f58(x96121,x96121,f225(x96121)),x96122),x96124)),f319(f319(f225(x96121),x96123),x96122)))
% 28.73/28.53 [9613]~P107(x96131)+~P1(f319(f55(x96131),x96134))+P1(f319(f319(f321(x96131),f655(x96132,x96133,x96134,x96131)),x96134))+P1(f319(f319(f226(x96131),f319(f319(f58(x96131,x96131,f102(x96131)),x96132),x96134)),f319(f319(f102(x96131),x96133),x96132)))
% 28.73/28.53 [9742]~P107(x97421)+~P1(f319(f55(x97421),x97423))+~P1(f319(f319(f226(x97421),f655(x97422,x97424,x97423,x97421)),x97424))+P1(f319(f319(f226(x97421),f319(f319(f58(x97421,x97421,f102(x97421)),x97422),x97423)),f319(f319(f102(x97421),x97424),x97422)))
% 28.73/28.53 [9743]~P4(x97431)+~P1(f319(f55(x97431),x97433))+~P1(f319(f319(f226(x97431),f652(x97432,x97434,x97433,x97431)),x97434))+P1(f319(f319(f226(x97431),f319(f319(f58(x97431,x97431,f225(x97431)),x97432),x97433)),f319(f319(f225(x97431),x97434),x97432)))
% 28.73/28.53 [9745]~P1(f319(f319(f226(a1),f2(a1)),x97454))+~P1(f319(f319(f227(a1),f2(a1)),x97453))+~P1(f319(f319(f227(a1),x97454),x97451))+P1(f319(f319(f227(a1),f319(f319(f74(a1),f319(f319(f75(a1),x97451),f39(a1,x97452,x97453))),x97454)),f319(f319(f75(a1),x97451),x97453)))
% 28.73/28.53 [10155]E(x101551,x101552)+P1(f319(f319(f321(f931(f926(x101553),f926(x101553))),f319(f319(f244(f926(x101553),f926(x101553)),x101552),x101551)),f139(x101553,x101554)))+P1(f319(f319(f321(f931(f926(x101553),f926(x101553))),f319(f319(f244(f926(x101553),f926(x101553)),x101551),x101552)),f139(x101553,x101554)))+~P1(f319(f319(f321(f931(x101553,x101553)),f319(f319(f244(x101553,x101553),f680(x101551,x101552,x101554,x101553)),f683(x101551,x101552,x101554,x101553))),x101554))
% 28.73/28.53 [10156]E(x101561,x101562)+P1(f319(f319(f321(f931(f926(x101563),f926(x101563))),f319(f319(f244(f926(x101563),f926(x101563)),x101562),x101561)),f139(x101563,x101564)))+P1(f319(f319(f321(f931(f926(x101563),f926(x101563))),f319(f319(f244(f926(x101563),f926(x101563)),x101561),x101562)),f139(x101563,x101564)))+~P1(f319(f319(f321(f931(x101563,x101563)),f319(f319(f244(x101563,x101563),f683(x101561,x101562,x101564,x101563)),f680(x101561,x101562,x101564,x101563))),x101564))
% 28.73/28.53 [7671]~P107(x76711)+~P1(f319(f319(f226(x76711),x76713),x76714))+~P1(f319(f319(f226(x76711),x76712),x76714))+P1(f319(f319(f226(x76711),f319(f319(f102(x76711),x76712),x76713)),x76714))
% 28.73/28.53 [7672]~P107(x76721)+~P1(f319(f319(f226(x76721),x76723),x76724))+~P1(f319(f319(f226(x76721),x76722),x76724))+P1(f319(f319(f226(x76721),f319(f319(f102(x76721),x76722),x76723)),x76724))
% 28.73/28.53 [7673]~P107(x76731)+~P1(f319(f319(f226(x76731),x76733),x76734))+~P1(f319(f319(f226(x76731),x76732),x76734))+P1(f319(f319(f226(x76731),f319(f319(f102(x76731),x76732),x76733)),x76734))
% 28.73/28.53 [7674]~P4(x76741)+~P1(f319(f319(f226(x76741),x76743),x76744))+~P1(f319(f319(f226(x76741),x76742),x76744))+P1(f319(f319(f226(x76741),f319(f319(f225(x76741),x76742),x76743)),x76744))
% 28.73/28.53 [7675]~P4(x76751)+~P1(f319(f319(f226(x76751),x76753),x76754))+~P1(f319(f319(f226(x76751),x76752),x76754))+P1(f319(f319(f226(x76751),f319(f319(f225(x76751),x76752),x76753)),x76754))
% 28.73/28.53 [7676]~P4(x76761)+~P1(f319(f319(f226(x76761),x76763),x76764))+~P1(f319(f319(f226(x76761),x76762),x76764))+P1(f319(f319(f226(x76761),f319(f319(f225(x76761),x76762),x76763)),x76764))
% 28.73/28.53 [7677]~P4(x76771)+~P1(f319(f319(f227(x76771),x76773),x76774))+~P1(f319(f319(f227(x76771),x76772),x76774))+P1(f319(f319(f227(x76771),f319(f319(f225(x76771),x76772),x76773)),x76774))
% 28.73/28.53 [7993]~E(x79931,x79933)+E(f131(a925,f319(f294(a925,x79931),x79932)),f319(f319(f143(a925),x79933),x79934))+~E(f131(a925,f319(f294(a925,f319(f319(f74(a925),x79931),f72(a925))),x79932)),x79934)+~P1(f319(f319(f227(a925),x79931),x79932))
% 28.73/28.53 [8001]~P4(x80011)+P1(f319(f319(f226(x80011),x80012),x80013))+P1(f319(f319(f226(x80011),x80014),x80013))+~P1(f319(f319(f226(x80011),f319(f319(f224(x80011),x80014),x80012)),x80013))
% 28.73/28.53 [8002]~P4(x80021)+P1(f319(f319(f227(x80021),x80022),x80023))+P1(f319(f319(f227(x80021),x80024),x80023))+~P1(f319(f319(f227(x80021),f319(f319(f224(x80021),x80024),x80022)),x80023))
% 28.73/28.53 [8282]~P74(x82821)+~P1(f319(f319(f227(x82821),f2(x82821)),x82823))+~P1(f319(f319(f226(x82821),x82822),f319(f319(f283(x82821),x82824),x82823)))+P1(f319(f319(f226(x82821),f319(f319(f75(x82821),x82822),x82823)),x82824))
% 28.73/28.53 [8283]~P75(x82831)+~P1(f319(f319(f227(x82831),f2(x82831)),x82833))+~P1(f319(f319(f226(x82831),x82832),f319(f319(f283(x82831),x82834),x82833)))+P1(f319(f319(f226(x82831),f319(f319(f75(x82831),x82832),x82833)),x82834))
% 28.73/28.53 [8284]~P75(x82841)+~P1(f319(f319(f227(x82841),f2(x82841)),x82843))+~P1(f319(f319(f226(x82841),x82842),f319(f319(f75(x82841),x82844),x82843)))+P1(f319(f319(f226(x82841),f319(f319(f283(x82841),x82842),x82843)),x82844))
% 28.73/28.53 [8285]~P74(x82851)+~P1(f319(f319(f227(x82851),f2(x82851)),x82853))+~P1(f319(f319(f226(x82851),x82852),f319(f319(f75(x82851),x82854),x82853)))+P1(f319(f319(f226(x82851),f319(f319(f283(x82851),x82852),x82853)),x82854))
% 28.73/28.53 [8286]~P75(x82861)+~P1(f319(f319(f227(x82861),f2(x82861)),x82863))+~P1(f319(f319(f226(x82861),x82862),f319(f319(f75(x82861),x82864),x82863)))+P1(f319(f319(f226(x82861),f319(f319(f283(x82861),x82862),x82863)),x82864))
% 28.73/28.53 [8287]~P74(x82871)+~P1(f319(f319(f227(x82871),f2(x82871)),x82873))+~P1(f319(f319(f227(x82871),x82872),f319(f319(f283(x82871),x82874),x82873)))+P1(f319(f319(f227(x82871),f319(f319(f75(x82871),x82872),x82873)),x82874))
% 28.73/28.53 [8288]~P75(x82881)+~P1(f319(f319(f227(x82881),f2(x82881)),x82883))+~P1(f319(f319(f227(x82881),x82882),f319(f319(f283(x82881),x82884),x82883)))+P1(f319(f319(f227(x82881),f319(f319(f75(x82881),x82882),x82883)),x82884))
% 28.73/28.53 [8289]~P75(x82891)+~P1(f319(f319(f227(x82891),f2(x82891)),x82893))+~P1(f319(f319(f227(x82891),x82892),f319(f319(f75(x82891),x82894),x82893)))+P1(f319(f319(f227(x82891),f319(f319(f283(x82891),x82892),x82893)),x82894))
% 28.73/28.53 [8290]~P74(x82901)+~P1(f319(f319(f227(x82901),f2(x82901)),x82903))+~P1(f319(f319(f227(x82901),x82902),f319(f319(f75(x82901),x82904),x82903)))+P1(f319(f319(f227(x82901),f319(f319(f283(x82901),x82902),x82903)),x82904))
% 28.73/28.53 [8291]~P75(x82911)+~P1(f319(f319(f227(x82911),f2(x82911)),x82913))+~P1(f319(f319(f227(x82911),x82912),f319(f319(f75(x82911),x82914),x82913)))+P1(f319(f319(f227(x82911),f319(f319(f283(x82911),x82912),x82913)),x82914))
% 28.73/28.53 [8420]~P74(x84201)+~P1(f319(f319(f227(x84201),f2(x84201)),x84204))+P1(f319(f319(f226(x84201),x84202),f319(f319(f75(x84201),x84203),x84204)))+~P1(f319(f319(f226(x84201),f319(f319(f283(x84201),x84202),x84204)),x84203))
% 28.73/28.53 [8421]~P75(x84211)+~P1(f319(f319(f227(x84211),f2(x84211)),x84214))+P1(f319(f319(f226(x84211),x84212),f319(f319(f283(x84211),x84213),x84214)))+~P1(f319(f319(f226(x84211),f319(f319(f75(x84211),x84212),x84214)),x84213))
% 28.73/28.53 [8422]~P74(x84221)+~P1(f319(f319(f227(x84221),f2(x84221)),x84224))+P1(f319(f319(f226(x84221),x84222),f319(f319(f283(x84221),x84223),x84224)))+~P1(f319(f319(f226(x84221),f319(f319(f75(x84221),x84222),x84224)),x84223))
% 28.73/28.53 [8423]~P75(x84231)+~P1(f319(f319(f227(x84231),f2(x84231)),x84234))+P1(f319(f319(f226(x84231),x84232),f319(f319(f75(x84231),x84233),x84234)))+~P1(f319(f319(f226(x84231),f319(f319(f283(x84231),x84232),x84234)),x84233))
% 28.73/28.53 [8424]~P75(x84241)+~P1(f319(f319(f227(x84241),f2(x84241)),x84244))+P1(f319(f319(f226(x84241),x84242),f319(f319(f283(x84241),x84243),x84244)))+~P1(f319(f319(f226(x84241),f319(f319(f75(x84241),x84242),x84244)),x84243))
% 28.73/28.53 [8425]~P74(x84251)+~P1(f319(f319(f227(x84251),f2(x84251)),x84254))+P1(f319(f319(f227(x84251),x84252),f319(f319(f75(x84251),x84253),x84254)))+~P1(f319(f319(f227(x84251),f319(f319(f283(x84251),x84252),x84254)),x84253))
% 28.73/28.53 [8426]~P75(x84261)+~P1(f319(f319(f227(x84261),f2(x84261)),x84264))+P1(f319(f319(f227(x84261),x84262),f319(f319(f283(x84261),x84263),x84264)))+~P1(f319(f319(f227(x84261),f319(f319(f75(x84261),x84262),x84264)),x84263))
% 28.73/28.53 [8427]~P74(x84271)+~P1(f319(f319(f227(x84271),f2(x84271)),x84274))+P1(f319(f319(f227(x84271),x84272),f319(f319(f283(x84271),x84273),x84274)))+~P1(f319(f319(f227(x84271),f319(f319(f75(x84271),x84272),x84274)),x84273))
% 28.73/28.53 [8428]~P75(x84281)+~P1(f319(f319(f227(x84281),f2(x84281)),x84284))+P1(f319(f319(f227(x84281),x84282),f319(f319(f75(x84281),x84283),x84284)))+~P1(f319(f319(f227(x84281),f319(f319(f283(x84281),x84282),x84284)),x84283))
% 28.73/28.53 [8429]~P75(x84291)+~P1(f319(f319(f227(x84291),f2(x84291)),x84294))+P1(f319(f319(f227(x84291),x84292),f319(f319(f283(x84291),x84293),x84294)))+~P1(f319(f319(f227(x84291),f319(f319(f75(x84291),x84292),x84294)),x84293))
% 28.73/28.53 [8591]~P75(x85911)+~P1(f319(f319(f227(x85911),x85913),f2(x85911)))+~P1(f319(f319(f226(x85911),f319(f319(f283(x85911),x85914),x85913)),x85912))+P1(f319(f319(f226(x85911),f319(f319(f75(x85911),x85912),x85913)),x85914))
% 28.73/28.53 [8592]~P75(x85921)+~P1(f319(f319(f227(x85921),x85923),f2(x85921)))+~P1(f319(f319(f226(x85921),f319(f319(f75(x85921),x85924),x85923)),x85922))+P1(f319(f319(f226(x85921),f319(f319(f283(x85921),x85922),x85923)),x85924))
% 28.73/28.53 [8593]~P75(x85931)+~P1(f319(f319(f227(x85931),x85933),f2(x85931)))+~P1(f319(f319(f227(x85931),f319(f319(f283(x85931),x85934),x85933)),x85932))+P1(f319(f319(f227(x85931),f319(f319(f75(x85931),x85932),x85933)),x85934))
% 28.73/28.53 [8594]~P75(x85941)+~P1(f319(f319(f227(x85941),x85943),f2(x85941)))+~P1(f319(f319(f227(x85941),f319(f319(f75(x85941),x85944),x85943)),x85942))+P1(f319(f319(f227(x85941),f319(f319(f283(x85941),x85942),x85943)),x85944))
% 28.73/28.53 [8606]~P1(f319(x86061,x86064))+~P1(f319(f319(f227(a925),x86062),f319(f319(f75(a925),x86063),f319(a104,x86064))))+P1(f319(x86061,f319(f319(f30(a925),x86062),x86063)))+~P1(f319(f319(f226(a925),f319(f319(f75(a925),x86063),x86064)),x86062))
% 28.73/28.53 [8820]~P107(x88201)+~P1(f319(f55(x88201),x88204))+~P1(f319(f319(f321(x88201),x88202),x88204))+P1(f319(f319(f226(x88201),f319(f319(f102(x88201),x88202),x88203)),f319(f319(f58(x88201,x88201,f102(x88201)),x88203),x88204)))
% 28.73/28.53 [8821]~P4(x88211)+~P1(f319(f55(x88211),x88214))+~P1(f319(f319(f321(x88211),x88212),x88214))+P1(f319(f319(f226(x88211),f319(f319(f225(x88211),x88212),x88213)),f319(f319(f58(x88211,x88211,f225(x88211)),x88213),x88214)))
% 28.73/28.53 [8974]~P1(f319(f55(x89741),x89742))+E(f319(f29(x89741),f319(f319(f23(f932(x89741,a923)),x89742),f319(f319(f301(x89741),x89743),x89744))),f319(f319(f23(a925),f319(f29(x89741),f319(f319(f23(f932(x89741,a923)),x89742),x89744))),f72(a925)))+P1(f319(f319(f321(x89741),x89743),x89744))+~P1(f319(f319(f321(x89741),x89743),x89742))
% 28.73/28.53 [9052]E(f319(f319(f74(a1),f383(x90521,x90522,x90523,x90524)),f384(x90521,x90522,x90523,x90524)),x90524)+~P1(f319(f319(f227(a1),f2(a1)),x90523))+~P1(f319(f319(f226(a1),x90524),x90521))+P1(f319(f319(f226(a1),f319(f319(f23(a1),x90524),x90523)),x90521))
% 28.73/28.53 [9053]E(f319(f319(f74(a1),f405(x90531,x90532,x90533,x90534)),f406(x90531,x90532,x90533,x90534)),x90534)+~P1(f319(f319(f227(a1),f2(a1)),x90533))+~P1(f319(f319(f227(a1),x90534),x90531))+P1(f319(f319(f227(a1),f319(f319(f23(a1),x90534),x90533)),x90531))
% 28.73/28.53 [9264]~P1(f319(f319(f227(a1),f2(a1)),x92643))+~P1(f319(f319(f226(a1),x92644),x92641))+P1(f319(f319(f321(a1),f383(x92641,x92642,x92643,x92644)),x92642))+P1(f319(f319(f226(a1),f319(f319(f23(a1),x92644),x92643)),x92641))
% 28.73/28.53 [9265]~P1(f319(f319(f227(a1),f2(a1)),x92653))+~P1(f319(f319(f227(a1),x92654),x92651))+P1(f319(f319(f321(a1),f405(x92651,x92652,x92653,x92654)),x92652))+P1(f319(f319(f227(a1),f319(f319(f23(a1),x92654),x92653)),x92651))
% 28.73/28.53 [9352]~P1(f319(f319(f227(a1),f2(a1)),x93522))+~P1(f319(f319(f226(a1),x93521),x93523))+P1(f319(f319(f321(a1),f384(x93523,x93524,x93522,x93521)),f295(a1,f72(a1),x93522)))+P1(f319(f319(f226(a1),f319(f319(f23(a1),x93521),x93522)),x93523))
% 28.73/28.53 [9353]~P1(f319(f319(f227(a1),f2(a1)),x93532))+~P1(f319(f319(f227(a1),x93531),x93533))+P1(f319(f319(f321(a1),f406(x93533,x93534,x93532,x93531)),f295(a1,f72(a1),x93532)))+P1(f319(f319(f227(a1),f319(f319(f23(a1),x93531),x93532)),x93533))
% 28.73/28.53 [9371]~P1(f319(f319(f226(a1),f2(a1)),x93714))+~P1(f319(f319(f227(a1),f2(a1)),x93713))+~P1(f319(f319(f227(a1),x93714),x93711))+P1(f319(f319(f226(a1),f2(a1)),f319(f319(f74(a1),f319(f319(f75(a1),x93711),f39(a1,x93712,x93713))),x93714)))
% 28.73/28.53 [9401]E(x94011,x94012)+~P40(x94013,x94014)+~P1(f319(f319(f321(f931(x94013,x94013)),f319(f319(f244(x94013,x94013),x94012),x94011)),x94014))+~P1(f319(f319(f321(f931(x94013,x94013)),f319(f319(f244(x94013,x94013),x94011),x94012)),x94014))
% 28.73/28.53 [9402]E(x94021,x94022)+~P40(x94023,x94024)+~P1(f319(f319(f321(f931(x94023,x94023)),f319(f319(f244(x94023,x94023),x94022),x94021)),x94024))+~P1(f319(f319(f321(f931(x94023,x94023)),f319(f319(f244(x94023,x94023),x94021),x94022)),x94024))
% 28.73/28.53 [9435]~P108(x94351)+~P1(f319(f55(x94351),x94354))+~P1(f319(f319(f226(x94351),x94352),f650(x94353,x94352,x94354,x94351)))+P1(f319(f319(f226(x94351),f319(f319(f93(x94351),x94352),x94353)),f319(f319(f58(x94351,x94351,f93(x94351)),x94353),x94354)))
% 28.73/28.53 [9436]~P4(x94361)+~P1(f319(f55(x94361),x94364))+~P1(f319(f319(f226(x94361),x94362),f651(x94363,x94362,x94364,x94361)))+P1(f319(f319(f226(x94361),f319(f319(f224(x94361),x94362),x94363)),f319(f319(f58(x94361,x94361,f224(x94361)),x94363),x94364)))
% 28.73/28.53 [9452]~P1(f319(f319(f226(a1),x94524),f2(a1)))+~P1(f319(f319(f227(a1),f2(a1)),x94522))+~P1(f319(f319(f227(a1),x94521),x94524))+P1(f319(f319(f227(a1),f319(f319(f75(a1),x94521),x94522)),f319(f319(f74(a1),f319(f319(f75(a1),x94521),f39(a1,x94523,x94522))),x94524)))
% 28.73/28.53 [9477]P1(f319(f55(x94771),x94772))+~P1(f319(f55(x94771),x94773))+~P1(f319(f319(f321(f932(x94771,a923)),x94772),f319(f319(f54(x94771),x94773),x94774)))+~P1(f319(f319(f226(f932(f931(x94771,x94771),a923)),x94774),f319(f319(f246(x94771,x94771),x94773),f319(f16(f932(x94771,a923),x94771),x94773))))
% 28.73/28.53 [9502]~P4(x95021)+~P1(f319(f55(x95021),x95024))+P1(f319(f319(f321(x95021),f651(x95022,x95023,x95024,x95021)),x95024))+P1(f319(f319(f226(x95021),f319(f319(f224(x95021),x95023),x95022)),f319(f319(f58(x95021,x95021,f224(x95021)),x95022),x95024)))
% 28.73/28.53 [9503]~P108(x95031)+~P1(f319(f55(x95031),x95034))+P1(f319(f319(f321(x95031),f650(x95032,x95033,x95034,x95031)),x95034))+P1(f319(f319(f226(x95031),f319(f319(f93(x95031),x95033),x95032)),f319(f319(f58(x95031,x95031,f93(x95031)),x95032),x95034)))
% 28.73/28.53 [9515]~P41(f932(x95151,a923),f932(x95151,a923),x95153)+~P1(f319(f319(f321(x95151),x95152),x95154))+P1(f319(f319(f321(x95151),x95152),f88(f932(x95151,a923),x95153)))+~P1(f319(f319(f226(f932(x95151,a923)),x95154),f319(x95153,f319(f319(f102(f932(x95151,a923)),x95154),f88(f932(x95151,a923),x95153)))))
% 28.73/28.53 [9698]~P41(f932(x96983,a923),f932(x96983,a923),x96984)+P1(f319(x96981,x96982))+~P1(f319(f319(f321(x96983),x96982),f87(f932(x96983,a923),x96984)))+P1(f319(f319(f321(x96983),f460(x96981,x96984,x96982,x96983)),f319(x96984,f319(f319(f93(f932(x96983,a923)),f87(f932(x96983,a923),x96984)),f319(f254(x96983),x96981)))))
% 28.73/28.53 [9914]~P1(f319(f55(x99142),x99144))+~P1(f319(f55(x99141),x99143))+~P1(f319(f319(f226(a925),f319(f29(x99142),x99144)),f319(f29(x99141),x99143)))+P1(f319(f319(f226(f932(x99141,a923)),f319(f302(x99142,x99141,f422(x99143,x99141,x99144,x99142)),x99144)),x99143))
% 28.73/28.53 [9553]~P1(f319(f319(f321(x95531),x95532),x95534))+P1(f319(f319(f321(x95531),x95532),x95533))+~P1(f319(f319(f227(f932(x95531,a923)),x95534),f319(f319(f301(x95531),x95532),x95533)))+P1(f319(f319(f227(f932(x95531,a923)),f319(f319(f23(f932(x95531,a923)),x95534),f319(f319(f301(x95531),x95532),f180(f932(x95531,a923))))),x95533))
% 28.73/28.53 [9723]~P1(f319(f319(f321(x97231),x97232),x97234))+P1(f319(f319(f321(x97231),x97232),x97233))+P1(f319(f319(f227(f932(x97231,a923)),x97234),f319(f319(f301(x97231),x97232),x97233)))+~P1(f319(f319(f227(f932(x97231,a923)),f319(f319(f23(f932(x97231,a923)),x97234),f319(f319(f301(x97231),x97232),f180(f932(x97231,a923))))),x97233))
% 28.73/28.53 [9748]P1(f319(f319(f321(x97481),x97482),x97483))+~P1(f319(f319(f226(f932(x97481,a923)),x97484),x97483))+P1(f319(f319(f227(f932(x97481,a923)),x97484),f319(f319(f301(x97481),x97482),x97483)))+~P1(f319(f319(f227(f932(x97481,a923)),f319(f319(f23(f932(x97481,a923)),x97484),f319(f319(f301(x97481),x97482),f180(f932(x97481,a923))))),x97483))
% 28.73/28.53 [9753]~P1(f319(f319(f321(x97531),x97533),x97532))+~P1(f319(f319(f227(f932(x97531,a923)),x97532),x97534))+P1(f319(f319(f227(f932(x97531,a923)),x97532),f319(f319(f301(x97531),x97533),x97534)))+~P1(f319(f319(f227(f932(x97531,a923)),f319(f319(f23(f932(x97531,a923)),x97532),f319(f319(f301(x97531),x97533),f180(f932(x97531,a923))))),x97534))
% 28.73/28.53 [9769]~P1(f319(f319(f226(f932(x97691,a923)),x97692),x97694))+~P1(f319(f319(f227(f932(x97691,a923)),x97692),x97694))+P1(f319(f319(f227(f932(x97691,a923)),x97692),f319(f319(f301(x97691),x97693),x97694)))+~P1(f319(f319(f227(f932(x97691,a923)),f319(f319(f23(f932(x97691,a923)),x97692),f319(f319(f301(x97691),x97693),f180(f932(x97691,a923))))),x97694))
% 28.73/28.53 [9816]~P113(x98162)+~P5(x98161)+~P1(f319(f319(f226(f932(x98161,x98162)),x98163),x98164))+P1(f319(f51(x98161),f319(f319(f18(x98161,x98162,a923),f319(f319(f8(x98162,f932(x98162,a923),x98161),f226(x98162)),x98163)),x98164)))
% 28.73/28.53 [9969]~P113(x99692)+~P5(x99691)+P1(f319(f319(f226(f932(x99691,x99692)),x99693),x99694))+~P1(f319(f51(x99691),f319(f319(f18(x99691,x99692,a923),f319(f319(f8(x99692,f932(x99692,a923),x99691),f226(x99692)),x99693)),x99694)))
% 28.73/28.53 [10487]~P41(f932(x104871,a923),f932(x104871,a923),x104873)+~P1(f319(f319(f321(x104871),x104872),x104874))+P1(f319(f319(f321(x104871),x104872),f88(f932(x104871,a923),x104873)))+~P1(f319(f319(f226(f932(x104871,a923)),x104874),f319(x104873,f87(f932(x104871,a923),f319(f319(f7(f932(x104871,a923),f932(x104871,a923),f932(x104871,a923)),f319(f319(f8(f932(x104871,a923),f932(f932(x104871,a923),f932(x104871,a923)),f932(x104871,a923)),f102(f932(x104871,a923))),f319(f319(f7(f932(x104871,a923),f932(x104871,a923),f932(x104871,a923)),f319(f319(f8(f932(x104871,a923),f932(f932(x104871,a923),f932(x104871,a923)),f932(x104871,a923)),f102(f932(x104871,a923))),x104873)),x104874))),f88(f932(x104871,a923),x104873))))))
% 28.73/28.53 [10146]E(f319(f319(f156(x101461),f319(f319(f156(f926(x101461)),f171(x101461,x101462)),x101463)),x101464),f319(f319(f156(x101461),f319(f319(f156(f926(x101461)),x101462),x101464)),x101463))+~P1(f319(f319(f227(a925),x101463),f319(f181(f926(f926(x101461))),f171(x101461,x101462))))+~P14(a925,f319(f160(a925),f319(f319(f146(f926(x101461),a925),f181(f926(x101461))),x101462)))+~P1(f319(f319(f227(a925),x101464),f319(f181(f926(f926(x101461))),f319(f128(f926(x101461),f319(f319(f8(a925,a923,f926(x101461)),f319(f227(a925),x101463)),f181(f926(x101461)))),x101462))))
% 28.73/28.53 [10167]~P1(f319(f319(f321(f931(a925,a925)),x101674),x101671))+~P1(f319(f319(f321(f931(f931(a925,a925),f931(a925,a925))),f319(f319(f244(f931(a925,a925),f931(a925,a925)),x101674),x101672)),a26))+~P1(f319(f319(f321(f931(f932(f931(a925,a925),a923),f932(f931(a925,a925),a923))),f319(f319(f244(f932(f931(a925,a925),a923),f932(f931(a925,a925),a923)),x101671),x101673)),a27))+P1(f319(f319(f321(f931(f932(f931(a925,a925),a923),f932(f931(a925,a925),a923))),f319(f319(f244(f932(f931(a925,a925),a923),f932(f931(a925,a925),a923)),x101671),f319(f319(f301(f931(a925,a925)),x101672),x101673))),a27))
% 28.73/28.53 [10168]~P1(f319(f319(f321(f931(a925,a925)),x101684),x101681))+~P1(f319(f319(f321(f931(f931(a925,a925),f931(a925,a925))),f319(f319(f244(f931(a925,a925),f931(a925,a925)),x101684),x101682)),a64))+~P1(f319(f319(f321(f931(f932(f931(a925,a925),a923),f932(f931(a925,a925),a923))),f319(f319(f244(f932(f931(a925,a925),a923),f932(f931(a925,a925),a923)),x101681),x101683)),a65))+P1(f319(f319(f321(f931(f932(f931(a925,a925),a923),f932(f931(a925,a925),a923))),f319(f319(f244(f932(f931(a925,a925),a923),f932(f931(a925,a925),a923)),x101681),f319(f319(f301(f931(a925,a925)),x101682),x101683))),a65))
% 28.73/28.53 [10055]~P113(x100552)+~P5(x100551)+~P1(f319(f319(f227(f932(x100551,x100552)),x100553),x100554))+P1(f319(f50(x100551),f319(f319(f8(a923,a923,x100551),a314),f319(f319(f18(x100551,x100552,a923),f319(f319(f8(x100552,f932(x100552,a923),x100551),a316),x100553)),x100554))))
% 28.73/28.53 [10179]~P1(f319(f319(f321(f931(a925,a925)),x101794),x101793))+~P1(f319(f319(f321(f931(f931(a925,a925),f931(a925,a925))),f319(f319(f244(f931(a925,a925),f931(a925,a925)),x101791),x101794)),a26))+~P1(f319(f319(f321(f931(f932(f931(a925,a925),a923),f932(f931(a925,a925),a923))),f319(f319(f244(f932(f931(a925,a925),a923),f932(f931(a925,a925),a923)),x101792),x101793)),a28))+P1(f319(f319(f321(f931(f932(f931(a925,a925),a923),f932(f931(a925,a925),a923))),f319(f319(f244(f932(f931(a925,a925),a923),f932(f931(a925,a925),a923)),f319(f319(f301(f931(a925,a925)),x101791),x101792)),x101793)),a28))
% 28.73/28.53 [10180]~P1(f319(f319(f321(f931(a925,a925)),x101804),x101803))+~P1(f319(f319(f321(f931(f931(a925,a925),f931(a925,a925))),f319(f319(f244(f931(a925,a925),f931(a925,a925)),x101801),x101804)),a64))+~P1(f319(f319(f321(f931(f932(f931(a925,a925),a923),f932(f931(a925,a925),a923))),f319(f319(f244(f932(f931(a925,a925),a923),f932(f931(a925,a925),a923)),x101802),x101803)),a63))+P1(f319(f319(f321(f931(f932(f931(a925,a925),a923),f932(f931(a925,a925),a923))),f319(f319(f244(f932(f931(a925,a925),a923),f932(f931(a925,a925),a923)),f319(f319(f301(f931(a925,a925)),x101801),x101802)),x101803)),a63))
% 28.73/28.53 [6257]~P8(x62574,x62571)+~P1(f319(f319(x62571,x62572),x62575))+P1(f319(f319(x62571,x62572),x62573))+~P1(f319(f319(x62571,x62575),x62573))
% 28.73/28.53 [6258]~P54(x62584,x62581)+~P1(f319(f319(x62581,x62582),x62585))+P1(f319(f319(x62581,x62582),x62583))+~P1(f319(f319(x62581,x62585),x62583))
% 28.73/28.53 [6259]~P17(x62594,x62591)+~P1(f319(f319(x62591,x62592),x62595))+P1(f319(f319(x62591,x62592),x62593))+~P1(f319(f319(x62591,x62595),x62593))
% 28.73/28.53 [8938]~P27(x89381,x89383,x89385,x89382,x89384)+E(f319(f29(x89381),x89382),f319(f29(x89383),x89384))+~P1(f319(f55(x89383),x89384))+~P1(f319(f55(x89381),x89382))
% 28.73/28.53 [8959]~P8(x89594,x89593)+~P1(f319(x89591,x89595))+P1(f319(x89592,f847(x89592,x89591,x89593,x89594)))+P1(f319(x89591,f846(x89592,x89591,x89593,x89594)))
% 28.73/28.53 [9199]~P8(x91994,x91993)+~P1(f319(x91992,x91995))+~P1(f319(x91991,f846(x91991,x91992,x91993,x91994)))+P1(f319(x91991,f847(x91991,x91992,x91993,x91994)))
% 28.73/28.53 [9384]~P8(x93844,x93843)+~P1(f319(x93841,x93845))+P1(f319(f319(f321(x93844),f847(x93842,x93841,x93843,x93844)),f262(x93844,x93843)))+P1(f319(x93841,f846(x93842,x93841,x93843,x93844)))
% 28.73/28.53 [9509]~P8(x95091,x95094)+~P1(f319(x95093,x95095))+~P1(f319(x95092,f846(x95092,x95093,x95094,x95091)))+P1(f319(f319(f321(x95091),f847(x95092,x95093,x95094,x95091)),f262(x95091,x95094)))
% 28.73/28.53 [9805]~P39(x98051,x98054)+P1(f319(f319(f321(f931(f926(x98051),f926(x98051))),f319(f319(f244(f926(x98051),f926(x98051)),x98052),x98053)),f139(x98051,x98054)))+~P1(f319(f319(f321(f931(f926(x98051),f926(x98051))),f319(f319(f244(f926(x98051),f926(x98051)),x98052),x98055)),f139(x98051,x98054)))+~P1(f319(f319(f321(f931(f926(x98051),f926(x98051))),f319(f319(f244(f926(x98051),f926(x98051)),x98055),x98053)),f139(x98051,x98054)))
% 28.73/28.53 [5494]~P70(x54945)+E(x54941,x54942)+~E(x54943,x54944)+~E(f319(f319(f23(x54945),x54943),x54944),f319(f319(f23(x54945),x54941),x54942))
% 28.73/28.53 [5495]~P70(x54955)+E(x54951,x54952)+~E(x54953,x54954)+~E(f319(f319(f23(x54955),x54953),x54954),f319(f319(f23(x54955),x54951),x54952))
% 28.73/28.53 [6368]~P19(x63685,x63681,x63683)+E(f319(f319(x63681,x63682),f319(x63683,x63684)),f319(x63683,x63684))+~P1(f319(f55(x63685),x63684))+~P1(f319(f319(f321(x63685),x63682),x63684))
% 28.77/28.53 [6556]~P68(x65561)+~E(f319(f319(f23(x65561),x65564),x65565),f319(f319(f23(x65561),x65562),x65563))+~P1(f319(f319(f226(x65561),x65564),x65565))+P1(f319(f319(f226(x65561),x65562),x65563))
% 28.77/28.53 [6557]~P68(x65571)+~E(f319(f319(f23(x65571),x65574),x65575),f319(f319(f23(x65571),x65572),x65573))+~P1(f319(f319(f226(x65571),x65574),x65575))+P1(f319(f319(f226(x65571),x65572),x65573))
% 28.77/28.53 [6558]~P68(x65581)+~E(f319(f319(f23(x65581),x65584),x65585),f319(f319(f23(x65581),x65582),x65583))+~P1(f319(f319(f227(x65581),x65584),x65585))+P1(f319(f319(f227(x65581),x65582),x65583))
% 28.77/28.53 [6559]~P68(x65591)+~E(f319(f319(f23(x65591),x65594),x65595),f319(f319(f23(x65591),x65592),x65593))+~P1(f319(f319(f227(x65591),x65594),x65595))+P1(f319(f319(f227(x65591),x65592),x65593))
% 28.77/28.53 [7542]~E(x75422,f319(f319(f143(x75421),x75424),x75425))+P1(f319(f319(f321(f926(x75421)),x75422),f153(x75421,x75423)))+~P1(f319(f319(f321(f926(x75421)),x75425),f153(x75421,x75423)))+~P1(f319(f319(f321(x75421),x75424),x75423))
% 28.77/28.53 [7942]~E(f319(f181(f926(x79421)),x79423),f319(f181(f926(x79422)),x79424))+~E(f319(f319(f146(f931(x79421,x79422),x79422),f248(x79421,x79422)),x79425),x79424)+~E(f319(f319(f146(f931(x79421,x79422),x79421),f243(x79421,x79422)),x79425),x79423)+E(f319(f319(f173(x79421,x79422),x79423),x79424),x79425)
% 28.77/28.53 [8278]~P113(x82781)+P1(f319(f319(f227(f932(x82781,a923)),f295(x82781,x82782,x82783)),f295(x82781,x82784,x82785)))+~P1(f319(f319(f226(x82781),x82784),x82785))+P1(f319(f319(f226(x82781),x82782),x82783))
% 28.77/28.53 [8377]~P113(x83771)+P1(f319(f319(f226(f932(x83771,a923)),f295(x83771,x83772,x83773)),f295(x83771,x83774,x83775)))+~P1(f319(f319(f226(x83771),x83773),x83775))+~P1(f319(f319(f226(x83771),x83774),x83772))
% 28.77/28.53 [8497]~P4(x84971)+P1(f319(f319(f226(x84971),x84972),x84973))+P1(f319(f319(f226(x84971),x84974),x84973))+~P1(f319(f319(f226(f932(x84971,a923)),f319(f294(x84971,x84973),x84972)),f319(f294(x84971,x84974),x84975)))
% 28.77/28.53 [8498]~P4(x84981)+P1(f319(f319(f226(x84981),x84982),x84983))+P1(f319(f319(f226(x84981),x84982),x84984))+~P1(f319(f319(f226(f932(x84981,a923)),f319(f294(x84981,x84983),x84982)),f319(f294(x84981,x84985),x84984)))
% 28.77/28.53 [8668]~P108(x86683)+~P108(x86681)+~P41(x86683,x86681,x86682)+P1(f319(f319(f226(x86681),f319(x86682,f319(f319(f93(x86683),x86684),x86685))),f319(f319(f93(x86681),f319(x86682,x86684)),f319(x86682,x86685))))
% 28.77/28.53 [8669]~P4(x86693)+~P108(x86691)+~P41(x86693,x86691,x86692)+P1(f319(f319(f226(x86691),f319(x86692,f319(f319(f224(x86693),x86694),x86695))),f319(f319(f93(x86691),f319(x86692,x86694)),f319(x86692,x86695))))
% 28.77/28.53 [8736]~P113(x87361)+~P1(f319(f319(f226(f932(x87361,a923)),f295(x87361,x87364,x87362)),f295(x87361,x87365,x87363)))+P1(f319(f319(f226(x87361),x87362),x87363))+~P1(f319(f319(f226(x87361),x87364),x87362))
% 28.77/28.53 [8737]~P113(x87371)+~P1(f319(f319(f227(f932(x87371,a923)),f295(x87371,x87374,x87372)),f295(x87371,x87375,x87373)))+P1(f319(f319(f226(x87371),x87372),x87373))+~P1(f319(f319(f226(x87371),x87374),x87372))
% 28.77/28.53 [8738]~P113(x87381)+~P1(f319(f319(f226(f932(x87381,a923)),f295(x87381,x87383,x87384)),f295(x87381,x87382,x87385)))+P1(f319(f319(f226(x87381),x87382),x87383))+~P1(f319(f319(f226(x87381),x87383),x87384))
% 28.77/28.53 [8739]~P113(x87391)+~P1(f319(f319(f227(f932(x87391,a923)),f295(x87391,x87393,x87394)),f295(x87391,x87392,x87395)))+P1(f319(f319(f226(x87391),x87392),x87393))+~P1(f319(f319(f226(x87391),x87393),x87394))
% 28.77/28.53 [6204]~P4(x62045)+~P4(x62041)+~P41(x62045,x62041,x62042)+E(f319(f319(f224(x62041),f319(x62042,x62043)),f319(x62042,x62044)),f319(x62042,f319(f319(f224(x62045),x62043),x62044)))
% 28.77/28.53 [6205]~P4(x62055)+~P4(x62051)+~P41(x62055,x62051,x62052)+E(f319(f319(f225(x62051),f319(x62052,x62053)),f319(x62052,x62054)),f319(x62052,f319(f319(f225(x62055),x62053),x62054)))
% 28.77/28.53 [6256]~P19(x62562,x62565,x62563)+E(x62561,f180(f932(x62562,a923)))+~P1(f319(f55(x62562),x62561))+E(f319(x62563,f319(f319(f301(x62562),x62564),x62561)),f319(f319(x62565,x62564),f319(x62563,x62561)))
% 28.77/28.53 [7034]~E(x70341,x70342)+~E(f319(f319(f93(f932(x70343,a923)),x70344),x70345),f180(f932(x70343,a923)))+~P1(f319(f319(f321(x70343),x70342),x70345))+~P1(f319(f319(f321(x70343),x70341),x70344))
% 28.77/28.53 [7117]~P20(x71172,x71175,x71171)+~P1(f319(f55(x71172),x71174))+E(f319(x71171,f319(f319(f301(x71172),x71173),x71174)),f319(f319(f58(x71172,x71172,x71175),x71173),x71174))+P1(f319(f319(f321(x71172),x71173),x71174))
% 28.77/28.53 [7182]~P79(x71822)+~P1(f319(f55(x71821),x71825))+E(f319(f319(f6(x71821,x71822),x71823),f319(f319(f301(x71821),x71824),x71825)),f319(f319(f74(x71822),f319(x71823,x71824)),f319(f319(f6(x71821,x71822),x71823),x71825)))+P1(f319(f319(f321(x71821),x71824),x71825))
% 28.77/28.53 [7183]~P79(x71832)+~P1(f319(f55(x71831),x71835))+E(f319(f319(f6(x71831,x71832),x71833),f319(f319(f301(x71831),x71834),x71835)),f319(f319(f74(x71832),f319(x71833,x71834)),f319(f319(f6(x71831,x71832),x71833),x71835)))+P1(f319(f319(f321(x71831),x71834),x71835))
% 28.77/28.53 [7184]~P78(x71842)+~P1(f319(f55(x71841),x71845))+E(f319(f319(f9(x71841,x71842),x71843),f319(f319(f301(x71841),x71844),x71845)),f319(f319(f75(x71842),f319(x71843,x71844)),f319(f319(f9(x71841,x71842),x71843),x71845)))+P1(f319(f319(f321(x71841),x71844),x71845))
% 28.77/28.53 [7185]~P78(x71852)+~P1(f319(f55(x71851),x71855))+E(f319(f319(f9(x71851,x71852),x71853),f319(f319(f301(x71851),x71854),x71855)),f319(f319(f75(x71852),f319(x71853,x71854)),f319(f319(f9(x71851,x71852),x71853),x71855)))+P1(f319(f319(f321(x71851),x71854),x71855))
% 28.77/28.53 [7686]~P20(x76862,x76865,x76861)+~P1(f319(f55(x76862),x76864))+E(f319(x76861,f319(f319(f301(x76862),x76863),x76864)),x76863)+~E(f319(f319(f23(f932(x76862,a923)),x76864),f319(f319(f301(x76862),x76863),f180(f932(x76862,a923)))),f180(f932(x76862,a923)))
% 28.77/28.53 [8042]~P65(x80421)+E(f319(f319(f30(x80421),f319(f319(f75(x80421),x80422),x80423)),f319(f319(f75(x80421),x80424),x80425)),f319(f319(f75(x80421),f319(f319(f30(x80421),x80422),x80424)),f319(f319(f30(x80421),x80423),x80425)))+~P1(f319(f319(f279(x80421),x80425),x80423))+~P1(f319(f319(f279(x80421),x80424),x80422))
% 28.77/28.53 [8046]~P107(x80461)+~P1(f319(f319(f226(x80461),x80463),x80465))+~P1(f319(f319(f226(x80461),x80462),x80464))+P1(f319(f319(f226(x80461),f319(f319(f102(x80461),x80462),x80463)),f319(f319(f102(x80461),x80464),x80465)))
% 28.77/28.53 [8047]~P108(x80471)+~P1(f319(f319(f226(x80471),x80473),x80475))+~P1(f319(f319(f226(x80471),x80472),x80474))+P1(f319(f319(f226(x80471),f319(f319(f93(x80471),x80472),x80473)),f319(f319(f93(x80471),x80474),x80475)))
% 28.77/28.53 [8048]~P91(x80481)+~P1(f319(f319(f226(x80481),x80483),x80485))+~P1(f319(f319(f226(x80481),x80482),x80484))+P1(f319(f319(f226(x80481),f319(f319(f74(x80481),x80482),x80483)),f319(f319(f74(x80481),x80484),x80485)))
% 28.77/28.53 [8049]~P4(x80491)+~P1(f319(f319(f226(x80491),x80493),x80495))+~P1(f319(f319(f226(x80491),x80492),x80494))+P1(f319(f319(f226(x80491),f319(f319(f224(x80491),x80492),x80493)),f319(f319(f224(x80491),x80494),x80495)))
% 28.77/28.53 [8050]~P4(x80501)+~P1(f319(f319(f226(x80501),x80503),x80505))+~P1(f319(f319(f226(x80501),x80502),x80504))+P1(f319(f319(f226(x80501),f319(f319(f225(x80501),x80502),x80503)),f319(f319(f225(x80501),x80504),x80505)))
% 28.77/28.53 [8051]~P89(x80511)+~P1(f319(f319(f226(x80511),x80513),x80515))+~P1(f319(f319(f227(x80511),x80512),x80514))+P1(f319(f319(f227(x80511),f319(f319(f74(x80511),x80512),x80513)),f319(f319(f74(x80511),x80514),x80515)))
% 28.77/28.53 [8052]~P89(x80521)+~P1(f319(f319(f226(x80521),x80522),x80524))+~P1(f319(f319(f227(x80521),x80523),x80525))+P1(f319(f319(f227(x80521),f319(f319(f74(x80521),x80522),x80523)),f319(f319(f74(x80521),x80524),x80525)))
% 28.77/28.53 [8053]~P89(x80531)+~P1(f319(f319(f227(x80531),x80533),x80535))+~P1(f319(f319(f227(x80531),x80532),x80534))+P1(f319(f319(f227(x80531),f319(f319(f74(x80531),x80532),x80533)),f319(f319(f74(x80531),x80534),x80535)))
% 28.77/28.53 [8054]~P121(x80541)+~P1(f319(f319(f279(x80541),x80543),x80545))+~P1(f319(f319(f279(x80541),x80542),x80544))+P1(f319(f319(f279(x80541),f319(f319(f75(x80541),x80542),x80543)),f319(f319(f75(x80541),x80544),x80545)))
% 28.77/28.53 [8192]~P148(x81925)+E(x81921,x81922)+E(x81923,x81924)+~E(f319(f319(f74(x81925),f319(f319(f75(x81925),x81923),x81921)),f319(f319(f75(x81925),x81924),x81922)),f319(f319(f74(x81925),f319(f319(f75(x81925),x81923),x81922)),f319(f319(f75(x81925),x81924),x81921)))
% 28.77/28.53 [8193]~P148(x81935)+E(x81931,x81932)+E(x81933,x81934)+~E(f319(f319(f74(x81935),f319(f319(f75(x81935),x81933),x81931)),f319(f319(f75(x81935),x81934),x81932)),f319(f319(f74(x81935),f319(f319(f75(x81935),x81933),x81932)),f319(f319(f75(x81935),x81934),x81931)))
% 28.77/28.53 [8398]~P4(x83984)+~P1(f319(f129(x83981),x83983))+P1(f319(f319(f321(x83981),x83982),f319(f164(x83981),x83983)))+P1(f319(f129(x83981),f319(f319(f140(x83981,x83984,x83985),x83982),x83983)))
% 28.77/28.53 [8545]~P70(x85451)+E(f319(f319(f23(x85451),f319(f319(f6(a925,x85451),x85452),f319(f294(a925,x85453),x85454))),f319(f319(f6(a925,x85451),x85452),f319(f294(a925,x85453),x85455))),f319(f319(f6(a925,x85451),x85452),f319(f294(a925,x85455),x85454)))+~P1(f319(f319(f226(a925),x85455),x85454))+~P1(f319(f319(f226(a925),x85453),x85455))
% 28.77/28.53 [8546]~P79(x85461)+E(f319(f319(f74(x85461),f319(f319(f6(a925,x85461),x85462),f319(f294(a925,x85463),x85464))),f319(f319(f6(a925,x85461),x85462),f319(f294(a925,x85464),x85465))),f319(f319(f6(a925,x85461),x85462),f319(f294(a925,x85463),x85465)))+~P1(f319(f319(f226(a925),x85464),x85465))+~P1(f319(f319(f226(a925),x85463),x85464))
% 28.77/28.53 [8880]~P73(x88802)+E(x88801,f2(x88802))+E(x88803,f2(x88802))+E(f319(f319(f283(x88802),f319(f319(f23(x88802),f319(f319(f75(x88802),x88804),x88801)),f319(f319(f75(x88802),x88805),x88803))),f319(f319(f75(x88802),x88803),x88801)),f319(f319(f23(x88802),f319(f319(f283(x88802),x88804),x88803)),f319(f319(f283(x88802),x88805),x88801)))
% 28.77/28.53 [8881]~P73(x88812)+E(x88811,f2(x88812))+E(x88813,f2(x88812))+E(f319(f319(f283(x88812),f319(f319(f74(x88812),f319(f319(f75(x88812),x88814),x88811)),f319(f319(f75(x88812),x88815),x88813))),f319(f319(f75(x88812),x88813),x88811)),f319(f319(f74(x88812),f319(f319(f283(x88812),x88814),x88813)),f319(f319(f283(x88812),x88815),x88811)))
% 28.77/28.53 [8890]~E(x88902,f319(x88903,x88901))+E(x88901,f892(x88902,x88903,x88904,x88905))+~P26(x88905,x88904,x88903,f234(f932(x88905,a923)))+~P1(f319(f319(f321(x88904),x88902),f319(f302(x88905,x88904,x88903),f234(f932(x88905,a923)))))
% 28.77/28.53 [9109]~P126(x91091)+~P1(f319(f319(f227(x91091),f319(f69(x91091),x91092)),x91094))+P1(f319(f319(f227(x91091),f319(f319(f75(x91091),f319(f69(x91091),x91092)),f319(f69(x91091),x91093))),f319(f319(f75(x91091),x91094),x91095)))+~P1(f319(f319(f227(x91091),f319(f69(x91091),x91093)),x91095))
% 28.77/28.53 [9225]~P26(x92251,x92253,x92255,x92252)+~P1(f319(f55(x92253),x92254))+P1(f319(f319(f226(a925),f319(f29(x92251),x92252)),f319(f29(x92253),x92254)))+~P1(f319(f319(f226(f932(x92253,a923)),f319(f302(x92251,x92253,x92255),x92252)),x92254))
% 28.77/28.53 [9293]~P79(x92932)+~P26(x92931,x92931,x92934,x92935)+~P1(f319(f55(x92931),x92935))+E(f319(f319(f6(x92931,x92932),f319(f66(x92931,x92932,x92931,x92933),x92934)),x92935),f319(f319(f6(x92931,x92932),x92933),f319(f302(x92931,x92931,x92934),x92935)))
% 28.77/28.53 [9294]~P78(x92942)+~P26(x92941,x92941,x92944,x92945)+~P1(f319(f55(x92941),x92945))+E(f319(f319(f9(x92941,x92942),f319(f66(x92941,x92942,x92941,x92943),x92944)),x92945),f319(f319(f9(x92941,x92942),x92943),f319(f302(x92941,x92941,x92944),x92945)))
% 28.77/28.53 [9375]~E(f893(x93752,x93754,x93751,x93753,x93755),x93755)+~E(x93752,f319(x93754,x93755))+~P26(x93753,x93751,x93754,f234(f932(x93753,a923)))+P1(f319(f319(f321(x93751),x93752),f319(f302(x93753,x93751,x93754),f234(f932(x93753,a923)))))
% 28.77/28.53 [9414]~P38(x94141,x94142)+~P1(f319(f319(f321(x94141),x94143),x94144))+~P1(f319(f319(f321(x94141),x94145),x94144))+~P1(f319(f319(f321(f931(x94141,x94141)),f319(f319(f244(x94141,x94141),x94145),f630(x94142,x94141,x94144))),x94142))
% 28.77/28.53 [9451]~P26(x94512,x94513,x94515,x94511)+E(x94511,f180(f932(x94512,a923)))+E(f319(f302(x94513,x94512,f894(x94514,x94513,x94512,x94511)),x94514),x94511)+~P1(f319(f319(f226(f932(x94513,a923)),f319(f302(x94512,x94513,x94515),x94511)),x94514))
% 28.77/28.53 [9491]~E(x94912,f319(x94911,x94915))+~P26(x94914,x94913,x94911,f234(f932(x94914,a923)))+E(f319(x94911,f893(x94912,x94911,x94913,x94914,x94915)),x94912)+P1(f319(f319(f321(x94913),x94912),f319(f302(x94914,x94913,x94911),f234(f932(x94914,a923)))))
% 28.77/28.53 [9945]~P4(x99455)+~P6(x99455)+P1(f319(f319(f321(x99451),f886(x99452,x99453,x99451,x99454,x99455)),x99453))+~P1(f319(f319(f227(x99455),x99454),f319(f319(f33(x99451,x99455),x99453),x99452)))
% 28.77/28.53 [9951]~P4(x99511)+~P6(x99511)+P1(f319(f319(f227(x99511),x99512),f319(x99513,f886(x99513,x99514,x99515,x99512,x99511))))+~P1(f319(f319(f227(x99511),x99512),f319(f319(f33(x99515,x99511),x99514),x99513)))
% 28.77/28.53 [10040]~P76(x100401)+~P1(f319(f60(x100401,x100401,f75(x100401),x100402,x100403),x100405))+P1(f319(f319(f321(x100401),x100402),x100403))+P1(f319(f60(x100401,x100401,f75(x100401),x100404,f319(f319(f301(x100401),x100402),x100403)),f319(f319(f75(x100401),x100404),x100405)))
% 28.77/28.53 [10260]~P79(x102602)+~P1(f319(f55(x102601),x102605))+E(f319(f319(f6(x102601,x102602),f319(f319(f7(x102601,x102602,x102602),f319(f319(f18(x102601,x102602,f932(x102602,x102602)),f319(f319(f8(a923,f932(x102602,f932(x102602,x102602)),x102601),f86(x102602)),f319(a316,x102603))),x102604)),f2(x102602))),x102605),f2(x102602))+P1(f319(f319(f321(x102601),x102603),x102605))
% 28.77/28.53 [10261]~P78(x102612)+~P1(f319(f55(x102611),x102615))+E(f319(f319(f9(x102611,x102612),f319(f319(f7(x102611,x102612,x102612),f319(f319(f18(x102611,x102612,f932(x102612,x102612)),f319(f319(f8(a923,f932(x102612,f932(x102612,x102612)),x102611),f86(x102612)),f319(a316,x102613))),x102614)),f72(x102612))),x102615),f72(x102612))+P1(f319(f319(f321(x102611),x102613),x102615))
% 28.77/28.53 [10262]~P79(x102622)+~P1(f319(f55(x102621),x102625))+E(f319(f319(f6(x102621,x102622),f319(f319(f7(x102621,x102622,x102622),f319(f319(f18(x102621,x102622,f932(x102622,x102622)),f319(f319(f8(a923,f932(x102622,f932(x102622,x102622)),x102621),f86(x102622)),f319(a316,x102623))),x102624)),f2(x102622))),x102625),f319(x102624,x102623))+~P1(f319(f319(f321(x102621),x102623),x102625))
% 28.77/28.53 [10263]~P78(x102632)+~P1(f319(f55(x102631),x102635))+E(f319(f319(f9(x102631,x102632),f319(f319(f7(x102631,x102632,x102632),f319(f319(f18(x102631,x102632,f932(x102632,x102632)),f319(f319(f8(a923,f932(x102632,f932(x102632,x102632)),x102631),f86(x102632)),f319(a316,x102633))),x102634)),f72(x102632))),x102635),f319(x102634,x102633))+~P1(f319(f319(f321(x102631),x102633),x102635))
% 28.77/28.53 [10323]~P79(x103232)+~P1(f319(f55(x103231),x103235))+E(f319(f319(f6(x103231,x103232),f319(f319(f7(x103231,x103232,x103232),f319(f319(f18(x103231,x103232,f932(x103232,x103232)),f319(f319(f8(a923,f932(x103232,f932(x103232,x103232)),x103231),f86(x103232)),f319(f319(f7(x103231,x103231,a923),a316),x103233))),x103234)),f2(x103232))),x103235),f2(x103232))+P1(f319(f319(f321(x103231),x103233),x103235))
% 28.77/28.53 [10324]~P78(x103242)+~P1(f319(f55(x103241),x103245))+E(f319(f319(f9(x103241,x103242),f319(f319(f7(x103241,x103242,x103242),f319(f319(f18(x103241,x103242,f932(x103242,x103242)),f319(f319(f8(a923,f932(x103242,f932(x103242,x103242)),x103241),f86(x103242)),f319(f319(f7(x103241,x103241,a923),a316),x103243))),x103244)),f72(x103242))),x103245),f72(x103242))+P1(f319(f319(f321(x103241),x103243),x103245))
% 28.77/28.53 [10326]~P79(x103262)+~P1(f319(f55(x103261),x103265))+E(f319(f319(f6(x103261,x103262),f319(f319(f7(x103261,x103262,x103262),f319(f319(f18(x103261,x103262,f932(x103262,x103262)),f319(f319(f8(a923,f932(x103262,f932(x103262,x103262)),x103261),f86(x103262)),f319(f319(f7(x103261,x103261,a923),a316),x103263))),x103264)),f2(x103262))),x103265),f319(x103264,x103263))+~P1(f319(f319(f321(x103261),x103263),x103265))
% 28.77/28.53 [10327]~P78(x103272)+~P1(f319(f55(x103271),x103275))+E(f319(f319(f9(x103271,x103272),f319(f319(f7(x103271,x103272,x103272),f319(f319(f18(x103271,x103272,f932(x103272,x103272)),f319(f319(f8(a923,f932(x103272,f932(x103272,x103272)),x103271),f86(x103272)),f319(f319(f7(x103271,x103271,a923),a316),x103273))),x103274)),f72(x103272))),x103275),f319(x103274,x103273))+~P1(f319(f319(f321(x103271),x103273),x103275))
% 28.77/28.53 [8045]~P70(x80452)+~P1(f319(f55(x80451),x80454))+E(f319(f319(f6(x80451,x80452),x80453),f319(f319(f23(f932(x80451,a923)),x80454),f319(f319(f301(x80451),x80455),f180(f932(x80451,a923))))),f319(f319(f6(x80451,x80452),x80453),x80454))+P1(f319(f319(f321(x80451),x80455),x80454))
% 28.77/28.53 [8554]~P116(x85542)+~P1(f319(f55(x85541),x85544))+E(f319(f319(f6(x85541,x85542),x85543),f319(f319(f23(f932(x85541,a923)),x85544),f319(f319(f301(x85541),x85545),f180(f932(x85541,a923))))),f319(f319(f23(x85542),f319(f319(f6(x85541,x85542),x85543),x85544)),f319(x85543,x85545)))+~P1(f319(f319(f321(x85541),x85545),x85544))
% 28.77/28.53 [8555]~P70(x85552)+~P1(f319(f55(x85551),x85554))+E(f319(f319(f6(x85551,x85552),x85553),f319(f319(f23(f932(x85551,a923)),x85554),f319(f319(f301(x85551),x85555),f180(f932(x85551,a923))))),f319(f319(f23(x85552),f319(f319(f6(x85551,x85552),x85553),x85554)),f319(x85553,x85555)))+~P1(f319(f319(f321(x85551),x85555),x85554))
% 28.77/28.53 [8584]~P70(x85841)+~P1(f319(f55(x85842),x85844))+E(f319(f319(f23(x85841),f319(f319(f6(x85842,x85841),x85843),x85844)),f319(f319(f6(x85842,x85841),x85843),x85845)),f319(f319(f6(x85842,x85841),x85843),f319(f319(f23(f932(x85842,a923)),x85844),x85845)))+~P1(f319(f319(f226(f932(x85842,a923)),x85845),x85844))
% 28.77/28.53 [8603]P1(f319(f55(x86031),f319(x86032,x86033)))+~P1(f319(f55(x86034),x86035))+~P1(f319(f319(f321(x86034),x86033),x86035))+~P1(f319(f55(x86031),f319(f319(f33(x86034,f932(x86031,a923)),x86035),x86032)))
% 28.77/28.53 [8717]~P107(x87175)+~P107(x87171)+~P41(x87175,x87171,x87172)+P1(f319(f319(f226(x87171),f319(f319(f102(x87171),f319(x87172,x87173)),f319(x87172,x87174))),f319(x87172,f319(f319(f102(x87175),x87173),x87174))))
% 28.77/28.53 [8718]~P4(x87185)+~P107(x87181)+~P41(x87185,x87181,x87182)+P1(f319(f319(f226(x87181),f319(f319(f102(x87181),f319(x87182,x87183)),f319(x87182,x87184))),f319(x87182,f319(f319(f225(x87185),x87183),x87184))))
% 28.77/28.53 [9064]~P9(x90641,x90645,x90644)+~E(f319(f277(x90641,x90641,x90644),f319(f319(f301(x90641),x90642),f180(f932(x90641,a923)))),f319(f277(x90641,x90641,x90644),f319(f319(f301(x90641),x90643),f180(f932(x90641,a923)))))+~P1(f319(f319(f321(x90641),x90643),x90645))+P1(f319(f319(f321(f931(x90641,x90641)),f319(f319(f244(x90641,x90641),x90642),x90643)),x90644))
% 28.77/28.53 [9369]~P1(f319(x93691,x93695))+P1(f319(x93691,f614(x93691,x93692,x93693,x93694)))+P1(f319(x93691,f602(x93691,x93692,x93693,x93694)))+~P1(f319(f319(f321(x93694),x93695),f319(f319(f102(f932(x93694,a923)),x93693),x93692)))
% 28.77/28.53 [9558]~P1(f319(x95581,x95585))+P1(f319(x95581,f602(x95581,x95582,x95583,x95584)))+P1(f319(f319(f321(x95584),f614(x95581,x95582,x95583,x95584)),x95582))+~P1(f319(f319(f321(x95584),x95585),f319(f319(f102(f932(x95584,a923)),x95583),x95582)))
% 28.77/28.53 [9559]~P1(f319(x95591,x95595))+P1(f319(x95591,f614(x95591,x95592,x95593,x95594)))+P1(f319(f319(f321(x95594),f602(x95591,x95592,x95593,x95594)),x95593))+~P1(f319(f319(f321(x95594),x95595),f319(f319(f102(f932(x95594,a923)),x95593),x95592)))
% 28.77/28.53 [9563]P1(f319(x95631,x95632))+~P1(f319(x95631,f592(x95631,x95633,x95634,x95635)))+~P1(f319(x95631,f579(x95631,x95633,x95634,x95635)))+~P1(f319(f319(f321(x95635),x95632),f319(f319(f102(f932(x95635,a923)),x95634),x95633)))
% 28.77/28.53 [9567]~P39(x95671,x95674)+~P1(f319(f319(f321(f931(x95671,x95671)),f319(f319(f244(x95671,x95671),x95672),x95675)),x95674))+P1(f319(f319(f321(f931(x95671,x95671)),f319(f319(f244(x95671,x95671),x95672),x95673)),x95674))+~P1(f319(f319(f321(f931(x95671,x95671)),f319(f319(f244(x95671,x95671),x95675),x95673)),x95674))
% 28.77/28.53 [9568]~P39(x95681,x95684)+~P1(f319(f319(f321(f931(x95681,x95681)),f319(f319(f244(x95681,x95681),x95682),x95685)),x95684))+P1(f319(f319(f321(f931(x95681,x95681)),f319(f319(f244(x95681,x95681),x95682),x95683)),x95684))+~P1(f319(f319(f321(f931(x95681,x95681)),f319(f319(f244(x95681,x95681),x95685),x95683)),x95684))
% 28.77/28.53 [9607]E(x96071,x96072)+~P1(f319(f319(f321(f931(x96073,x96073)),f319(f319(f244(x96073,x96073),x96071),x96072)),f299(x96073,x96075)))+P1(f319(f319(f321(x96073),x96071),x96074))+~P1(f319(f319(f226(f932(f931(x96073,x96073),a923)),x96075),f319(f319(f246(x96073,x96073),x96074),f319(f16(f932(x96073,a923),x96073),x96074))))
% 28.77/28.53 [9625]P1(f319(x96251,x96252))+~P1(f319(x96251,f579(x96251,x96254,x96255,x96253)))+P1(f319(f319(f321(x96253),f592(x96251,x96254,x96255,x96253)),x96254))+~P1(f319(f319(f321(x96253),x96252),f319(f319(f102(f932(x96253,a923)),x96255),x96254)))
% 28.77/28.53 [9626]P1(f319(x96261,x96262))+~P1(f319(x96261,f592(x96261,x96264,x96265,x96263)))+P1(f319(f319(f321(x96263),f579(x96261,x96264,x96265,x96263)),x96265))+~P1(f319(f319(f321(x96263),x96262),f319(f319(f102(f932(x96263,a923)),x96265),x96264)))
% 28.77/28.53 [9694]P1(f319(x96941,x96942))+P1(f319(f319(f321(x96943),f592(x96941,x96944,x96945,x96943)),x96944))+P1(f319(f319(f321(x96943),f579(x96941,x96944,x96945,x96943)),x96945))+~P1(f319(f319(f321(x96943),x96942),f319(f319(f102(f932(x96943,a923)),x96945),x96944)))
% 28.77/28.53 [9696]~P1(f319(x96962,x96965))+P1(f319(f319(f321(x96961),f614(x96962,x96963,x96964,x96961)),x96963))+P1(f319(f319(f321(x96961),f602(x96962,x96963,x96964,x96961)),x96964))+~P1(f319(f319(f321(x96961),x96965),f319(f319(f102(f932(x96961,a923)),x96964),x96963)))
% 28.77/28.53 [9847]~P9(x98471,x98475,x98474)+~P1(f319(f319(f321(x98471),x98473),x98475))+P1(f319(f319(f321(f931(x98471,x98471)),f319(f319(f244(x98471,x98471),x98472),x98473)),x98474))+~P1(f319(f319(f226(f932(x98471,a923)),f319(f277(x98471,x98471,x98474),f319(f319(f301(x98471),x98473),f180(f932(x98471,a923))))),f319(f277(x98471,x98471,x98474),f319(f319(f301(x98471),x98472),f180(f932(x98471,a923))))))
% 28.77/28.53 [9987]~P4(x99875)+~P6(x99875)+P1(f319(f319(f321(x99871),f887(x99872,x99873,x99874,x99871,x99875)),x99874))+~P1(f319(f319(f227(x99875),f319(f319(f34(x99871,x99875),x99874),x99873)),x99872))
% 28.77/28.53 [10022]~P91(x100225)+~P88(x100225)+P1(f319(f319(f321(x100221),f716(x100222,x100223,x100224,x100221,x100225)),f319(f164(x100221),x100224)))+P1(f319(f319(f226(x100225),f319(f157(x100225),f319(f319(f146(x100221,x100225),x100223),x100224))),f319(f157(x100225),f319(f319(f146(x100221,x100225),x100222),x100224))))
% 28.77/28.53 [10136]~P4(x101361)+~P6(x101361)+P1(f319(f319(f227(x101361),f319(x101362,f887(x101363,x101362,x101364,x101365,x101361))),x101363))+~P1(f319(f319(f227(x101361),f319(f319(f34(x101365,x101361),x101364),x101362)),x101363))
% 28.77/28.53 [10279]~P91(x102791)+~P88(x102791)+~P1(f319(f319(f226(x102791),f319(x102793,f716(x102795,x102793,x102794,x102792,x102791))),f319(x102795,f716(x102795,x102793,x102794,x102792,x102791))))+P1(f319(f319(f226(x102791),f319(f157(x102791),f319(f319(f146(x102792,x102791),x102793),x102794))),f319(f157(x102791),f319(f319(f146(x102792,x102791),x102795),x102794))))
% 28.77/28.53 [8902]~P79(x89021)+~P1(f319(f55(x89024),x89025))+~P1(f319(f319(f321(x89024),x89023),x89025))+E(f319(f319(f74(x89021),f319(x89022,x89023)),f319(f319(f6(x89024,x89021),x89022),f319(f319(f23(f932(x89024,a923)),x89025),f319(f319(f301(x89024),x89023),f180(f932(x89024,a923)))))),f319(f319(f6(x89024,x89021),x89022),x89025))
% 28.77/28.53 [8903]~P79(x89031)+~P1(f319(f55(x89034),x89035))+~P1(f319(f319(f321(x89034),x89033),x89035))+E(f319(f319(f74(x89031),f319(x89032,x89033)),f319(f319(f6(x89034,x89031),x89032),f319(f319(f23(f932(x89034,a923)),x89035),f319(f319(f301(x89034),x89033),f180(f932(x89034,a923)))))),f319(f319(f6(x89034,x89031),x89032),x89035))
% 28.77/28.53 [8904]~P78(x89041)+~P1(f319(f55(x89044),x89045))+~P1(f319(f319(f321(x89044),x89043),x89045))+E(f319(f319(f75(x89041),f319(x89042,x89043)),f319(f319(f9(x89044,x89041),x89042),f319(f319(f23(f932(x89044,a923)),x89045),f319(f319(f301(x89044),x89043),f180(f932(x89044,a923)))))),f319(f319(f9(x89044,x89041),x89042),x89045))
% 28.77/28.53 [8964]~P20(x89641,x89644,x89645)+~P1(f319(f55(x89641),x89642))+E(f319(f319(f23(f932(x89641,a923)),x89642),f319(f319(f301(x89641),x89643),f180(f932(x89641,a923)))),f180(f932(x89641,a923)))+E(f319(f319(x89644,x89643),f319(x89645,f319(f319(f23(f932(x89641,a923)),x89642),f319(f319(f301(x89641),x89643),f180(f932(x89641,a923)))))),f319(x89645,f319(f319(f301(x89641),x89643),x89642)))
% 28.77/28.53 [9347]~P78(x93471)+~P1(f319(f55(x93472),x93475))+~P1(f319(f55(x93472),x93474))+E(f319(f319(f75(x93471),f319(f319(f9(x93472,x93471),x93473),f319(f319(f102(f932(x93472,a923)),x93474),x93475))),f319(f319(f9(x93472,x93471),x93473),f319(f319(f93(f932(x93472,a923)),x93474),x93475))),f319(f319(f75(x93471),f319(f319(f9(x93472,x93471),x93473),x93474)),f319(f319(f9(x93472,x93471),x93473),x93475)))
% 28.77/28.53 [9348]~P78(x93481)+~P1(f319(f55(x93482),x93485))+~P1(f319(f55(x93482),x93484))+E(f319(f319(f75(x93481),f319(f319(f9(x93482,x93481),x93483),f319(f319(f102(f932(x93482,a923)),x93484),x93485))),f319(f319(f9(x93482,x93481),x93483),f319(f319(f93(f932(x93482,a923)),x93484),x93485))),f319(f319(f75(x93481),f319(f319(f9(x93482,x93481),x93483),x93484)),f319(f319(f9(x93482,x93481),x93483),x93485)))
% 28.77/28.53 [9349]~P79(x93491)+~P1(f319(f55(x93492),x93495))+~P1(f319(f55(x93492),x93494))+E(f319(f319(f74(x93491),f319(f319(f6(x93492,x93491),x93493),f319(f319(f102(f932(x93492,a923)),x93494),x93495))),f319(f319(f6(x93492,x93491),x93493),f319(f319(f93(f932(x93492,a923)),x93494),x93495))),f319(f319(f74(x93491),f319(f319(f6(x93492,x93491),x93493),x93494)),f319(f319(f6(x93492,x93491),x93493),x93495)))
% 28.77/28.53 [9490]~P70(x94901)+~P1(f319(f55(x94902),x94905))+~P1(f319(f55(x94902),x94904))+E(f319(f319(f23(x94901),f319(f319(f74(x94901),f319(f319(f6(x94902,x94901),x94903),x94904)),f319(f319(f6(x94902,x94901),x94903),x94905))),f319(f319(f6(x94902,x94901),x94903),f319(f319(f93(f932(x94902,a923)),x94904),x94905))),f319(f319(f6(x94902,x94901),x94903),f319(f319(f102(f932(x94902,a923)),x94904),x94905)))
% 28.77/28.53 [9707]~P26(x97071,x97072,x97073,x97075)+~P26(x97071,x97072,x97073,x97074)+P26(x97071,x97072,x97073,f319(f319(f102(f932(x97071,a923)),x97074),x97075))+~E(f319(f319(f93(f932(x97072,a923)),f319(f302(x97071,x97072,x97073),f319(f319(f23(f932(x97071,a923)),x97074),x97075))),f319(f302(x97071,x97072,x97073),f319(f319(f23(f932(x97071,a923)),x97075),x97074))),f180(f932(x97072,a923)))
% 28.77/28.53 [9822]E(x98221,f2(a1))+~P1(f319(f319(f227(a1),f2(a1)),x98223))+~P1(f319(f43(x98222,x98221),f319(f319(f244(a1,a1),x98224),x98225)))+P1(f319(f43(x98222,f319(f319(f75(a1),x98221),x98223)),f319(f319(f244(a1,a1),f319(f319(f30(a1),x98224),x98223)),f319(f319(f74(a1),f319(f319(f75(a1),x98221),f39(a1,x98224,x98223))),x98225))))
% 28.77/28.53 [9830]~P1(f319(f319(f227(a925),f2(a925)),x98303))+~P1(f319(f319(f227(a925),f2(a925)),x98302))+~P1(f319(f42(x98301,x98302),f319(f319(f244(a925,a925),x98304),x98305)))+P1(f319(f42(x98301,f319(f319(f75(a925),x98302),x98303)),f319(f319(f244(a925,a925),f319(f319(f30(a925),x98304),x98303)),f319(f319(f74(a925),f319(f319(f75(a925),x98302),f39(a925,x98304,x98303))),x98305))))
% 28.77/28.53 [9880]~P78(x98801)+~P1(f319(f55(x98802),x98805))+~P1(f319(f55(x98802),x98804))+E(f319(f319(f75(x98801),f319(f319(f319(f59(x98801,x98802,f75(x98801)),x98803),f72(x98801)),f319(f319(f102(f932(x98802,a923)),x98804),x98805))),f319(f319(f319(f59(x98801,x98802,f75(x98801)),x98803),f72(x98801)),f319(f319(f93(f932(x98802,a923)),x98804),x98805))),f319(f319(f75(x98801),f319(f319(f319(f59(x98801,x98802,f75(x98801)),x98803),f72(x98801)),x98804)),f319(f319(f319(f59(x98801,x98802,f75(x98801)),x98803),f72(x98801)),x98805)))
% 28.77/28.53 [9882]~E(f319(f319(f167(x98821),x98825),x98822),f319(f319(f167(x98821),x98825),x98823))+P1(f319(f319(f321(f931(f926(x98821),f926(x98821))),f319(f319(f244(f926(x98821),f926(x98821)),x98822),x98823)),f139(x98821,x98824)))+~P1(f319(f319(f227(a925),x98825),f319(f319(f224(a925),f319(f181(f926(x98821)),x98822)),f319(f181(f926(x98821)),x98823))))+~P1(f319(f319(f321(f931(x98821,x98821)),f319(f319(f244(x98821,x98821),f319(f319(f156(x98821),x98822),x98825)),f319(f319(f156(x98821),x98823),x98825))),x98824))
% 28.77/28.53 [10011]~P91(x100115)+~P149(x100115)+P1(f319(f319(f321(x100111),f424(x100112,x100113,x100114,x100111,x100115)),x100114))+P1(f319(f319(f226(x100115),f319(f319(f6(x100111,x100115),x100113),x100114)),f319(f319(f75(x100115),f319(f92(x100115),f319(f29(x100111),x100114))),x100112)))
% 28.77/28.53 [10195]~P91(x101951)+~P149(x101951)+~P1(f319(f319(f226(x101951),f319(x101953,f424(x101955,x101953,x101954,x101952,x101951))),x101955))+P1(f319(f319(f226(x101951),f319(f319(f6(x101952,x101951),x101953),x101954)),f319(f319(f75(x101951),f319(f92(x101951),f319(f29(x101952),x101954))),x101955)))
% 28.77/28.53 [8932]E(f319(f319(f126(x89321),x89322),x89323),f319(f319(f126(x89321),x89324),x89325))+~E(f319(f319(f167(x89321),f319(f181(f926(x89321)),x89322)),x89324),x89322)+~E(f319(f319(f126(x89321),f319(f319(f130(x89321),f319(f181(f926(x89321)),x89322)),x89324)),x89325),x89323)+P1(f319(f319(f226(a925),f319(f181(f926(x89321)),x89324)),f319(f181(f926(x89321)),x89322)))
% 28.77/28.53 [9063]E(f319(f319(f126(x90631),x90632),x90633),f319(f319(f126(x90631),x90634),x90635))+~E(f319(f319(f167(x90631),f319(f181(f926(x90631)),x90632)),x90634),x90632)+~E(x90633,f319(f319(f126(x90631),f319(f319(f130(x90631),f319(f181(f926(x90631)),x90632)),x90634)),x90635))+~P1(f319(f319(f226(a925),f319(f181(f926(x90631)),x90632)),f319(f181(f926(x90631)),x90634)))
% 28.77/28.53 [10344]~P1(f319(x103445,x103444))+~P1(f319(f55(x103442),f319(f254(x103442),x103445)))+P1(f319(f55(x103441),f319(f254(x103441),f319(f319(f7(x103441,x103442,a923),x103443),x103444))))+~P1(f319(f55(x103441),f319(f254(x103441),f319(f319(f8(f932(x103442,a923),a923,x103441),f81(x103442)),f319(f319(f8(f932(x103442,a923),f932(x103442,a923),x103441),f319(f18(x103442,a923,a923),f319(f319(f8(a923,f932(a923,a923),x103442),a317),x103445))),x103443)))))
% 28.77/28.53 [10416]~P1(f319(f55(x104162),x104165))+~P1(f319(f319(f321(x104162),x104164),x104165))+P1(f319(f55(x104161),f319(f254(x104161),f319(f319(f7(x104161,x104162,a923),x104163),x104164))))+~P1(f319(f55(x104161),f319(f254(x104161),f319(f319(f8(f932(x104162,a923),a923,x104161),f81(x104162)),f319(f319(f8(f932(x104162,a923),f932(x104162,a923),x104161),f319(f18(x104162,a923,a923),f319(f319(f8(a923,f932(a923,a923),x104162),a317),f319(f319(f7(x104162,f932(x104162,a923),a923),f321(x104162)),x104165)))),x104163)))))
% 28.77/28.53 [8715]~P21(x87155,x87151,x87156,x87152)+E(f319(f66(x87151,x87151,x87151,f319(x87152,x87153)),f319(x87152,x87154)),f319(f66(x87151,x87151,x87151,f319(x87152,x87154)),f319(x87152,x87153)))+~P1(f319(f55(x87155),x87154))+~P1(f319(f55(x87155),x87153))
% 28.77/28.53 [8102]~P26(x81021,x81022,x81024,x81023)+~E(f319(x81024,x81026),x81025)+E(f319(f71(x81021,x81022,x81023,x81024),x81025),x81026)+~P1(f319(f319(f321(x81021),x81026),x81023))
% 28.77/28.53 [8103]~P26(x81031,x81032,x81034,x81033)+~E(f319(x81034,x81036),x81035)+E(f319(f85(x81031,x81032,x81033,x81034),x81035),x81036)+~P1(f319(f319(f321(x81031),x81036),x81033))
% 28.77/28.53 [8299]~P22(x82996,x82991,x82994,x82992)+E(f319(f66(x82991,x82991,x82991,f319(x82992,x82993)),f319(x82994,x82995)),f319(x82992,x82993))+~P1(f319(f55(x82996),x82993))+~P1(f319(f319(f321(x82996),x82995),x82993))
% 28.77/28.53 [9443]E(x94431,x94432)+~E(f319(f85(x94433,x94434,x94435,x94436),x94431),f319(f85(x94433,x94434,x94435,x94436),x94432))+~P1(f319(f319(f321(x94434),x94432),f319(f302(x94433,x94434,x94436),x94435)))+~P1(f319(f319(f321(x94434),x94431),f319(f302(x94433,x94434,x94436),x94435)))
% 28.77/28.53 [9541]~P21(x95413,x95411,x95416,x95412)+E(f319(f66(x95411,x95411,x95411,f319(x95412,f319(f319(f23(f932(x95413,a923)),x95414),f319(f319(f301(x95413),x95415),f180(f932(x95413,a923)))))),f319(x95416,x95415)),f319(x95412,x95414))+~P1(f319(f55(x95413),x95414))+~P1(f319(f319(f321(x95413),x95415),x95414))
% 28.77/28.53 [7188]~P66(x71881)+~E(f39(x71881,x71883,x71884),f39(x71881,x71886,x71884))+~E(f39(x71881,x71882,x71884),f39(x71881,x71885,x71884))+E(f39(x71881,f319(f319(f23(x71881),x71882),x71883),x71884),f39(x71881,f319(f319(f23(x71881),x71885),x71886),x71884))
% 28.77/28.53 [7189]~P65(x71891)+~E(f39(x71891,x71893,x71894),f39(x71891,x71896,x71894))+~E(f39(x71891,x71892,x71894),f39(x71891,x71895,x71894))+E(f39(x71891,f319(f319(f75(x71891),x71892),x71893),x71894),f39(x71891,f319(f319(f75(x71891),x71895),x71896),x71894))
% 28.77/28.53 [7190]~P65(x71901)+~E(f39(x71901,x71903,x71904),f39(x71901,x71906,x71904))+~E(f39(x71901,x71902,x71904),f39(x71901,x71905,x71904))+E(f39(x71901,f319(f319(f74(x71901),x71902),x71903),x71904),f39(x71901,f319(f319(f74(x71901),x71905),x71906),x71904))
% 28.77/28.53 [7996]~P18(x79961,x79962,x79963)+~P1(f319(f55(x79961),x79966))+E(f319(f319(f58(x79961,x79962,x79963),x79964),f319(f319(f301(x79961),x79965),x79966)),f319(f319(f58(x79961,x79962,x79963),f319(f319(x79963,x79965),x79964)),x79966))+P1(f319(f319(f321(x79961),x79965),x79966))
% 28.77/28.53 [8061]~P6(x80611)+P1(f319(f319(f226(x80611),x80612),f319(x80613,x80614)))+~P1(f319(f319(f321(x80615),x80614),x80616))+~P1(f319(f319(f226(x80611),x80612),f319(f319(f34(x80615,x80611),x80616),x80613)))
% 28.77/28.53 [8221]~P18(x82211,x82212,x82213)+~P1(f319(f55(x82211),x82216))+E(f319(f319(f58(x82211,x82212,x82213),x82214),f319(f319(f301(x82211),x82215),x82216)),f319(f319(x82213,x82215),f319(f319(f58(x82211,x82212,x82213),x82214),x82216)))+P1(f319(f319(f321(x82211),x82215),x82216))
% 28.77/28.53 [8317]~P4(x83173)+~P1(f319(x83172,x83175))+~P14(x83173,f319(f319(f146(x83171,x83173),x83174),x83176))+E(f319(f128(x83171,x83172),f319(f319(f140(x83171,x83173,x83174),x83175),x83176)),f319(f319(f140(x83171,x83173,x83174),x83175),f319(f128(x83171,x83172),x83176)))
% 28.77/28.53 [8340]E(x83401,x83402)+E(x83403,f2(a1))+~P1(f319(f43(x83404,x83403),f319(f319(f244(a1,a1),x83405),x83402)))+~P1(f319(f43(x83404,x83403),f319(f319(f244(a1,a1),x83406),x83401)))
% 28.77/28.53 [8341]E(x83411,x83412)+E(x83413,f2(a1))+~P1(f319(f43(x83414,x83413),f319(f319(f244(a1,a1),x83412),x83415)))+~P1(f319(f43(x83414,x83413),f319(f319(f244(a1,a1),x83411),x83416)))
% 28.77/28.53 [8362]~P21(x83622,x83625,x83626,x83621)+~P1(f319(f55(x83622),x83624))+E(f319(x83621,f319(f319(f301(x83622),x83623),x83624)),f319(f66(x83625,x83625,x83625,f319(x83621,x83624)),f319(x83626,x83623)))+P1(f319(f319(f321(x83622),x83623),x83624))
% 28.77/28.53 [8587]~P22(x85875,x85871,x85876,x85872)+E(f319(f66(x85871,x85871,x85871,f319(x85872,x85873)),f319(x85872,x85874)),f319(x85872,x85873))+~P1(f319(f55(x85875),x85873))+~P1(f319(f319(f226(f932(x85875,a923)),x85874),x85873))
% 28.77/28.53 [9750]~P26(x97501,x97502,x97504,x97503)+~P1(f319(f319(f321(x97502),x97505),f319(f302(x97501,x97502,x97504),x97503)))+P1(f319(f319(f321(x97501),f319(f71(x97501,x97502,x97503,x97504),x97505)),x97506))+~P1(f319(f319(f226(f932(x97501,a923)),x97503),x97506))
% 28.77/28.53 [10147]~P79(x101472)+~E(f413(x101471,x101473,x101475,x101476,x101474,x101472),f414(x101471,x101473,x101475,x101476,x101474,x101472))+~P1(f319(f55(x101474),x101476))+E(f319(f319(f6(x101471,x101472),x101473),f319(f302(x101474,x101471,x101475),x101476)),f319(f319(f6(x101474,x101472),f319(f66(x101471,x101472,x101474,x101473),x101475)),x101476))
% 28.77/28.53 [10175]~P79(x101756)+E(f319(x101751,f413(x101752,x101753,x101751,x101754,x101755,x101756)),f319(x101751,f414(x101752,x101753,x101751,x101754,x101755,x101756)))+E(f319(f319(f6(x101752,x101756),x101753),f319(f302(x101755,x101752,x101751),x101754)),f319(f319(f6(x101755,x101756),f319(f66(x101752,x101756,x101755,x101753),x101751)),x101754))+~P1(f319(f55(x101755),x101754))
% 28.77/28.53 [10228]~P79(x102282)+~E(f319(x102283,f319(x102285,f414(x102281,x102283,x102285,x102286,x102284,x102282))),f2(x102282))+~P1(f319(f55(x102284),x102286))+E(f319(f319(f6(x102281,x102282),x102283),f319(f302(x102284,x102281,x102285),x102286)),f319(f319(f6(x102284,x102282),f319(f66(x102281,x102282,x102284,x102283),x102285)),x102286))
% 28.77/28.53 [10288]~P79(x102882)+~P1(f319(f55(x102884),x102886))+E(f319(f319(f6(x102881,x102882),x102883),f319(f302(x102884,x102881,x102885),x102886)),f319(f319(f6(x102884,x102882),f319(f66(x102881,x102882,x102884,x102883),x102885)),x102886))+P1(f319(f319(f321(x102884),f414(x102881,x102883,x102885,x102886,x102884,x102882)),x102886))
% 28.77/28.53 [10289]~P79(x102892)+~P1(f319(f55(x102894),x102896))+E(f319(f319(f6(x102891,x102892),x102893),f319(f302(x102894,x102891,x102895),x102896)),f319(f319(f6(x102894,x102892),f319(f66(x102891,x102892,x102894,x102893),x102895)),x102896))+P1(f319(f319(f321(x102894),f413(x102891,x102893,x102895,x102896,x102894,x102892)),x102896))
% 28.77/28.53 [10369]~P41(f932(f931(x103694,x103695),a923),f932(f931(x103694,x103695),a923),x103696)+~P1(f319(f319(x103691,f548(x103691,x103696,x103693,x103692,x103695,x103694)),f553(x103691,x103696,x103693,x103692,x103695,x103694)))+P1(f319(f319(x103691,x103692),x103693))+~P1(f319(f319(f321(f931(x103694,x103695)),f319(f319(f244(x103694,x103695),x103692),x103693)),f87(f932(f931(x103694,x103695),a923),x103696)))
% 28.77/28.53 [10415]~P78(x104151)+~P1(f319(f55(x104152),x104156))+E(f319(f319(f319(f59(x104151,x104152,f75(x104151)),f319(f319(f18(x104152,f932(x104153,a923),x104151),f319(f319(f7(x104152,x104151,f932(f932(x104153,a923),x104151)),f319(f319(f8(f932(x104153,x104151),f932(x104151,f932(f932(x104153,a923),x104151)),x104152),f59(x104151,x104153,f75(x104151))),x104154)),f72(x104151))),x104155)),f72(x104151)),x104156),f319(f319(f319(f59(x104151,f931(x104152,x104153),f75(x104151)),f319(f249(x104152,x104153,x104151),x104154)),f72(x104151)),f319(f319(f246(x104152,x104153),x104156),x104155)))+P1(f319(f319(f321(x104152),f580(x104154,x104155,x104153,x104156,x104152,x104151)),x104156))
% 28.77/28.53 [10437]~P78(x104371)+~P1(f319(f55(x104372),x104376))+E(f319(f319(f319(f59(x104371,x104372,f75(x104371)),f319(f319(f18(x104372,f932(x104373,a923),x104371),f319(f319(f7(x104372,x104371,f932(f932(x104373,a923),x104371)),f319(f319(f8(f932(x104373,x104371),f932(x104371,f932(f932(x104373,a923),x104371)),x104372),f59(x104371,x104373,f75(x104371))),x104374)),f72(x104371))),x104375)),f72(x104371)),x104376),f319(f319(f319(f59(x104371,f931(x104372,x104373),f75(x104371)),f319(f249(x104372,x104373,x104371),x104374)),f72(x104371)),f319(f319(f246(x104372,x104373),x104376),x104375)))+~P1(f319(f55(x104373),f319(x104375,f580(x104374,x104375,x104373,x104376,x104372,x104371))))
% 28.77/28.53 [8496]~P22(x84962,x84965,x84966,x84961)+~P1(f319(f55(x84962),x84964))+~P1(f319(f55(x84962),x84963))+E(f319(x84961,f319(f319(f102(f932(x84962,a923)),x84963),x84964)),f319(f66(x84965,x84965,x84965,f319(x84961,x84963)),f319(x84961,x84964)))
% 28.77/28.53 [8716]~P6(x87161)+P1(f319(f319(f226(x87161),f319(x87162,x87163)),x87164))+~P1(f319(f319(f321(x87165),x87163),x87166))+~P1(f319(f319(f226(x87161),f319(f319(f33(x87165,x87161),x87166),x87162)),x87164))
% 28.77/28.53 [9152]~P26(x91522,x91521,x91523,x91526)+E(f319(f319(f93(f932(x91521,a923)),f319(f302(x91522,x91521,x91523),x91524)),f319(f302(x91522,x91521,x91523),x91525)),f319(f302(x91522,x91521,x91523),f319(f319(f93(f932(x91522,a923)),x91524),x91525)))+~P1(f319(f319(f226(f932(x91522,a923)),x91525),x91526))+~P1(f319(f319(f226(f932(x91522,a923)),x91524),x91526))
% 28.77/28.53 [9153]~P26(x91532,x91531,x91533,x91536)+E(f319(f319(f23(f932(x91531,a923)),f319(f302(x91532,x91531,x91533),x91534)),f319(f302(x91532,x91531,x91533),x91535)),f319(f302(x91532,x91531,x91533),f319(f319(f23(f932(x91532,a923)),x91534),x91535)))+~P1(f319(f319(f226(f932(x91532,a923)),x91535),x91536))+~P1(f319(f319(f226(f932(x91532,a923)),x91534),x91536))
% 28.77/28.53 [9415]E(x94151,x94152)+~P59(x94153,x94154,x94155)+~P1(f319(f319(f321(f931(x94153,x94154)),f319(f319(f244(x94153,x94154),x94156),x94152)),x94155))+~P1(f319(f319(f321(f931(x94153,x94154)),f319(f319(f244(x94153,x94154),x94156),x94151)),x94155))
% 28.77/28.53 [9416]E(x94161,x94162)+~P59(x94163,x94164,x94165)+~P1(f319(f319(f321(f931(x94163,x94164)),f319(f319(f244(x94163,x94164),x94166),x94162)),x94165))+~P1(f319(f319(f321(f931(x94163,x94164)),f319(f319(f244(x94163,x94164),x94166),x94161)),x94165))
% 28.77/28.53 [10223]~P76(x102231)+~E(f319(x102233,f527(x102234,x102236,x102233,x102235,x102232,x102231)),f319(x102236,f527(x102234,x102236,x102233,x102235,x102232,x102231)))+~P1(f319(f55(x102232),x102235))+E(f319(f319(f319(f59(x102231,x102232,f75(x102231)),x102233),x102234),x102235),f319(f319(f319(f59(x102231,x102232,f75(x102231)),x102236),x102234),x102235))
% 28.77/28.53 [10285]~P76(x102851)+~P1(f319(f55(x102852),x102855))+E(f319(f319(f319(f59(x102851,x102852,f75(x102851)),x102853),x102854),x102855),f319(f319(f319(f59(x102851,x102852,f75(x102851)),x102856),x102854),x102855))+P1(f319(f319(f321(x102852),f527(x102854,x102853,x102856,x102855,x102852,x102851)),x102855))
% 28.77/28.53 [8946]~P76(x89461)+~P1(f319(f55(x89462),x89466))+P1(f319(f319(f321(x89462),x89465),x89466))+E(f319(f319(f319(f59(x89461,x89462,f75(x89461)),x89463),x89464),f319(f319(f301(x89462),x89465),x89466)),f319(f319(f75(x89461),f319(x89463,x89465)),f319(f319(f319(f59(x89461,x89462,f75(x89461)),x89463),x89464),x89466)))
% 28.77/28.53 [9000]~P9(x90001,x90006,x90003)+~P12(x90001,f932(x90002,a923),x90003,x90005)+~P1(f319(f319(f321(x90001),x90004),x90006))+E(f319(f319(f33(x90001,f932(x90002,a923)),f319(f277(x90001,x90001,x90003),f319(f319(f301(x90001),x90004),f180(f932(x90001,a923))))),x90005),f319(x90005,x90004))
% 28.77/28.53 [9127]~P18(x91273,x91274,x91271)+~P1(f319(f55(x91273),x91276))+~P1(f319(f319(f321(x91273),x91272),x91276))+E(f319(f319(x91271,x91272),f319(f319(f58(x91273,x91274,x91271),x91275),f319(f319(f23(f932(x91273,a923)),x91276),f319(f319(f301(x91273),x91272),f180(f932(x91273,a923)))))),f319(f319(f58(x91273,x91274,x91271),x91275),x91276))
% 28.77/28.53 [9427]~P21(x94273,x94271,x94276,x94272)+~P1(f319(f55(x94273),x94275))+~P1(f319(f55(x94273),x94274))+E(f319(f66(x94271,x94271,x94271,f319(x94272,f319(f319(f102(f932(x94273,a923)),x94274),x94275))),f319(x94272,f319(f319(f93(f932(x94273,a923)),x94274),x94275))),f319(f66(x94271,x94271,x94271,f319(x94272,x94274)),f319(x94272,x94275)))
% 28.77/28.53 [10447]~P41(f932(f931(x104474,x104475),a923),f932(f931(x104474,x104475),a923),x104476)+P1(f319(f319(x104471,x104472),x104473))+~P1(f319(f319(f321(f931(x104474,x104475)),f319(f319(f244(x104474,x104475),x104472),x104473)),f87(f932(f931(x104474,x104475),a923),x104476)))+P1(f319(f319(f321(f931(x104474,x104475)),f319(f319(f244(x104474,x104475),f548(x104471,x104476,x104473,x104472,x104475,x104474)),f553(x104471,x104476,x104473,x104472,x104475,x104474))),f319(x104476,f319(f319(f93(f932(f931(x104474,x104475),a923)),f87(f932(f931(x104474,x104475),a923),x104476)),f319(f254(f931(x104474,x104475)),f319(f249(x104474,x104475,a923),x104471))))))
% 28.77/28.53 [9775]~E(x97753,f319(f319(f151(x97751,x97752),x97755),x97756))+P1(f319(f319(f321(f931(f926(x97751),f926(x97751))),f319(f319(f244(f926(x97751),f926(x97751)),x97752),x97753)),f149(x97751,x97754)))+~P1(f319(f319(f227(a925),x97755),f319(f181(f926(x97751)),x97752)))+~P1(f319(f319(f321(f931(x97751,x97751)),f319(f319(f244(x97751,x97751),f319(f319(f156(x97751),x97752),x97755)),x97756)),x97754))
% 28.77/28.53 [10302]~P79(x103022)+~P1(f319(f55(x103021),x103026))+P1(f319(f319(f321(x103021),f581(x103024,x103025,x103023,x103026,x103021,x103022)),x103026))+E(f319(f319(f6(x103021,x103022),f319(f319(f18(x103021,f932(x103023,a923),x103022),f319(f319(f8(f932(x103023,x103022),f932(f932(x103023,a923),x103022),x103021),f6(x103023,x103022)),x103024)),x103025)),x103026),f319(f319(f6(f931(x103021,x103023),x103022),f319(f249(x103021,x103023,x103022),x103024)),f319(f319(f246(x103021,x103023),x103026),x103025)))
% 28.77/28.53 [10303]~P78(x103032)+~P1(f319(f55(x103031),x103036))+P1(f319(f319(f321(x103031),f582(x103034,x103035,x103033,x103036,x103031,x103032)),x103036))+E(f319(f319(f9(x103031,x103032),f319(f319(f18(x103031,f932(x103033,a923),x103032),f319(f319(f8(f932(x103033,x103032),f932(f932(x103033,a923),x103032),x103031),f9(x103033,x103032)),x103034)),x103035)),x103036),f319(f319(f9(f931(x103031,x103033),x103032),f319(f249(x103031,x103033,x103032),x103034)),f319(f319(f246(x103031,x103033),x103036),x103035)))
% 28.77/28.53 [10342]~P79(x103422)+~P1(f319(f55(x103421),x103426))+~P1(f319(f55(x103423),f319(x103425,f581(x103424,x103425,x103423,x103426,x103421,x103422))))+E(f319(f319(f6(x103421,x103422),f319(f319(f18(x103421,f932(x103423,a923),x103422),f319(f319(f8(f932(x103423,x103422),f932(f932(x103423,a923),x103422),x103421),f6(x103423,x103422)),x103424)),x103425)),x103426),f319(f319(f6(f931(x103421,x103423),x103422),f319(f249(x103421,x103423,x103422),x103424)),f319(f319(f246(x103421,x103423),x103426),x103425)))
% 28.77/28.53 [10343]~P78(x103432)+~P1(f319(f55(x103431),x103436))+~P1(f319(f55(x103433),f319(x103435,f582(x103434,x103435,x103433,x103436,x103431,x103432))))+E(f319(f319(f9(x103431,x103432),f319(f319(f18(x103431,f932(x103433,a923),x103432),f319(f319(f8(f932(x103433,x103432),f932(f932(x103433,a923),x103432),x103431),f9(x103433,x103432)),x103434)),x103435)),x103436),f319(f319(f9(f931(x103431,x103433),x103432),f319(f249(x103431,x103433,x103432),x103434)),f319(f319(f246(x103431,x103433),x103436),x103435)))
% 28.77/28.53 [10325]~P78(x103252)+~P1(f319(f55(x103251),x103256))+P1(f319(f319(f321(x103251),x103253),x103256))+E(f319(f319(f9(x103251,x103252),f319(f319(f7(x103251,x103252,x103252),f319(f319(f18(x103251,x103252,f932(x103252,x103252)),f319(f319(f8(a923,f932(x103252,f932(x103252,x103252)),x103251),f86(x103252)),f319(f319(f7(x103251,x103251,a923),a316),x103253))),x103254)),x103255)),x103256),f319(f319(f236(x103252),x103255),f319(f29(x103251),x103256)))
% 28.77/28.53 [10328]~P78(x103282)+~P1(f319(f55(x103281),x103286))+~P1(f319(f319(f321(x103281),x103283),x103286))+E(f319(f319(f9(x103281,x103282),f319(f319(f7(x103281,x103282,x103282),f319(f319(f18(x103281,x103282,f932(x103282,x103282)),f319(f319(f8(a923,f932(x103282,f932(x103282,x103282)),x103281),f86(x103282)),f319(f319(f7(x103281,x103281,a923),a316),x103283))),x103284)),x103285)),x103286),f319(f319(f75(x103282),f319(x103284,x103283)),f319(f319(f236(x103282),x103285),f319(f319(f23(a925),f319(f29(x103281),x103286)),f72(a925)))))
% 28.77/28.53 [10405]~P1(f319(f55(x104051),x104055))+~P1(f319(f55(x104052),x104053))+P1(f319(f319(f321(x104052),f459(x104056,x104054,x104053,x104052,x104055,x104051)),x104053))+E(f319(f319(f6(x104051,a925),f319(f319(f8(f932(x104052,a923),a925,x104051),f29(x104052)),f319(f319(f8(f932(x104052,a923),f932(x104052,a923),x104051),f254(x104052)),f319(f319(f8(f932(x104052,a923),f932(x104052,a923),x104051),f319(f18(x104052,a923,a923),f319(f319(f8(a923,f932(a923,a923),x104052),a317),f319(f319(f7(x104052,f932(x104052,a923),a923),f321(x104052)),x104053)))),x104054)))),x104055),f319(f319(f75(a925),x104056),f319(f29(x104052),x104053)))
% 28.77/28.53 [10406]~P1(f319(f55(x104061),x104065))+~P1(f319(f55(x104062),x104063))+P1(f319(f319(f321(x104062),f464(x104066,x104064,x104063,x104062,x104065,x104061)),x104063))+E(f319(f319(f6(x104061,a925),f319(f319(f8(f932(x104062,a923),a925,x104061),f29(x104062)),f319(f319(f8(f932(x104062,a923),f932(x104062,a923),x104061),f254(x104062)),f319(f319(f8(f932(x104062,a923),f932(x104062,a923),x104061),f319(f18(x104062,a923,a923),f319(f319(f8(a923,f932(a923,a923),x104062),a317),f319(f319(f7(x104062,f932(x104062,a923),a923),f321(x104062)),x104063)))),x104064)))),x104065),f319(f319(f6(x104062,a925),x104066),x104063))
% 28.77/28.53 [10451]~P1(f319(f55(x104512),x104513))+~P1(f319(f55(x104511),x104515))+~E(f319(f29(x104511),f319(f254(x104511),f319(f319(f18(x104511,a923,a923),f319(f319(f8(a923,f932(a923,a923),x104511),a317),f319(f319(f7(x104511,f932(x104511,a923),a923),f321(x104511)),x104515))),f319(f319(f7(x104511,x104512,a923),x104514),f459(x104516,x104514,x104513,x104512,x104515,x104511))))),x104516)+E(f319(f319(f6(x104511,a925),f319(f319(f8(f932(x104512,a923),a925,x104511),f29(x104512)),f319(f319(f8(f932(x104512,a923),f932(x104512,a923),x104511),f254(x104512)),f319(f319(f8(f932(x104512,a923),f932(x104512,a923),x104511),f319(f18(x104512,a923,a923),f319(f319(f8(a923,f932(a923,a923),x104512),a317),f319(f319(f7(x104512,f932(x104512,a923),a923),f321(x104512)),x104513)))),x104514)))),x104515),f319(f319(f75(a925),x104516),f319(f29(x104512),x104513)))
% 28.77/28.53 [10453]~P1(f319(f55(x104532),x104533))+~P1(f319(f55(x104531),x104535))+~E(f319(f29(x104531),f319(f254(x104531),f319(f319(f18(x104531,a923,a923),f319(f319(f8(a923,f932(a923,a923),x104531),a317),f319(f319(f7(x104531,f932(x104531,a923),a923),f321(x104531)),x104535))),f319(f319(f7(x104531,x104532,a923),x104534),f464(x104536,x104534,x104533,x104532,x104535,x104531))))),f319(x104536,f464(x104536,x104534,x104533,x104532,x104535,x104531)))+E(f319(f319(f6(x104531,a925),f319(f319(f8(f932(x104532,a923),a925,x104531),f29(x104532)),f319(f319(f8(f932(x104532,a923),f932(x104532,a923),x104531),f254(x104532)),f319(f319(f8(f932(x104532,a923),f932(x104532,a923),x104531),f319(f18(x104532,a923,a923),f319(f319(f8(a923,f932(a923,a923),x104532),a317),f319(f319(f7(x104532,f932(x104532,a923),a923),f321(x104532)),x104533)))),x104534)))),x104535),f319(f319(f6(x104532,a925),x104536),x104533))
% 28.77/28.53 [10070]E(x100701,x100702)+~P18(x100703,x100704,x100705)+~P1(f319(f60(x100703,x100704,x100705,x100706,x100707),x100702))+~P1(f319(f60(x100703,x100704,x100705,x100706,x100707),x100701))
% 28.77/28.53 [9697]~P35(x96971,x96972,x96973,x96975,x96977)+~P35(x96971,x96972,x96973,x96974,x96976)+P35(x96971,x96972,x96973,f319(f319(f126(x96971),x96974),x96975),f319(f319(f126(x96972),x96976),x96977))+~E(f319(f181(f926(x96971)),x96974),f319(f181(f926(x96972)),x96976))
% 28.77/28.53 [9852]P1(f319(x98521,x98522))+~P1(f319(f319(f321(x98527),x98522),f319(x98526,x98524)))+~P1(f319(x98521,f353(x98521,x98526,x98525,x98523,x98527)))+~P1(f319(f319(f321(x98523),x98524),x98525))
% 28.77/28.53 [10316]~P18(x103167,x103166,x103161)+E(f319(f319(x103161,x103162),f653(x103162,x103163,x103164,x103165,x103161,x103166,x103167)),x103163)+~P1(f319(f60(x103167,x103166,x103161,x103165,x103164),x103163))+~P1(f319(f319(f321(x103167),x103162),x103164))
% 28.77/28.53 [10383]~P18(x103831,x103832,x103833)+~P1(f319(f60(x103831,x103832,x103833,x103834,x103835),x103837))+P1(f319(f60(x103831,x103832,x103833,x103834,f319(f319(f23(f932(x103831,a923)),x103835),f319(f319(f301(x103831),x103836),f180(f932(x103831,a923))))),f653(x103836,x103837,x103835,x103834,x103833,x103832,x103831)))+~P1(f319(f319(f321(x103831),x103836),x103835))
% 28.77/28.53 [9498]P27(x94981,x94982,x94983,x94984,x94985)+~P27(x94981,x94982,x94983,x94986,x94987)+~E(f319(f302(x94981,x94982,x94983),x94984),x94985)+~P1(f319(f319(f226(f932(x94981,a923)),x94984),x94986))
% 28.77/28.53 [9741]~P27(x97411,x97412,x97413,x97415,x97417)+~P27(x97411,x97412,x97413,x97414,x97416)+P27(x97411,x97412,x97413,f319(f319(f102(f932(x97411,a923)),x97414),x97415),f319(f319(f102(f932(x97412,a923)),x97416),x97417))+~E(f319(f319(f93(f932(x97412,a923)),x97416),x97417),f180(f932(x97412,a923)))
% 28.77/28.53 [9746]~P76(x97461)+~P26(x97465,x97462,x97466,x97467)+~P1(f319(f55(x97465),x97467))+E(f319(f319(f319(f59(x97461,x97462,f75(x97461)),x97463),x97464),f319(f302(x97465,x97462,x97466),x97467)),f319(f319(f319(f59(x97461,x97465,f75(x97461)),f319(f66(x97462,x97461,x97465,x97463),x97466)),x97464),x97467))
% 28.77/28.53 [9875]~E(f319(f319(f301(x98751),x98755),x98756),f319(f319(f301(x98751),x98752),x98753))+~P1(f319(f60(x98751,x98751,x98754,x98752,x98753),x98757))+P1(f319(f319(f321(x98751),x98752),x98753))+P1(f319(f56(x98751,x98754,f319(f319(f301(x98751),x98755),x98756)),x98757))
% 28.77/28.53 [9968]P1(f319(x99681,x99682))+~P1(f319(f319(f321(x99683),x99682),f319(x99684,x99687)))+~P1(f319(f319(f321(x99686),x99687),x99685))+P1(f319(f319(f321(x99683),f353(x99681,x99684,x99685,x99686,x99683)),f319(f319(f33(x99686,f932(x99683,a923)),x99685),x99684)))
% 28.77/28.53 [9988]~P26(x99882,x99881,x99885,x99884)+~P26(x99881,x99883,x99886,f319(f302(x99882,x99881,x99885),x99884))+E(f319(f319(f66(x99881,x99882,x99883,f71(x99882,x99881,x99884,x99885)),f71(x99881,x99883,f319(f302(x99882,x99881,x99885),x99884),x99886)),x99887),f319(f71(x99882,x99883,x99884,f319(f66(x99881,x99883,x99882,x99886),x99885)),x99887))+~P1(f319(f319(f321(x99883),x99887),f319(f302(x99881,x99883,x99886),f319(f302(x99882,x99881,x99885),x99884))))
% 28.77/28.53 [9989]~P26(x99892,x99891,x99895,x99894)+~P26(x99891,x99893,x99896,f319(f302(x99892,x99891,x99895),x99894))+E(f319(f319(f66(x99891,x99892,x99893,f85(x99892,x99891,x99894,x99895)),f85(x99891,x99893,f319(f302(x99892,x99891,x99895),x99894),x99896)),x99897),f319(f85(x99892,x99893,x99894,f319(f66(x99891,x99893,x99892,x99896),x99895)),x99897))+~P1(f319(f319(f321(x99893),x99897),f319(f302(x99891,x99893,x99896),f319(f302(x99892,x99891,x99895),x99894))))
% 28.77/28.53 [10317]~P18(x103177,x103176,x103171)+E(f319(f319(x103171,x103172),f654(x103173,x103174,x103172,x103175,x103171,x103176,x103177)),x103173)+P1(f319(f319(f321(x103177),x103172),x103174))+~P1(f319(f60(x103177,x103176,x103171,x103175,f319(f319(f301(x103177),x103172),x103174)),x103173))
% 28.77/28.53 [10382]~P18(x103821,x103824,x103825)+P1(f319(f60(x103821,x103824,x103825,x103826,x103823),f654(x103827,x103823,x103822,x103826,x103825,x103824,x103821)))+P1(f319(f319(f321(x103821),x103822),x103823))+~P1(f319(f60(x103821,x103824,x103825,x103826,f319(f319(f301(x103821),x103822),x103823)),x103827))
% 28.77/28.53 [10052]E(x100521,f2(a1))+~P1(f319(f43(x100523,x100521),f319(f319(f244(a1,a1),x100525),x100527)))+~P1(f319(f43(x100522,x100521),f319(f319(f244(a1,a1),x100524),x100526)))+P1(f319(f43(f319(f319(f74(a1),x100522),x100523),x100521),f319(f319(f244(a1,a1),f319(f319(f74(a1),f319(f319(f74(a1),x100524),x100525)),f319(f319(f30(a1),f319(f319(f74(a1),x100526),x100527)),x100521))),f39(a1,f319(f319(f74(a1),x100526),x100527),x100521))))
% 28.77/28.53 [10054]~P1(f319(f319(f227(a925),f2(a925)),x100543))+~P1(f319(f42(x100542,x100543),f319(f319(f244(a925,a925),x100545),x100547)))+~P1(f319(f42(x100541,x100543),f319(f319(f244(a925,a925),x100544),x100546)))+P1(f319(f42(f319(f319(f74(a925),x100541),x100542),x100543),f319(f319(f244(a925,a925),f319(f319(f74(a925),f319(f319(f74(a925),x100544),x100545)),f319(f319(f30(a925),f319(f319(f74(a925),x100546),x100547)),x100543))),f39(a925,f319(f319(f74(a925),x100546),x100547),x100543))))
% 28.77/28.53 [10450]~P79(x104502)+~P1(f319(f55(x104503),x104505))+~P1(f319(f55(x104501),x104507))+E(f319(f319(f6(x104501,x104502),f319(f319(f18(x104501,f932(x104503,a923),x104502),f319(f319(f8(f932(x104503,x104502),f932(f932(x104503,a923),x104502),x104501),f6(x104503,x104502)),x104504)),f319(f319(f8(f932(x104503,a923),f932(x104503,a923),x104501),f254(x104503)),f319(f319(f8(f932(x104503,a923),f932(x104503,a923),x104501),f319(f18(x104503,a923,a923),f319(f319(f8(a923,f932(a923,a923),x104503),a317),f319(f319(f7(x104503,f932(x104503,a923),a923),f321(x104503)),x104505)))),x104506)))),x104507),f319(f319(f6(x104503,x104502),f319(f319(f18(x104503,f932(x104501,a923),x104502),f319(f319(f8(f932(x104501,x104502),f932(f932(x104501,a923),x104502),x104503),f6(x104501,x104502)),f319(f7(x104501,x104503,x104502),x104504))),f319(f319(f8(f932(x104501,a923),f932(x104501,a923),x104503),f254(x104501)),f319(f319(f8(f932(x104501,a923),f932(x104501,a923),x104503),f319(f18(x104501,a923,a923),f319(f319(f8(a923,f932(a923,a923),x104501),a317),f319(f319(f7(x104501,f932(x104501,a923),a923),f321(x104501)),x104507)))),f319(f7(x104501,x104503,a923),x104506))))),x104505))
% 28.77/28.53 [10403]~P23(x104038,x104037,x104036,x104035,x104031)+~E(f319(x104032,f866(x104034,x104032,x104033,x104031,x104035,x104036,x104037)),f319(x104034,f866(x104034,x104032,x104033,x104031,x104035,x104036,x104037)))+E(f319(f319(x104031,x104032),x104033),f319(f319(x104031,x104034),x104033))+~P1(f319(f55(x104037),x104033))
% 28.77/28.53 [9913]~P24(x99137,x99136,x99131,x99138,x99132,x99134)+E(f319(f319(x99131,f319(x99132,x99133)),f319(x99134,x99135)),f319(x99134,x99135))+~P1(f319(f55(x99136),x99135))+~P1(f319(f319(f321(x99136),x99133),x99135))
% 28.77/28.53 [9917]~P13(x99176,x99171,x99172,x99178,x99173,x99174)+~P9(x99176,x99177,x99178)+P12(x99171,x99172,x99173,f319(x99174,x99175))+~P1(f319(f319(f321(x99176),x99175),x99177))
% 28.77/28.53 [10422]~P23(x104228,x104225,x104227,x104226,x104221)+E(f319(f319(x104221,x104222),x104223),f319(f319(x104221,x104224),x104223))+~P1(f319(f55(x104225),x104223))+P1(f319(f319(f321(x104225),f866(x104222,x104224,x104223,x104221,x104226,x104227,x104225)),x104223))
% 28.77/28.53 [10502]~P1(f319(f319(x105021,x105026),x105025))+P1(f319(f319(x105021,f848(x105021,x105024,x105025,x105026,x105023,x105022,x105027,x105028)),f853(x105021,x105024,x105025,x105026,x105023,x105022,x105027,x105028)))+P1(f319(f319(x105021,x105022),x105023))+~P1(f319(f319(f321(f931(f931(x105028,x105027),f931(x105028,x105027))),f319(f319(f244(f931(x105028,x105027),f931(x105028,x105027)),f319(f319(f244(x105028,x105027),x105022),x105023)),f319(f319(f244(x105028,x105027),x105026),x105025))),f299(f931(x105028,x105027),x105024)))
% 28.77/28.53 [10503]~P1(f319(f319(x105031,x105036),x105035))+P1(f319(f319(x105031,f854(x105031,x105034,x105033,x105032,x105035,x105036,x105037,x105038)),f855(x105031,x105034,x105033,x105032,x105035,x105036,x105037,x105038)))+P1(f319(f319(x105031,x105032),x105033))+~P1(f319(f319(f321(f931(f931(x105038,x105037),f931(x105038,x105037))),f319(f319(f244(f931(x105038,x105037),f931(x105038,x105037)),f319(f319(f244(x105038,x105037),x105036),x105035)),f319(f319(f244(x105038,x105037),x105032),x105033))),f299(f931(x105038,x105037),x105034)))
% 28.77/28.53 [10514]~P1(f319(f319(x105141,f849(x105141,x105146,x105145,x105144,x105143,x105142,x105147,x105148)),f852(x105141,x105146,x105145,x105144,x105143,x105142,x105147,x105148)))+P1(f319(f319(x105141,x105142),x105143))+~P1(f319(f319(x105141,x105144),x105145))+~P1(f319(f319(f321(f931(f931(x105148,x105147),f931(x105148,x105147))),f319(f319(f244(f931(x105148,x105147),f931(x105148,x105147)),f319(f319(f244(x105148,x105147),x105142),x105143)),f319(f319(f244(x105148,x105147),x105144),x105145))),f299(f931(x105148,x105147),x105146)))
% 28.77/28.53 [10515]~P1(f319(f319(x105151,f862(x105151,x105156,x105153,x105152,x105155,x105154,x105157,x105158)),f863(x105151,x105156,x105153,x105152,x105155,x105154,x105157,x105158)))+P1(f319(f319(x105151,x105152),x105153))+~P1(f319(f319(x105151,x105154),x105155))+~P1(f319(f319(f321(f931(f931(x105158,x105157),f931(x105158,x105157))),f319(f319(f244(f931(x105158,x105157),f931(x105158,x105157)),f319(f319(f244(x105158,x105157),x105154),x105155)),f319(f319(f244(x105158,x105157),x105152),x105153))),f299(f931(x105158,x105157),x105156)))
% 28.77/28.53 [10528]~P1(f319(f319(x105281,x105286),x105287))+P1(f319(f319(x105281,x105282),x105283))+P1(f319(f319(f321(f931(f931(x105284,x105285),f931(x105284,x105285))),f319(f319(f244(f931(x105284,x105285),f931(x105284,x105285)),f319(f319(f244(x105284,x105285),x105286),x105287)),f319(f319(f244(x105284,x105285),f854(x105281,x105288,x105283,x105282,x105287,x105286,x105285,x105284)),f855(x105281,x105288,x105283,x105282,x105287,x105286,x105285,x105284)))),f299(f931(x105284,x105285),x105288)))+~P1(f319(f319(f321(f931(f931(x105284,x105285),f931(x105284,x105285))),f319(f319(f244(f931(x105284,x105285),f931(x105284,x105285)),f319(f319(f244(x105284,x105285),x105286),x105287)),f319(f319(f244(x105284,x105285),x105282),x105283))),f299(f931(x105284,x105285),x105288)))
% 28.77/28.53 [10530]~P1(f319(f319(x105301,x105308),x105307))+P1(f319(f319(x105301,x105302),x105303))+P1(f319(f319(f321(f931(f931(x105304,x105305),f931(x105304,x105305))),f319(f319(f244(f931(x105304,x105305),f931(x105304,x105305)),f319(f319(f244(x105304,x105305),f848(x105301,x105306,x105307,x105308,x105303,x105302,x105305,x105304)),f853(x105301,x105306,x105307,x105308,x105303,x105302,x105305,x105304))),f319(f319(f244(x105304,x105305),x105308),x105307))),f299(f931(x105304,x105305),x105306)))+~P1(f319(f319(f321(f931(f931(x105304,x105305),f931(x105304,x105305))),f319(f319(f244(f931(x105304,x105305),f931(x105304,x105305)),f319(f319(f244(x105304,x105305),x105302),x105303)),f319(f319(f244(x105304,x105305),x105308),x105307))),f299(f931(x105304,x105305),x105306)))
% 28.77/28.53 [9524]~P21(x95247,x95241,x95248,x95243)+~P1(f319(f55(x95247),x95245))+~P1(f319(f55(x95247),x95244))+E(f319(f66(x95241,x95241,x95242,f319(x95243,x95244)),f319(f66(x95241,x95241,x95242,f319(x95243,x95245)),x95246)),f319(f66(x95241,x95241,x95242,f319(x95243,x95245)),f319(f66(x95241,x95241,x95242,f319(x95243,x95244)),x95246)))
% 28.77/28.53 [9533]~P35(x95331,x95332,x95333,x95334,x95337)+P35(x95331,x95332,x95333,f319(f319(f151(x95331,x95334),x95335),x95336),f319(f319(f151(x95332,x95337),x95335),x95338))+~P1(f319(f319(x95333,x95336),x95338))+~P1(f319(f319(f227(a925),x95335),f319(f181(f926(x95331)),x95334)))
% 28.77/28.53 [9534]~P35(x95341,x95342,x95343,x95344,x95347)+P35(x95341,x95342,x95343,f319(f319(f151(x95341,x95344),x95345),x95346),f319(f319(f151(x95342,x95347),x95345),x95348))+~P1(f319(f319(x95343,x95346),x95348))+~P1(f319(f319(f227(a925),x95345),f319(f181(f926(x95342)),x95347)))
% 28.77/28.53 [9614]~P26(x96142,x96142,x96145,x96146)+~P23(x96143,x96142,x96147,x96148,x96141)+~P1(f319(f55(x96142),x96146))+E(f319(f319(x96141,f319(f66(x96142,x96143,x96142,x96144),x96145)),x96146),f319(f319(x96141,x96144),f319(f302(x96142,x96142,x96145),x96146)))
% 28.77/28.53 [9850]~P27(x98501,x98503,x98505,x98506,x98508)+~P27(x98503,x98502,x98504,x98508,x98507)+P27(x98501,x98502,f319(f66(x98503,x98502,x98501,x98504),x98505),x98506,x98507)+~P1(f319(f319(f226(f932(x98503,a923)),f319(f302(x98501,x98503,x98505),x98506)),x98508))
% 28.77/28.53 [9876]P27(x98761,x98762,x98763,x98764,x98765)+~P27(x98762,x98766,x98767,x98765,x98768)+~P27(x98761,x98766,f319(f66(x98762,x98766,x98761,x98767),x98763),x98764,x98768)+~P1(f319(f319(f226(f932(x98762,a923)),f319(f302(x98761,x98762,x98763),x98764)),x98765))
% 28.77/28.53 [9915]~P25(x99157,x99152,x99155,x99158,x99156,x99151)+~P1(f319(f55(x99152),x99154))+E(f319(x99151,f319(f319(f301(x99152),x99153),x99154)),f319(f319(x99155,f319(x99156,x99153)),f319(x99151,x99154)))+P1(f319(f319(f321(x99152),x99153),x99154))
% 28.77/28.53 [9927]~P24(x99276,x99275,x99271,x99277,x99278,x99272)+E(f319(f319(x99271,f319(x99272,x99273)),f319(x99272,x99274)),f319(x99272,x99274))+~P1(f319(f55(x99275),x99274))+~P1(f319(f319(f226(f932(x99275,a923)),x99273),x99274))
% 28.77/28.53 [9510]P1(f319(f319(f321(f931(f926(x95101),f926(x95101))),f319(f319(f244(f926(x95101),f926(x95101)),x95102),x95103)),f149(x95101,x95104)))+~E(x95103,f319(f319(f126(x95101),x95105),f319(f319(f143(x95101),x95106),x95107)))+~E(x95102,f319(f319(f126(x95101),x95105),f319(f319(f143(x95101),x95108),x95107)))+~P1(f319(f319(f321(f931(x95101,x95101)),f319(f319(f244(x95101,x95101),x95108),x95106)),x95104))
% 28.77/28.53 [9920]~P24(x99206,x99202,x99205,x99207,x99208,x99201)+~P1(f319(f55(x99202),x99204))+~P1(f319(f55(x99202),x99203))+E(f319(x99201,f319(f319(f102(f932(x99202,a923)),x99203),x99204)),f319(f319(x99205,f319(x99201,x99203)),f319(x99201,x99204)))
% 28.77/28.53 [10492]~P26(x104924,x104922,x104925,x104928)+E(f319(f319(f34(x104921,f932(x104922,a923)),x104923),f319(f319(f8(f932(x104924,a923),f932(x104922,a923),x104921),f302(x104924,x104922,x104925)),x104926)),f319(f302(x104924,x104922,x104925),f319(f319(f34(x104921,f932(x104924,a923)),x104923),x104926)))+~P1(f319(f319(f321(x104921),x104927),x104923))+P1(f319(f319(f321(x104921),f899(x104927,x104926,x104923,x104921,x104928,x104925,x104922,x104924)),x104923))
% 28.77/28.53 [10519]~P26(x105194,x105192,x105195,x105197)+E(f319(f319(f34(x105191,f932(x105192,a923)),x105193),f319(f319(f8(f932(x105194,a923),f932(x105192,a923),x105191),f302(x105194,x105192,x105195)),x105196)),f319(f302(x105194,x105192,x105195),f319(f319(f34(x105191,f932(x105194,a923)),x105193),x105196)))+~P1(f319(f319(f321(x105191),x105198),x105193))+~P1(f319(f319(f226(f932(x105194,a923)),f319(x105196,f899(x105198,x105196,x105193,x105191,x105197,x105195,x105192,x105194))),x105197))
% 28.77/28.53 [10531]~P1(f319(f319(x105311,x105318),x105317))+P1(f319(f319(x105311,x105312),x105313))+~P1(f319(f319(f321(f931(f931(x105314,x105315),f931(x105314,x105315))),f319(f319(f244(f931(x105314,x105315),f931(x105314,x105315)),f319(f319(f244(x105314,x105315),x105312),x105313)),f319(f319(f244(x105314,x105315),x105318),x105317))),f299(f931(x105314,x105315),x105316)))+P1(f319(f319(f321(f931(f931(x105314,x105315),f931(x105314,x105315))),f319(f319(f244(f931(x105314,x105315),f931(x105314,x105315)),f319(f319(f244(x105314,x105315),f849(x105311,x105316,x105317,x105318,x105313,x105312,x105315,x105314)),f852(x105311,x105316,x105317,x105318,x105313,x105312,x105315,x105314))),f319(f319(f244(x105314,x105315),f848(x105311,x105316,x105317,x105318,x105313,x105312,x105315,x105314)),f853(x105311,x105316,x105317,x105318,x105313,x105312,x105315,x105314)))),x105316))
% 28.77/28.53 [10532]~P1(f319(f319(x105321,x105328),x105327))+P1(f319(f319(x105321,x105322),x105323))+~P1(f319(f319(f321(f931(f931(x105324,x105325),f931(x105324,x105325))),f319(f319(f244(f931(x105324,x105325),f931(x105324,x105325)),f319(f319(f244(x105324,x105325),x105328),x105327)),f319(f319(f244(x105324,x105325),x105322),x105323))),f299(f931(x105324,x105325),x105326)))+P1(f319(f319(f321(f931(f931(x105324,x105325),f931(x105324,x105325))),f319(f319(f244(f931(x105324,x105325),f931(x105324,x105325)),f319(f319(f244(x105324,x105325),f854(x105321,x105326,x105323,x105322,x105327,x105328,x105325,x105324)),f855(x105321,x105326,x105323,x105322,x105327,x105328,x105325,x105324))),f319(f319(f244(x105324,x105325),f862(x105321,x105326,x105323,x105322,x105327,x105328,x105325,x105324)),f863(x105321,x105326,x105323,x105322,x105327,x105328,x105325,x105324)))),x105326))
% 28.77/28.53 [9999]~P25(x99997,x99995,x99991,x99998,x99992,x99994)+~P1(f319(f55(x99995),x99996))+~P1(f319(f319(f321(x99995),x99993),x99996))+E(f319(f319(x99991,f319(x99992,x99993)),f319(x99994,f319(f319(f23(f932(x99995,a923)),x99996),f319(f319(f301(x99995),x99993),f180(f932(x99995,a923)))))),f319(x99994,x99996))
% 28.77/28.53 [10007]~P25(x100076,x100073,x100071,x100077,x100078,x100072)+~P1(f319(f55(x100073),x100075))+~P1(f319(f55(x100073),x100074))+E(f319(f319(x100071,f319(x100072,f319(f319(f102(f932(x100073,a923)),x100074),x100075))),f319(x100072,f319(f319(f93(f932(x100073,a923)),x100074),x100075))),f319(f319(x100071,f319(x100072,x100074)),f319(x100072,x100075)))
% 28.77/28.53 [10097]P44(x100971,x100972,x100973,x100974,x100975,f319(f319(x100973,x100976),x100977))+~P44(x100971,x100972,x100973,x100974,f319(f319(f23(f932(x100971,a923)),x100975),f319(f319(f301(x100971),x100978),f180(f932(x100971,a923)))),x100979)+~E(f319(f319(x100973,x100976),x100977),f319(f319(x100973,x100978),x100979))+~P1(f319(f319(f321(x100971),x100978),x100975))
% 28.77/28.53 [10034]~P13(x100346,x100347,x100348,x100349,x1003410,x100341)+E(f319(f319(x100341,x100342),x100343),f319(f319(x100341,x100344),x100345))+~P1(f319(f319(f321(f931(x100347,x100347)),f319(f319(f244(x100347,x100347),x100343),x100345)),x1003410))+~P1(f319(f319(f321(f931(x100346,x100346)),f319(f319(f244(x100346,x100346),x100342),x100344)),x100349))
% 28.77/28.53 [9774]E(x97741,f2(a1))+E(x97742,f2(a1))+E(f319(f319(f80(a1,f931(a1,a1)),f319(f319(a209,x97742),x97741)),f319(f319(f18(a1,a1,f931(a1,a1)),f319(f319(f8(a1,f932(a1,f931(a1,a1)),a1),f244(a1,a1)),f319(f30(a1),x97742))),f319(f30(a1),x97741))),f207(x97742,x97741))+P1(f319(f319(f227(a1),x97741),f2(a1)))+~P1(f319(f307(f931(a1,a1),a213),f319(f319(f244(a1,a1),x97742),x97741)))
% 28.77/28.53 [9616]~P102(x96162)+E(x96161,f180(f932(x96162,a923)))+~P1(f319(f55(x96162),x96161))+P1(f319(f319(f321(x96162),f10(x96162,x96161)),x96161))+~P1(f319(f319(f321(x96162),f319(f319(f93(x96162),f911(x96161,x96162)),f913(x96161,x96162))),f319(f319(f301(x96162),f911(x96161,x96162)),f319(f319(f301(x96162),f913(x96161,x96162)),f180(f932(x96162,a923))))))
% 28.77/28.53 [9617]~P102(x96172)+E(x96171,f180(f932(x96172,a923)))+~P1(f319(f55(x96172),x96171))+P1(f319(f319(f321(x96172),f13(x96172,x96171)),x96171))+~P1(f319(f319(f321(x96172),f319(f319(f102(x96172),f915(x96171,x96172)),f918(x96171,x96172))),f319(f319(f301(x96172),f915(x96171,x96172)),f319(f319(f301(x96172),f918(x96171,x96172)),f180(f932(x96172,a923))))))
% 28.77/28.53 [9618]~P4(x96182)+E(x96181,f180(f932(x96182,a923)))+~P1(f319(f55(x96182),x96181))+P1(f319(f319(f321(x96182),f14(x96182,x96181)),x96181))+~P1(f319(f319(f321(x96182),f319(f319(f224(x96182),f489(x96181,x96182)),f491(x96181,x96182))),f319(f319(f301(x96182),f489(x96181,x96182)),f319(f319(f301(x96182),f491(x96181,x96182)),f180(f932(x96182,a923))))))
% 28.77/28.53 [9619]~P4(x96192)+E(x96191,f180(f932(x96192,a923)))+~P1(f319(f55(x96192),x96191))+P1(f319(f319(f321(x96192),f15(x96192,x96191)),x96191))+~P1(f319(f319(f321(x96192),f319(f319(f225(x96192),f480(x96191,x96192)),f490(x96191,x96192))),f319(f319(f301(x96192),f480(x96191,x96192)),f319(f319(f301(x96192),f490(x96191,x96192)),f180(f932(x96192,a923))))))
% 28.77/28.53 [9651]~P76(x96512)+E(x96511,f180(f932(x96512,a923)))+~P1(f319(f55(x96512),x96511))+P1(f319(f319(f321(x96512),f319(f57(x96512,f75(x96512)),x96511)),x96511))+~P1(f319(f319(f321(x96512),f319(f319(f75(x96512),f346(x96511,x96512)),f347(x96511,x96512))),f319(f319(f301(x96512),f346(x96511,x96512)),f319(f319(f301(x96512),f347(x96511,x96512)),f180(f932(x96512,a923))))))
% 28.77/28.53 [9656]~P4(x96562)+E(x96561,f180(f932(x96562,a923)))+~P1(f319(f55(x96562),x96561))+P1(f319(f319(f321(x96562),f11(x96562,f224(x96562),x96561)),x96561))+~P1(f319(f319(f321(x96562),f319(f319(f224(x96562),f481(x96561,x96562)),f482(x96561,x96562))),f319(f319(f301(x96562),f481(x96561,x96562)),f319(f319(f301(x96562),f482(x96561,x96562)),f180(f932(x96562,a923))))))
% 28.77/28.53 [9657]~P4(x96572)+E(x96571,f180(f932(x96572,a923)))+~P1(f319(f55(x96572),x96571))+P1(f319(f319(f321(x96572),f12(x96572,f225(x96572),x96571)),x96571))+~P1(f319(f319(f321(x96572),f319(f319(f225(x96572),f483(x96571,x96572)),f484(x96571,x96572))),f319(f319(f301(x96572),f483(x96571,x96572)),f319(f319(f301(x96572),f484(x96571,x96572)),f180(f932(x96572,a923))))))
% 28.77/28.53 [6749]~P93(x67492)+E(x67491,f2(x67492))+~E(f319(f319(f74(x67492),x67493),x67491),f2(x67492))+~P1(f319(f319(f226(x67492),f2(x67492)),x67493))+~P1(f319(f319(f226(x67492),f2(x67492)),x67491))
% 28.77/28.53 [6750]~P93(x67502)+E(x67501,f2(x67502))+~E(f319(f319(f74(x67502),x67501),x67503),f2(x67502))+~P1(f319(f319(f226(x67502),f2(x67502)),x67503))+~P1(f319(f319(f226(x67502),f2(x67502)),x67501))
% 28.77/28.53 [7288]~P4(x72882)+~P14(x72882,x72881)+E(x72881,f105(x72882))+~P1(f319(f319(f321(x72882),x72883),f319(f164(x72882),f729(x72881,x72882))))+P1(f319(f319(f226(x72882),f748(x72881,x72882)),x72883))
% 28.77/28.53 [7460]~P4(x74601)+E(f14(x74601,x74602),x74603)+~P1(f319(f55(x74601),x74602))+~P1(f319(f319(f226(x74601),x74603),f525(x74603,x74602,x74601)))+~P1(f319(f319(f321(x74601),x74603),x74602))
% 28.77/28.53 [7493]~P4(x74931)+~P14(x74931,x74932)+~P14(x74931,x74933)+P14(x74931,f319(f319(f126(x74931),x74932),x74933))+P1(f319(f319(f321(x74931),f735(x74933,x74932,x74931)),f319(f164(x74931),x74932)))
% 28.77/28.53 [7494]~P4(x74941)+~P14(x74941,x74942)+~P14(x74941,x74943)+P14(x74941,f319(f319(f126(x74941),x74942),x74943))+P1(f319(f319(f321(x74941),f736(x74943,x74942,x74941)),f319(f164(x74941),x74943)))
% 28.77/28.53 [7554]~P4(x75541)+E(f14(x75541,x75542),x75543)+~P1(f319(f55(x75541),x75542))+P1(f319(f319(f321(x75541),f525(x75543,x75542,x75541)),x75542))+~P1(f319(f319(f321(x75541),x75543),x75542))
% 28.77/28.53 [7555]~P4(x75551)+E(f15(x75551,x75552),x75553)+~P1(f319(f55(x75551),x75552))+P1(f319(f319(f321(x75551),f526(x75553,x75552,x75551)),x75552))+~P1(f319(f319(f321(x75551),x75553),x75552))
% 28.77/28.53 [8122]~P4(x81221)+E(f15(x81221,x81222),x81223)+~P1(f319(f55(x81221),x81222))+~P1(f319(f319(f321(x81221),x81223),x81222))+~P1(f319(f319(f226(x81221),f526(x81223,x81222,x81221)),x81223))
% 28.77/28.53 [8443]~P4(x84431)+~P14(x84431,x84432)+~P14(x84431,x84433)+P14(x84431,f319(f319(f126(x84431),x84432),x84433))+~P1(f319(f319(f226(x84431),f735(x84433,x84432,x84431)),f736(x84433,x84432,x84431)))
% 28.77/28.53 [9248]~P102(x92482)+E(x92481,f180(f932(x92482,a923)))+~E(f319(f319(f93(x92482),f319(x92483,f914(x92481,x92483,x92482))),f319(x92483,f919(x92481,x92483,x92482))),f319(x92483,f319(f319(f93(x92482),f914(x92481,x92483,x92482)),f919(x92481,x92483,x92482))))+E(f10(x92482,f319(f302(x92482,x92482,x92483),x92481)),f319(x92483,f10(x92482,x92481)))+~P1(f319(f55(x92482),x92481))
% 28.77/28.53 [9249]~P102(x92492)+E(x92491,f180(f932(x92492,a923)))+~E(f319(f319(f102(x92492),f319(x92493,f920(x92491,x92493,x92492))),f319(x92493,f337(x92491,x92493,x92492))),f319(x92493,f319(f319(f102(x92492),f920(x92491,x92493,x92492)),f337(x92491,x92493,x92492))))+E(f13(x92492,f319(f302(x92492,x92492,x92493),x92491)),f319(x92493,f13(x92492,x92491)))+~P1(f319(f55(x92492),x92491))
% 28.77/28.53 [9250]~P4(x92502)+E(x92501,f180(f932(x92502,a923)))+~E(f319(f319(f224(x92502),f319(x92503,f485(x92501,x92503,x92502))),f319(x92503,f499(x92501,x92503,x92502))),f319(x92503,f319(f319(f224(x92502),f485(x92501,x92503,x92502)),f499(x92501,x92503,x92502))))+E(f14(x92502,f319(f302(x92502,x92502,x92503),x92501)),f319(x92503,f14(x92502,x92501)))+~P1(f319(f55(x92502),x92501))
% 28.77/28.53 [9251]~P4(x92512)+E(x92511,f180(f932(x92512,a923)))+~E(f319(f319(f225(x92512),f319(x92513,f486(x92511,x92513,x92512))),f319(x92513,f498(x92511,x92513,x92512))),f319(x92513,f319(f319(f225(x92512),f486(x92511,x92513,x92512)),f498(x92511,x92513,x92512))))+E(f15(x92512,f319(f302(x92512,x92512,x92513),x92511)),f319(x92513,f15(x92512,x92511)))+~P1(f319(f55(x92512),x92511))
% 28.77/28.53 [9320]~P4(x93202)+E(x93201,f180(f932(x93202,a923)))+~E(f319(f319(f224(x93202),f319(x93203,f487(x93201,x93203,x93202))),f319(x93203,f496(x93201,x93203,x93202))),f319(x93203,f319(f319(f224(x93202),f487(x93201,x93203,x93202)),f496(x93201,x93203,x93202))))+E(f11(x93202,f224(x93202),f319(f302(x93202,x93202,x93203),x93201)),f319(x93203,f11(x93202,f224(x93202),x93201)))+~P1(f319(f55(x93202),x93201))
% 28.77/28.53 [9321]~P4(x93212)+E(x93211,f180(f932(x93212,a923)))+~E(f319(f319(f225(x93212),f319(x93213,f488(x93211,x93213,x93212))),f319(x93213,f494(x93211,x93213,x93212))),f319(x93213,f319(f319(f225(x93212),f488(x93211,x93213,x93212)),f494(x93211,x93213,x93212))))+E(f12(x93212,f225(x93212),f319(f302(x93212,x93212,x93213),x93211)),f319(x93213,f12(x93212,f225(x93212),x93211)))+~P1(f319(f55(x93212),x93211))
% 28.77/28.53 [6379]~P102(x63792)+E(x63791,f180(f932(x63792,a923)))+~P1(f319(f55(x63792),x63791))+E(f10(x63792,f319(f319(f301(x63792),x63793),x63791)),f319(f319(f93(x63792),x63793),f10(x63792,x63791)))+P1(f319(f319(f321(x63792),x63793),x63791))
% 28.77/28.53 [6380]~P102(x63802)+E(x63801,f180(f932(x63802,a923)))+~P1(f319(f55(x63802),x63801))+E(f13(x63802,f319(f319(f301(x63802),x63803),x63801)),f319(f319(f102(x63802),x63803),f13(x63802,x63801)))+P1(f319(f319(f321(x63802),x63803),x63801))
% 28.77/28.53 [6381]~P4(x63812)+E(x63811,f180(f932(x63812,a923)))+~P1(f319(f55(x63812),x63811))+E(f14(x63812,f319(f319(f301(x63812),x63813),x63811)),f319(f319(f224(x63812),x63813),f14(x63812,x63811)))+P1(f319(f319(f321(x63812),x63813),x63811))
% 28.77/28.53 [6382]~P4(x63822)+E(x63821,f180(f932(x63822,a923)))+~P1(f319(f55(x63822),x63821))+E(f15(x63822,f319(f319(f301(x63822),x63823),x63821)),f319(f319(f225(x63822),x63823),f15(x63822,x63821)))+P1(f319(f319(f321(x63822),x63823),x63821))
% 28.77/28.53 [6765]~P76(x67652)+E(x67651,f180(f932(x67652,a923)))+~P1(f319(f55(x67652),x67651))+E(f319(f57(x67652,f75(x67652)),f319(f319(f301(x67652),x67653),x67651)),f319(f319(f75(x67652),x67653),f319(f57(x67652,f75(x67652)),x67651)))+P1(f319(f319(f321(x67652),x67653),x67651))
% 28.77/28.53 [6854]~P4(x68542)+E(x68541,f180(f932(x68542,a923)))+~P1(f319(f55(x68542),x68541))+E(f11(x68542,f224(x68542),f319(f319(f301(x68542),x68543),x68541)),f319(f319(f224(x68542),x68543),f11(x68542,f224(x68542),x68541)))+P1(f319(f319(f321(x68542),x68543),x68541))
% 28.77/28.53 [6855]~P4(x68552)+E(x68551,f180(f932(x68552,a923)))+~P1(f319(f55(x68552),x68551))+E(f12(x68552,f225(x68552),f319(f319(f301(x68552),x68553),x68551)),f319(f319(f225(x68552),x68553),f12(x68552,f225(x68552),x68551)))+P1(f319(f319(f321(x68552),x68553),x68551))
% 28.77/28.53 [7295]~P102(x72952)+E(f319(f319(f102(x72952),f13(x72952,x72951)),f13(x72952,x72953)),f13(x72952,x72953))+E(x72951,f180(f932(x72952,a923)))+~P1(f319(f55(x72952),x72953))+~P1(f319(f319(f226(f932(x72952,a923)),x72951),x72953))
% 28.77/28.53 [7296]~P102(x72962)+E(f319(f319(f93(x72962),f10(x72962,x72961)),f10(x72962,x72963)),f10(x72962,x72963))+E(x72961,f180(f932(x72962,a923)))+~P1(f319(f55(x72962),x72963))+~P1(f319(f319(f226(f932(x72962,a923)),x72961),x72963))
% 28.77/28.53 [7297]~P4(x72972)+E(f319(f319(f224(x72972),f14(x72972,x72971)),f14(x72972,x72973)),f14(x72972,x72973))+E(x72971,f180(f932(x72972,a923)))+~P1(f319(f55(x72972),x72973))+~P1(f319(f319(f226(f932(x72972,a923)),x72971),x72973))
% 28.77/28.53 [7298]~P4(x72982)+E(f319(f319(f225(x72982),f15(x72982,x72981)),f15(x72982,x72983)),f15(x72982,x72983))+E(x72981,f180(f932(x72982,a923)))+~P1(f319(f55(x72982),x72983))+~P1(f319(f319(f226(f932(x72982,a923)),x72981),x72983))
% 28.77/28.53 [7601]~P4(x76012)+E(x76011,f180(f932(x76012,a923)))+~P1(f319(f55(x76012),x76013))+P1(f319(f319(f226(x76012),f14(x76012,x76013)),f14(x76012,x76011)))+~P1(f319(f319(f226(f932(x76012,a923)),x76011),x76013))
% 28.77/28.53 [7602]~P4(x76022)+E(x76021,f180(f932(x76022,a923)))+~P1(f319(f55(x76022),x76023))+P1(f319(f319(f226(x76022),f15(x76022,x76021)),f15(x76022,x76023)))+~P1(f319(f319(f226(f932(x76022,a923)),x76021),x76023))
% 28.77/28.53 [7655]~P102(x76551)+E(f10(x76551,x76552),x76553)+~P1(f319(f55(x76551),x76552))+~E(f319(f319(f23(f932(x76551,a923)),x76552),f319(f319(f301(x76551),x76553),f180(f932(x76551,a923)))),f180(f932(x76551,a923)))+~P1(f319(f319(f321(x76551),x76553),x76552))
% 28.77/28.53 [7656]~P102(x76561)+E(f13(x76561,x76562),x76563)+~P1(f319(f55(x76561),x76562))+~E(f319(f319(f23(f932(x76561,a923)),x76562),f319(f319(f301(x76561),x76563),f180(f932(x76561,a923)))),f180(f932(x76561,a923)))+~P1(f319(f319(f321(x76561),x76563),x76562))
% 28.77/28.53 [7657]~P4(x76571)+E(f14(x76571,x76572),x76573)+~P1(f319(f55(x76571),x76572))+~E(f319(f319(f23(f932(x76571,a923)),x76572),f319(f319(f301(x76571),x76573),f180(f932(x76571,a923)))),f180(f932(x76571,a923)))+~P1(f319(f319(f321(x76571),x76573),x76572))
% 28.77/28.53 [7658]~P4(x76581)+E(f15(x76581,x76582),x76583)+~P1(f319(f55(x76581),x76582))+~E(f319(f319(f23(f932(x76581,a923)),x76582),f319(f319(f301(x76581),x76583),f180(f932(x76581,a923)))),f180(f932(x76581,a923)))+~P1(f319(f319(f321(x76581),x76583),x76582))
% 28.77/28.53 [7751]~P4(x77511)+E(f11(x77511,f224(x77511),x77512),x77513)+~P1(f319(f55(x77511),x77512))+~E(f319(f319(f23(f932(x77511,a923)),x77512),f319(f319(f301(x77511),x77513),f180(f932(x77511,a923)))),f180(f932(x77511,a923)))+~P1(f319(f319(f321(x77511),x77513),x77512))
% 28.77/28.53 [7752]~P4(x77521)+E(f12(x77521,f225(x77521),x77522),x77523)+~P1(f319(f55(x77521),x77522))+~E(f319(f319(f23(f932(x77521,a923)),x77522),f319(f319(f301(x77521),x77523),f180(f932(x77521,a923)))),f180(f932(x77521,a923)))+~P1(f319(f319(f321(x77521),x77523),x77522))
% 28.77/28.53 [7787]~P108(x77872)+E(x77871,f180(f932(x77872,a923)))+~P1(f319(f55(x77872),x77871))+~P1(f319(f319(f226(x77872),x77873),f338(x77873,x77871,x77872)))+P1(f319(f319(f226(x77872),x77873),f319(f57(x77872,f93(x77872)),x77871)))
% 28.77/28.53 [7788]~P4(x77882)+E(x77881,f180(f932(x77882,a923)))+~P1(f319(f55(x77882),x77881))+~P1(f319(f319(f226(x77882),x77883),f475(x77883,x77881,x77882)))+P1(f319(f319(f226(x77882),x77883),f319(f57(x77882,f224(x77882)),x77881)))
% 28.77/28.53 [7789]~P4(x77892)+E(x77891,f180(f932(x77892,a923)))+~P1(f319(f55(x77892),x77891))+~P1(f319(f319(f227(x77892),x77893),f477(x77893,x77891,x77892)))+P1(f319(f319(f227(x77892),x77893),f319(f57(x77892,f224(x77892)),x77891)))
% 28.77/28.53 [7876]~P108(x78762)+E(x78761,f180(f932(x78762,a923)))+~P1(f319(f55(x78762),x78761))+P1(f319(f319(f321(x78762),f338(x78763,x78761,x78762)),x78761))+P1(f319(f319(f226(x78762),x78763),f319(f57(x78762,f93(x78762)),x78761)))
% 28.77/28.53 [7877]~P4(x78772)+E(x78771,f180(f932(x78772,a923)))+~P1(f319(f55(x78772),x78771))+P1(f319(f319(f321(x78772),f475(x78773,x78771,x78772)),x78771))+P1(f319(f319(f226(x78772),x78773),f319(f57(x78772,f224(x78772)),x78771)))
% 28.77/28.53 [7878]~P4(x78782)+E(x78781,f180(f932(x78782,a923)))+~P1(f319(f55(x78782),x78781))+P1(f319(f319(f321(x78782),f477(x78783,x78781,x78782)),x78781))+P1(f319(f319(f227(x78782),x78783),f319(f57(x78782,f224(x78782)),x78781)))
% 28.77/28.53 [7998]~P4(x79982)+E(x79981,f180(f932(x79982,a923)))+E(f319(f319(f224(x79982),f11(x79982,f224(x79982),x79981)),f11(x79982,f224(x79982),x79983)),f11(x79982,f224(x79982),x79983))+~P1(f319(f55(x79982),x79983))+~P1(f319(f319(f226(f932(x79982,a923)),x79981),x79983))
% 28.77/28.53 [7999]~P4(x79992)+E(x79991,f180(f932(x79992,a923)))+E(f319(f319(f225(x79992),f12(x79992,f225(x79992),x79991)),f12(x79992,f225(x79992),x79993)),f12(x79992,f225(x79992),x79993))+~P1(f319(f55(x79992),x79993))+~P1(f319(f319(f226(f932(x79992,a923)),x79991),x79993))
% 28.77/28.53 [8201]~E(f502(x82011,x82013,x82012),f503(x82011,x82013,x82012))+~E(f319(f29(x82012),f504(x82011,x82013,x82012)),x82011)+E(f319(f319(f75(a925),x82011),f319(f29(f932(x82012,a923)),x82013)),f319(f29(x82012),f31(f932(x82012,a923),x82013)))+~P1(f319(f55(x82012),f31(f932(x82012,a923),x82013)))+~P1(f319(f55(f932(x82012,a923)),x82013))
% 28.77/28.53 [8382]~P4(x83822)+E(x83821,f180(f932(x83822,a923)))+~P1(f319(f55(x83822),x83823))+P1(f319(f319(f226(x83822),f319(f57(x83822,f224(x83822)),x83823)),f319(f57(x83822,f224(x83822)),x83821)))+~P1(f319(f319(f226(f932(x83822,a923)),x83821),x83823))
% 28.77/28.53 [8686]~E(f502(x86861,x86863,x86862),f503(x86861,x86863,x86862))+E(f319(f319(f75(a925),x86861),f319(f29(f932(x86862,a923)),x86863)),f319(f29(x86862),f31(f932(x86862,a923),x86863)))+P1(f319(f319(f321(f932(x86862,a923)),f504(x86861,x86863,x86862)),x86863))+~P1(f319(f55(x86862),f31(f932(x86862,a923),x86863)))+~P1(f319(f55(f932(x86862,a923)),x86863))
% 28.77/28.53 [8712]~E(f319(f29(x87122),f504(x87121,x87123,x87122)),x87121)+E(f319(f319(f75(a925),x87121),f319(f29(f932(x87122,a923)),x87123)),f319(f29(x87122),f31(f932(x87122,a923),x87123)))+P1(f319(f319(f321(f932(x87122,a923)),f503(x87121,x87123,x87122)),x87123))+~P1(f319(f55(x87122),f31(f932(x87122,a923),x87123)))+~P1(f319(f55(f932(x87122,a923)),x87123))
% 28.77/28.53 [8713]~E(f319(f29(x87132),f504(x87131,x87133,x87132)),x87131)+E(f319(f319(f75(a925),x87131),f319(f29(f932(x87132,a923)),x87133)),f319(f29(x87132),f31(f932(x87132,a923),x87133)))+P1(f319(f319(f321(f932(x87132,a923)),f502(x87131,x87133,x87132)),x87133))+~P1(f319(f55(x87132),f31(f932(x87132,a923),x87133)))+~P1(f319(f55(f932(x87132,a923)),x87133))
% 28.77/28.53 [8740]~E(f319(f29(x87402),f504(x87401,x87403,x87402)),x87401)+~E(f319(f319(f93(f932(x87402,a923)),f503(x87401,x87403,x87402)),f502(x87401,x87403,x87402)),f180(f932(x87402,a923)))+E(f319(f319(f75(a925),x87401),f319(f29(f932(x87402,a923)),x87403)),f319(f29(x87402),f31(f932(x87402,a923),x87403)))+~P1(f319(f55(f932(x87402,a923)),x87403))+~P1(f319(f55(x87402),f31(f932(x87402,a923),x87403)))
% 28.77/28.53 [9006]E(f319(f319(f75(a925),x90061),f319(f29(f932(x90062,a923)),x90063)),f319(f29(x90062),f31(f932(x90062,a923),x90063)))+P1(f319(f319(f321(f932(x90062,a923)),f504(x90061,x90063,x90062)),x90063))+P1(f319(f319(f321(f932(x90062,a923)),f503(x90061,x90063,x90062)),x90063))+~P1(f319(f55(f932(x90062,a923)),x90063))+~P1(f319(f55(x90062),f31(f932(x90062,a923),x90063)))
% 28.77/28.53 [9007]E(f319(f319(f75(a925),x90071),f319(f29(f932(x90072,a923)),x90073)),f319(f29(x90072),f31(f932(x90072,a923),x90073)))+P1(f319(f319(f321(f932(x90072,a923)),f504(x90071,x90073,x90072)),x90073))+P1(f319(f319(f321(f932(x90072,a923)),f502(x90071,x90073,x90072)),x90073))+~P1(f319(f55(f932(x90072,a923)),x90073))+~P1(f319(f55(x90072),f31(f932(x90072,a923),x90073)))
% 28.77/28.53 [9033]~E(f319(f319(f93(f932(x90332,a923)),f503(x90331,x90333,x90332)),f502(x90331,x90333,x90332)),f180(f932(x90332,a923)))+E(f319(f319(f75(a925),x90331),f319(f29(f932(x90332,a923)),x90333)),f319(f29(x90332),f31(f932(x90332,a923),x90333)))+~P1(f319(f55(f932(x90332,a923)),x90333))+P1(f319(f319(f321(f932(x90332,a923)),f504(x90331,x90333,x90332)),x90333))+~P1(f319(f55(x90332),f31(f932(x90332,a923),x90333)))
% 28.77/28.53 [9295]~P101(x92952)+E(x92951,f180(f932(x92952,a923)))+~E(f319(f319(f75(x92952),f319(x92953,f345(x92951,x92953,x92952))),f319(x92953,f348(x92951,x92953,x92952))),f319(x92953,f319(f319(f75(x92952),f345(x92951,x92953,x92952)),f348(x92951,x92953,x92952))))+~P1(f319(f55(x92952),x92951))+E(f319(f57(x92952,f75(x92952)),f319(f302(x92952,x92952,x92953),x92951)),f319(x92953,f319(f57(x92952,f75(x92952)),x92951)))
% 28.77/28.53 [10258]P1(f319(f319(x102581,x102582),x102583))+P1(f319(f319(f227(a1),f536(x102581,x102583,x102582)),f538(x102581,x102583,x102582)))+P1(f319(f319(f226(a1),f538(x102581,x102583,x102582)),f2(a1)))+P1(f319(f319(x102581,f536(x102581,x102583,x102582)),f319(f319(f75(a1),f319(f95(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),f538(x102581,x102583,x102582))))+~P1(f319(f307(f931(a1,a1),a52),f319(f319(f244(a1,a1),x102582),x102583)))
% 28.77/28.53 [10264]P1(f319(f319(x102641,x102642),x102643))+P1(f319(f319(f226(a1),f535(x102641,x102643,x102642)),f2(a1)))+P1(f319(f319(x102641,f531(x102641,x102643,x102642)),f319(f319(f75(a1),f319(f95(a1),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),f535(x102641,x102643,x102642))))+P1(f319(f319(f226(a1),f2(a1)),f319(f319(f74(a1),f531(x102641,x102643,x102642)),f535(x102641,x102643,x102642))))+~P1(f319(f307(f931(a1,a1),a46),f319(f319(f244(a1,a1),x102642),x102643)))
% 28.77/28.53 [8172]~P126(x81721)+~P1(f319(f319(f226(x81721),x81722),f72(x81721)))+~P1(f319(f319(f226(x81721),f2(x81721)),x81722))+~P1(f319(f319(f226(x81721),f2(x81721)),x81723))+P1(f319(f319(f226(x81721),f319(f319(f75(x81721),x81722),x81723)),x81723))
% 28.77/28.53 [8173]~P126(x81731)+~P1(f319(f319(f226(x81731),x81733),f72(x81731)))+~P1(f319(f319(f226(x81731),f2(x81731)),x81733))+~P1(f319(f319(f226(x81731),f2(x81731)),x81732))+P1(f319(f319(f226(x81731),f319(f319(f75(x81731),x81732),x81733)),x81732))
% 28.77/28.53 [8530]~P4(x85302)+E(x85301,f180(f932(x85302,a923)))+~P1(f319(f55(x85302),x85301))+P1(f319(f319(f226(x85302),f476(x85303,x85301,x85302)),x85303))+~P1(f319(f319(f226(x85302),f319(f57(x85302,f224(x85302)),x85301)),x85303))
% 28.77/28.53 [8531]~P4(x85312)+E(x85311,f180(f932(x85312,a923)))+~P1(f319(f55(x85312),x85311))+P1(f319(f319(f321(x85312),f476(x85313,x85311,x85312)),x85311))+~P1(f319(f319(f226(x85312),f319(f57(x85312,f224(x85312)),x85311)),x85313))
% 28.77/28.53 [8532]~P4(x85322)+E(x85321,f180(f932(x85322,a923)))+~P1(f319(f55(x85322),x85321))+P1(f319(f319(f321(x85322),f478(x85323,x85321,x85322)),x85321))+~P1(f319(f319(f227(x85322),f319(f57(x85322,f224(x85322)),x85321)),x85323))
% 28.77/28.53 [8533]~P4(x85332)+E(x85331,f180(f932(x85332,a923)))+~P1(f319(f55(x85332),x85331))+P1(f319(f319(f227(x85332),f478(x85333,x85331,x85332)),x85333))+~P1(f319(f319(f227(x85332),f319(f57(x85332,f224(x85332)),x85331)),x85333))
% 28.77/28.53 [8620]~P1(f319(x86201,x86203))+P1(f319(x86201,f390(x86201,x86202)))+P1(f319(x86201,f379(x86201,x86202)))+~P1(f319(f319(f227(a1),f2(a1)),x86202))+P1(f319(x86201,f319(f319(f23(a1),f379(x86201,x86202)),f319(f319(f75(a1),f391(x86201,x86202)),x86202))))
% 28.77/28.53 [8842]~P1(f319(x88421,x88423))+P1(f319(x88421,f379(x88421,x88422)))+~P1(f319(f319(f227(a1),f2(a1)),x88422))+P1(f319(f319(f321(a1),f390(x88421,x88422)),f295(a1,f72(a1),x88422)))+P1(f319(x88421,f319(f319(f23(a1),f379(x88421,x88422)),f319(f319(f75(a1),f391(x88421,x88422)),x88422))))
% 28.77/28.53 [9055]~P1(f319(x90551,x90553))+~P1(f319(x90551,f379(x90551,x90552)))+P1(f319(x90551,f390(x90551,x90552)))+~P1(f319(f319(f227(a1),f2(a1)),x90552))+~P1(f319(x90551,f319(f319(f23(a1),f379(x90551,x90552)),f319(f319(f75(a1),f391(x90551,x90552)),x90552))))
% 28.77/28.53 [9184]~P1(f319(x91841,x91843))+~P1(f319(x91841,f379(x91841,x91842)))+~P1(f319(f319(f227(a1),f2(a1)),x91842))+P1(f319(f319(f321(a1),f390(x91841,x91842)),f295(a1,f72(a1),x91842)))+~P1(f319(x91841,f319(f319(f23(a1),f379(x91841,x91842)),f319(f319(f75(a1),f391(x91841,x91842)),x91842))))
% 28.77/28.53 [8960]~P102(x89601)+~P1(f319(f55(x89601),x89602))+E(f319(f319(f23(f932(x89601,a923)),x89602),f319(f319(f301(x89601),x89603),f180(f932(x89601,a923)))),f180(f932(x89601,a923)))+~P1(f319(f319(f321(x89601),x89603),x89602))+E(f319(f319(f93(x89601),x89603),f10(x89601,f319(f319(f23(f932(x89601,a923)),x89602),f319(f319(f301(x89601),x89603),f180(f932(x89601,a923)))))),f10(x89601,x89602))
% 28.77/28.53 [8961]~P102(x89611)+~P1(f319(f55(x89611),x89612))+E(f319(f319(f23(f932(x89611,a923)),x89612),f319(f319(f301(x89611),x89613),f180(f932(x89611,a923)))),f180(f932(x89611,a923)))+~P1(f319(f319(f321(x89611),x89613),x89612))+E(f319(f319(f102(x89611),x89613),f13(x89611,f319(f319(f23(f932(x89611,a923)),x89612),f319(f319(f301(x89611),x89613),f180(f932(x89611,a923)))))),f13(x89611,x89612))
% 28.77/28.53 [8962]~P4(x89621)+~P1(f319(f55(x89621),x89622))+E(f319(f319(f23(f932(x89621,a923)),x89622),f319(f319(f301(x89621),x89623),f180(f932(x89621,a923)))),f180(f932(x89621,a923)))+~P1(f319(f319(f321(x89621),x89623),x89622))+E(f319(f319(f224(x89621),x89623),f14(x89621,f319(f319(f23(f932(x89621,a923)),x89622),f319(f319(f301(x89621),x89623),f180(f932(x89621,a923)))))),f14(x89621,x89622))
% 28.77/28.53 [8963]~P4(x89631)+~P1(f319(f55(x89631),x89632))+E(f319(f319(f23(f932(x89631,a923)),x89632),f319(f319(f301(x89631),x89633),f180(f932(x89631,a923)))),f180(f932(x89631,a923)))+~P1(f319(f319(f321(x89631),x89633),x89632))+E(f319(f319(f225(x89631),x89633),f15(x89631,f319(f319(f23(f932(x89631,a923)),x89632),f319(f319(f301(x89631),x89633),f180(f932(x89631,a923)))))),f15(x89631,x89632))
% 28.77/28.53 [9026]~P4(x90261)+~P1(f319(f55(x90261),x90262))+E(f319(f319(f23(f932(x90261,a923)),x90262),f319(f319(f301(x90261),x90263),f180(f932(x90261,a923)))),f180(f932(x90261,a923)))+~P1(f319(f319(f321(x90261),x90263),x90262))+E(f319(f319(f224(x90261),x90263),f11(x90261,f224(x90261),f319(f319(f23(f932(x90261,a923)),x90262),f319(f319(f301(x90261),x90263),f180(f932(x90261,a923)))))),f11(x90261,f224(x90261),x90262))
% 28.77/28.53 [9027]~P4(x90271)+~P1(f319(f55(x90271),x90272))+E(f319(f319(f23(f932(x90271,a923)),x90272),f319(f319(f301(x90271),x90273),f180(f932(x90271,a923)))),f180(f932(x90271,a923)))+~P1(f319(f319(f321(x90271),x90273),x90272))+E(f319(f319(f225(x90271),x90273),f12(x90271,f225(x90271),f319(f319(f23(f932(x90271,a923)),x90272),f319(f319(f301(x90271),x90273),f180(f932(x90271,a923)))))),f12(x90271,f225(x90271),x90272))
% 28.77/28.53 [9042]~P102(x90421)+~P1(f319(f55(x90421),x90423))+~P1(f319(f55(x90421),x90422))+E(f319(f319(f93(f932(x90421,a923)),x90422),x90423),f180(f932(x90421,a923)))+E(f319(f319(f102(x90421),f13(x90421,f319(f319(f102(f932(x90421,a923)),x90422),x90423))),f13(x90421,f319(f319(f93(f932(x90421,a923)),x90422),x90423))),f319(f319(f102(x90421),f13(x90421,x90422)),f13(x90421,x90423)))
% 28.77/28.53 [9043]~P102(x90431)+~P1(f319(f55(x90431),x90433))+~P1(f319(f55(x90431),x90432))+E(f319(f319(f93(f932(x90431,a923)),x90432),x90433),f180(f932(x90431,a923)))+E(f319(f319(f93(x90431),f10(x90431,f319(f319(f102(f932(x90431,a923)),x90432),x90433))),f10(x90431,f319(f319(f93(f932(x90431,a923)),x90432),x90433))),f319(f319(f93(x90431),f10(x90431,x90432)),f10(x90431,x90433)))
% 28.77/28.53 [9044]~P4(x90441)+~P1(f319(f55(x90441),x90443))+~P1(f319(f55(x90441),x90442))+E(f319(f319(f93(f932(x90441,a923)),x90442),x90443),f180(f932(x90441,a923)))+E(f319(f319(f224(x90441),f14(x90441,f319(f319(f102(f932(x90441,a923)),x90442),x90443))),f14(x90441,f319(f319(f93(f932(x90441,a923)),x90442),x90443))),f319(f319(f224(x90441),f14(x90441,x90442)),f14(x90441,x90443)))
% 28.77/28.53 [9045]~P4(x90451)+~P1(f319(f55(x90451),x90453))+~P1(f319(f55(x90451),x90452))+E(f319(f319(f93(f932(x90451,a923)),x90452),x90453),f180(f932(x90451,a923)))+E(f319(f319(f225(x90451),f15(x90451,f319(f319(f102(f932(x90451,a923)),x90452),x90453))),f15(x90451,f319(f319(f93(f932(x90451,a923)),x90452),x90453))),f319(f319(f225(x90451),f15(x90451,x90452)),f15(x90451,x90453)))
% 28.77/28.53 [9267]~P4(x92671)+~P1(f319(f55(x92671),x92673))+~P1(f319(f55(x92671),x92672))+E(f319(f319(f93(f932(x92671,a923)),x92672),x92673),f180(f932(x92671,a923)))+E(f319(f319(f224(x92671),f11(x92671,f224(x92671),f319(f319(f102(f932(x92671,a923)),x92672),x92673))),f11(x92671,f224(x92671),f319(f319(f93(f932(x92671,a923)),x92672),x92673))),f319(f319(f224(x92671),f11(x92671,f224(x92671),x92672)),f11(x92671,f224(x92671),x92673)))
% 28.77/28.53 [9268]~P4(x92681)+~P1(f319(f55(x92681),x92683))+~P1(f319(f55(x92681),x92682))+E(f319(f319(f93(f932(x92681,a923)),x92682),x92683),f180(f932(x92681,a923)))+E(f319(f319(f225(x92681),f12(x92681,f225(x92681),f319(f319(f102(f932(x92681,a923)),x92682),x92683))),f12(x92681,f225(x92681),f319(f319(f93(f932(x92681,a923)),x92682),x92683))),f319(f319(f225(x92681),f12(x92681,f225(x92681),x92682)),f12(x92681,f225(x92681),x92683)))
% 28.77/28.53 [10094]~P129(x100943)+E(x100941,x100942)+~P1(f319(f319(f226(x100943),f2(x100943)),x100942))+~P1(f319(f319(f226(x100943),f2(x100943)),x100941))+~E(f319(f319(f236(x100943),x100941),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),f319(f319(f236(x100943),x100942),f319(f95(a925),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))))
% 28.77/28.53 [5300]~P72(x53001)+~P100(x53001)+~E(x53004,f2(x53001))+~E(f319(f95(x53001),x53002),f2(x53001))+E(f319(f95(x53001),x53002),f319(f319(f283(x53001),x53003),x53004))
% 28.77/28.53 [5301]~P72(x53011)+~P100(x53011)+~E(x53013,f2(x53011))+~E(f319(f95(x53011),x53014),f2(x53011))+E(f319(f319(f283(x53011),x53012),x53013),f319(f95(x53011),x53014))
% 28.77/28.53 [5394]~P72(x53942)+~P100(x53942)+~E(x53941,f2(x53942))+~E(f319(f95(x53942),x53944),f2(x53942))+E(x53941,f319(f319(f283(x53942),x53943),f319(f95(x53942),x53944)))
% 28.77/28.53 [5395]~P72(x53951)+~P100(x53951)+~E(x53954,f2(x53951))+~E(f319(f95(x53951),x53953),f2(x53951))+E(f319(f319(f283(x53951),x53952),f319(f95(x53951),x53953)),x53954)
% 28.77/28.53 [5427]~P72(x54271)+~P100(x54271)+~E(x54273,f2(x54271))+E(f319(f95(x54271),x54272),f2(x54271))+~E(f319(f95(x54271),x54272),f319(f319(f283(x54271),x54274),x54273))
% 28.77/28.53 [5428]~P72(x54281)+~P100(x54281)+~E(x54283,f2(x54281))+E(f319(f95(x54281),x54282),f2(x54281))+~E(f319(f319(f283(x54281),x54284),x54283),f319(f95(x54281),x54282))
% 28.77/28.53 [5590]~P72(x55902)+~P100(x55902)+E(x55901,f2(x55902))+~E(f319(f95(x55902),x55903),f2(x55902))+~E(x55901,f319(f319(f283(x55902),x55904),f319(f95(x55902),x55903)))
% 28.77/28.53 [5591]~P72(x55912)+~P100(x55912)+E(x55911,f2(x55912))+~E(f319(f95(x55912),x55913),f2(x55912))+~E(f319(f319(f283(x55912),x55914),f319(f95(x55912),x55913)),x55911)
% 28.77/28.53 [5818]~P72(x58182)+~P100(x58182)+~E(x58181,f2(x58182))+E(x58181,f319(f319(f283(x58182),x58183),f319(f95(x58182),x58184)))+~E(f319(f319(f75(x58182),x58181),f319(f95(x58182),x58184)),x58183)
% 28.77/28.53 [5819]~P72(x58191)+~P100(x58191)+~E(x58194,f2(x58191))+~E(x58192,f319(f319(f75(x58191),x58194),f319(f95(x58191),x58193)))+E(f319(f319(f283(x58191),x58192),f319(f95(x58191),x58193)),x58194)
% 28.77/28.53 [5885]~P72(x58851)+~P100(x58851)+E(f319(f95(x58851),x58852),f2(x58851))+~E(f319(f319(f283(x58851),x58853),f319(f95(x58851),x58852)),x58854)+E(x58853,f319(f319(f75(x58851),x58854),f319(f95(x58851),x58852)))
% 28.77/28.53 [5886]~P72(x58861)+~P100(x58861)+E(f319(f95(x58861),x58862),f2(x58861))+~E(f319(f319(f75(x58861),x58863),f319(f95(x58861),x58862)),x58864)+E(x58863,f319(f319(f283(x58861),x58864),f319(f95(x58861),x58862)))
% 28.77/28.53 [5887]~P72(x58871)+~P100(x58871)+E(f319(f95(x58871),x58872),f2(x58871))+~E(x58873,f319(f319(f283(x58871),x58874),f319(f95(x58871),x58872)))+E(f319(f319(f75(x58871),x58873),f319(f95(x58871),x58872)),x58874)
% 28.77/28.53 [5888]~P72(x58881)+~P100(x58881)+E(f319(f95(x58881),x58882),f2(x58881))+~E(x58883,f319(f319(f75(x58881),x58884),f319(f95(x58881),x58882)))+E(f319(f319(f283(x58881),x58883),f319(f95(x58881),x58882)),x58884)
% 28.77/28.53 [6096]~P65(x60962)+E(x60961,f2(x60962))+~E(f319(f319(f30(x60962),x60963),x60961),x60964)+E(x60963,f319(f319(f75(x60962),x60964),x60961))+~P1(f319(f319(f279(x60962),x60961),x60963))
% 28.77/28.53 [6097]~P65(x60972)+E(x60971,f2(x60972))+~E(x60973,f319(f319(f75(x60972),x60974),x60971))+E(f319(f319(f30(x60972),x60973),x60971),x60974)+~P1(f319(f319(f279(x60972),x60971),x60973))
% 28.77/28.53 [6561]E(f355(x65611,x65612,x65613),x65614)+E(f319(x65611,x65614),f2(a925))+~E(f319(f319(f6(x65613,a925),x65611),x65612),f72(a925))+~P1(f319(f55(x65613),x65612))+~P1(f319(f319(f321(x65613),x65614),x65612))
% 28.77/28.53 [6625]E(f418(x66251,x66252,x66253),x66254)+E(f319(x66251,x66254),f2(a925))+~E(f319(f319(f6(x66253,a925),x66251),x66252),f319(a104,f2(a925)))+~P1(f319(f55(x66253),x66252))+~P1(f319(f319(f321(x66253),x66254),x66252))
% 28.77/28.53 [6735]~P4(x67351)+~P6(x67351)+P1(f319(f319(f227(x67351),x67352),f31(x67351,x67353)))+~P1(f319(f319(f227(x67351),x67352),x67354))+~P1(f319(f319(f321(x67351),x67354),x67353))
% 28.77/28.53 [6913]~P4(x69131)+~P6(x69131)+~P1(f319(f319(f227(x69131),x69134),x69133))+P1(f319(f319(f227(x69131),f32(x69131,x69132)),x69133))+~P1(f319(f319(f321(x69131),x69134),x69132))
% 28.77/28.53 [7174]~P129(x71743)+E(x71741,x71742)+~E(f319(f319(f236(x71743),x71741),f319(a104,x71744)),f319(f319(f236(x71743),x71742),f319(a104,x71744)))+~P1(f319(f319(f226(x71743),f2(x71743)),x71742))+~P1(f319(f319(f226(x71743),f2(x71743)),x71741))
% 28.77/28.53 [7386]~E(f359(x73862,x73863,x73861,x73864),x73864)+~E(f319(x73862,x73864),f72(a925))+E(f319(f319(f6(x73861,a925),x73862),x73863),f72(a925))+~P1(f319(f55(x73861),x73863))+~P1(f319(f319(f321(x73861),x73864),x73863))
% 28.77/28.53 [7393]~P121(x73934)+~P138(x73934)+E(f319(x73931,f455(x73931,x73932,x73933,x73934)),f2(x73934))+~E(f319(f319(f9(x73933,x73934),x73931),x73932),f2(x73934))+~P1(f319(f55(x73933),x73932))
% 28.77/28.53 [7483]~E(f421(x74832,x74833,x74831,x74834),x74834)+~E(f319(x74832,x74834),f319(a104,f2(a925)))+E(f319(f319(f6(x74831,a925),x74832),x74833),f319(a104,f2(a925)))+~P1(f319(f55(x74831),x74833))+~P1(f319(f319(f321(x74831),x74834),x74833))
% 28.77/28.53 [8214]~E(f319(x82142,x82144),f72(a925))+~E(f319(x82142,f359(x82142,x82143,x82141,x82144)),f2(a925))+E(f319(f319(f6(x82141,a925),x82142),x82143),f72(a925))+~P1(f319(f55(x82141),x82143))+~P1(f319(f319(f321(x82141),x82144),x82143))
% 28.77/28.53 [8252]~E(f319(x82522,x82524),f319(a104,f2(a925)))+~E(f319(x82522,f421(x82522,x82523,x82521,x82524)),f2(a925))+E(f319(f319(f6(x82521,a925),x82522),x82523),f319(a104,f2(a925)))+~P1(f319(f55(x82521),x82523))+~P1(f319(f319(f321(x82521),x82524),x82523))
% 28.77/28.53 [8338]~P143(x83382)+~P123(x83382)+~P1(f319(x83381,x83384))+~P1(f319(f319(f279(x83382),x83383),f319(f319(f74(x83382),x83384),f2(x83382))))+P1(f319(x83381,f319(f319(f75(x83382),x83383),f872(x83383,x83381,x83382))))
% 28.77/28.53 [8809]~P4(x88091)+~P14(x88091,x88094)+P14(x88091,x88092)+~E(x88092,f319(f319(f143(x88091),x88093),x88094))+~P1(f319(f319(f226(x88091),x88093),f749(x88092,x88091,x88094,x88093)))
% 28.77/28.53 [8846]E(x88461,x88462)+E(f319(f319(f23(a1),f393(x88463,x88462,x88464,x88461)),f394(x88463,x88462,x88464,x88461)),x88461)+~E(f319(f319(f74(a1),x88461),x88464),x88462)+~P1(f319(f319(f227(a1),f2(a1)),x88464))+~P1(f319(f319(f321(a1),x88462),x88463))
% 28.77/28.53 [8847]E(x88471,x88472)+E(f319(f319(f74(a1),f396(x88473,x88472,x88474,x88471)),f397(x88473,x88472,x88474,x88471)),x88471)+~E(f319(f319(f23(a1),x88471),x88474),x88472)+~P1(f319(f319(f227(a1),f2(a1)),x88474))+~P1(f319(f319(f321(a1),x88472),x88473))
% 28.77/28.53 [9040]E(f319(x90401,f616(x90402,x90401,x90403,x90404)),x90402)+P1(f319(f319(f226(a925),x90404),f617(x90402,x90401,x90403,x90404)))+~P1(f319(f319(f226(a1),x90402),f319(x90401,x90403)))+~P1(f319(f319(f227(a925),x90404),x90403))+~P1(f319(f319(f226(a1),f319(x90401,x90404)),x90402))
% 28.77/28.53 [9041]~P4(x90411)+~P14(x90411,x90413)+P14(x90411,x90412)+~E(x90412,f319(f319(f143(x90411),x90414),x90413))+P1(f319(f319(f321(x90411),f749(x90412,x90411,x90413,x90414)),f319(f164(x90411),x90413)))
% 28.77/28.53 [9059]~P121(x90594)+~P138(x90594)+~E(f319(f319(f9(x90591,x90594),x90592),x90593),f2(x90594))+~P1(f319(f55(x90591),x90593))+P1(f319(f319(f321(x90591),f455(x90592,x90593,x90591,x90594)),x90593))
% 28.77/28.53 [9098]~E(f319(x90982,x90984),f72(a925))+E(f319(f319(f6(x90981,a925),x90982),x90983),f72(a925))+~P1(f319(f55(x90981),x90983))+~P1(f319(f319(f321(x90981),x90984),x90983))+P1(f319(f319(f321(x90981),f359(x90982,x90983,x90981,x90984)),x90983))
% 28.77/28.53 [9110]E(x91101,x91102)+~E(f319(f319(f74(a1),x91102),x91104),x91101)+~P1(f319(f319(f227(a1),f2(a1)),x91104))+~P1(f319(f319(f321(a1),x91101),x91103))+P1(f319(f319(f321(a1),f393(x91103,x91101,x91104,x91102)),x91103))
% 28.77/28.53 [9111]E(x91111,x91112)+~E(f319(f319(f23(a1),x91112),x91114),x91111)+~P1(f319(f319(f227(a1),f2(a1)),x91114))+~P1(f319(f319(f321(a1),x91111),x91113))+P1(f319(f319(f321(a1),f396(x91113,x91111,x91114,x91112)),x91113))
% 28.77/28.53 [9113]~E(f319(x91132,x91134),f319(a104,f2(a925)))+E(f319(f319(f6(x91131,a925),x91132),x91133),f319(a104,f2(a925)))+~P1(f319(f55(x91131),x91133))+~P1(f319(f319(f321(x91131),x91134),x91133))+P1(f319(f319(f321(x91131),f421(x91132,x91133,x91131,x91134)),x91133))
% 28.77/28.53 [9118]P63(x91182,x91183,x91184,x91181)+E(x91181,f180(f932(x91182,a923)))+~P1(f319(f55(x91182),x91184))+~P1(f319(f55(x91182),x91181))+P1(f319(f319(f321(x91182),f817(x91183,x91181,x91184,x91182)),x91184))
% 28.77/28.53 [9119]P63(x91192,x91193,x91194,x91191)+E(x91191,f180(f932(x91192,a923)))+~P1(f319(f55(x91192),x91194))+~P1(f319(f55(x91192),x91191))+P1(f319(f319(f321(x91192),f561(x91191,x91194,x91193,x91192)),x91194))
% 28.77/28.53 [9120]P63(x91202,x91203,x91204,x91201)+E(x91201,f180(f932(x91202,a923)))+~P1(f319(f55(x91202),x91204))+~P1(f319(f55(x91202),x91201))+P1(f319(f319(f321(x91202),f818(x91201,x91204,x91203,x91202)),x91204))
% 28.77/28.53 [9197]E(x91971,x91972)+~E(f319(f319(f74(a1),x91972),x91974),x91971)+~P1(f319(f319(f227(a1),f2(a1)),x91974))+~P1(f319(f319(f321(a1),x91971),x91973))+P1(f319(f319(f321(a1),f394(x91973,x91971,x91974,x91972)),f295(a1,f72(a1),x91974)))
% 28.77/28.53 [9198]E(x91981,x91982)+~E(f319(f319(f23(a1),x91982),x91984),x91981)+~P1(f319(f319(f227(a1),f2(a1)),x91984))+~P1(f319(f319(f321(a1),x91981),x91983))+P1(f319(f319(f321(a1),f397(x91983,x91981,x91984,x91982)),f295(a1,f72(a1),x91984)))
% 28.77/28.53 [9273]P1(f319(f319(f226(a925),x92731),f616(x92732,x92733,x92734,x92731)))+~P1(f319(f319(f226(a1),x92732),f319(x92733,x92734)))+P1(f319(f319(f226(a925),x92731),f617(x92732,x92733,x92734,x92731)))+~P1(f319(f319(f227(a925),x92731),x92734))+~P1(f319(f319(f226(a1),f319(x92733,x92731)),x92732))
% 28.77/28.53 [9390]E(f319(x93901,f616(x93902,x93901,x93903,x93904)),x93902)+~P1(f319(f319(f226(a1),x93902),f319(x93901,x93903)))+P1(f319(f319(f227(a925),f617(x93902,x93901,x93903,x93904)),x93903))+~P1(f319(f319(f227(a925),x93904),x93903))+~P1(f319(f319(f226(a1),f319(x93901,x93904)),x93902))
% 28.77/28.53 [9521]~P1(f319(f319(f226(a1),x95212),f319(x95213,x95214)))+P1(f319(f319(f226(a925),x95211),f617(x95212,x95213,x95214,x95211)))+P1(f319(f319(f226(a925),f616(x95212,x95213,x95214,x95211)),x95214))+~P1(f319(f319(f227(a925),x95211),x95214))+~P1(f319(f319(f226(a1),f319(x95213,x95211)),x95212))
% 28.77/28.53 [9522]~P1(f319(f319(f226(a1),x95222),f319(x95223,x95224)))+P1(f319(f319(f226(a925),x95221),f616(x95222,x95223,x95224,x95221)))+P1(f319(f319(f227(a925),f617(x95222,x95223,x95224,x95221)),x95224))+~P1(f319(f319(f227(a925),x95221),x95224))+~P1(f319(f319(f226(a1),f319(x95223,x95221)),x95222))
% 28.77/28.53 [9631]~P1(f319(f319(f226(a1),x96311),f319(x96312,x96313)))+P1(f319(f319(f227(a925),f617(x96311,x96312,x96313,x96314)),x96313))+~P1(f319(f319(f227(a925),x96314),x96313))+~P1(f319(f319(f226(a1),f319(x96312,x96314)),x96311))+P1(f319(f319(f226(a925),f616(x96311,x96312,x96313,x96314)),x96313))
% 28.77/28.53 [9719]E(x97191,f180(f932(x97192,a923)))+~P1(f319(f55(x97192),x97194))+~P1(f319(f55(x97192),x97191))+P1(f319(f319(f321(f931(f932(x97192,a923),f932(x97192,a923))),f319(f319(f244(f932(x97192,a923),f932(x97192,a923)),x97194),x97191)),f311(x97192,x97193)))+P1(f319(f319(f321(x97192),f571(x97193,x97191,x97194,x97192)),x97194))
% 28.77/28.53 [9720]E(x97201,f180(f932(x97202,a923)))+~P1(f319(f55(x97202),x97204))+~P1(f319(f55(x97202),x97201))+P1(f319(f319(f321(f931(f932(x97202,a923),f932(x97202,a923))),f319(f319(f244(f932(x97202,a923),f932(x97202,a923)),x97204),x97201)),f311(x97202,x97203)))+P1(f319(f319(f321(x97202),f618(x97203,x97201,x97204,x97202)),x97204))
% 28.77/28.53 [10417]E(f319(x104171,f616(x104172,x104171,x104173,x104174)),x104172)+~P1(f319(f319(f226(a1),x104172),f319(x104171,x104173)))+~P1(f319(f319(f226(a1),f319(f69(a1),f319(f319(f23(a1),f319(x104171,f319(f319(f74(a925),f617(x104172,x104171,x104173,x104174)),f72(a925)))),f319(x104171,f617(x104172,x104171,x104173,x104174))))),f72(a1)))+~P1(f319(f319(f227(a925),x104174),x104173))+~P1(f319(f319(f226(a1),f319(x104171,x104174)),x104172))
% 28.77/28.53 [10418]~P1(f319(f319(f226(a1),x104182),f319(x104183,x104184)))+P1(f319(f319(f226(a925),x104181),f616(x104182,x104183,x104184,x104181)))+~P1(f319(f319(f226(a1),f319(f69(a1),f319(f319(f23(a1),f319(x104183,f319(f319(f74(a925),f617(x104182,x104183,x104184,x104181)),f72(a925)))),f319(x104183,f617(x104182,x104183,x104184,x104181))))),f72(a1)))+~P1(f319(f319(f227(a925),x104181),x104184))+~P1(f319(f319(f226(a1),f319(x104183,x104181)),x104182))
% 28.77/28.53 [10419]~P1(f319(f319(f226(a1),x104191),f319(x104192,x104193)))+~P1(f319(f319(f226(a1),f319(f69(a1),f319(f319(f23(a1),f319(x104192,f319(f319(f74(a925),f617(x104191,x104192,x104193,x104194)),f72(a925)))),f319(x104192,f617(x104191,x104192,x104193,x104194))))),f72(a1)))+~P1(f319(f319(f227(a925),x104194),x104193))+~P1(f319(f319(f226(a1),f319(x104192,x104194)),x104191))+P1(f319(f319(f226(a925),f616(x104191,x104192,x104193,x104194)),x104193))
% 28.77/28.53 [5842]~P72(x58422)+~P100(x58422)+E(x58421,f2(x58422))+~E(f319(f319(f283(x58422),x58423),x58421),f319(f95(x58422),x58424))+E(x58423,f319(f319(f75(x58422),f319(f95(x58422),x58424)),x58421))
% 28.77/28.53 [5843]~P72(x58432)+~P100(x58432)+E(x58431,f2(x58432))+~E(f319(f95(x58432),x58433),f319(f319(f283(x58432),x58434),x58431))+E(f319(f319(f75(x58432),f319(f95(x58432),x58433)),x58431),x58434)
% 28.77/28.53 [5999]~P72(x59992)+~P100(x59992)+E(x59991,f2(x59992))+E(f319(f95(x59992),x59993),f319(f319(f283(x59992),x59994),x59991))+~E(f319(f319(f75(x59992),f319(f95(x59992),x59993)),x59991),x59994)
% 28.77/28.53 [6000]~P72(x60002)+~P100(x60002)+E(x60001,f2(x60002))+E(f319(f319(f283(x60002),x60003),x60001),f319(f95(x60002),x60004))+~E(x60003,f319(f319(f75(x60002),f319(f95(x60002),x60004)),x60001))
% 28.77/28.53 [6132]~P72(x61321)+~P100(x61321)+~E(f319(f95(x61321),x61322),f2(x61321))+E(f319(f95(x61321),x61322),f319(f319(f283(x61321),x61323),x61324))+~E(f319(f319(f75(x61321),f319(f95(x61321),x61322)),x61324),x61323)
% 28.77/28.53 [6133]~P72(x61331)+~P100(x61331)+~E(f319(f95(x61331),x61334),f2(x61331))+E(f319(f319(f283(x61331),x61332),x61333),f319(f95(x61331),x61334))+~E(x61332,f319(f319(f75(x61331),f319(f95(x61331),x61334)),x61333))
% 28.77/28.53 [7446]~P74(x74461)+P1(f319(f319(f227(x74461),x74462),f2(x74461)))+~P1(f319(f319(f226(x74461),x74463),f2(x74461)))+P1(f319(f319(f227(x74461),f2(x74461)),x74462))+P1(f319(f319(f226(x74461),x74463),f319(f319(f283(x74461),x74464),x74462)))
% 28.77/28.53 [7447]~P74(x74471)+P1(f319(f319(f227(x74471),x74472),f2(x74471)))+~P1(f319(f319(f227(x74471),x74473),f2(x74471)))+P1(f319(f319(f227(x74471),f2(x74471)),x74472))+P1(f319(f319(f227(x74471),x74473),f319(f319(f283(x74471),x74474),x74472)))
% 28.77/28.53 [7692]~P74(x76921)+P1(f319(f319(f226(x76921),x76922),f2(x76921)))+P1(f319(f319(f227(x76921),x76923),f2(x76921)))+P1(f319(f319(f227(x76921),f2(x76921)),x76923))+~P1(f319(f319(f226(x76921),x76922),f319(f319(f283(x76921),x76924),x76923)))
% 28.77/28.53 [7693]~P74(x76931)+P1(f319(f319(f227(x76931),x76932),f2(x76931)))+P1(f319(f319(f227(x76931),x76933),f2(x76931)))+P1(f319(f319(f227(x76931),f2(x76931)),x76933))+~P1(f319(f319(f227(x76931),x76932),f319(f319(f283(x76931),x76934),x76933)))
% 28.77/28.53 [7807]E(x78071,x78072)+~E(f319(f319(f156(x78073),x78074),x78071),f319(f319(f156(x78073),x78074),x78072))+~P1(f319(f129(x78073),x78074))+~P1(f319(f319(f227(a925),x78072),f319(f181(f926(x78073)),x78074)))+~P1(f319(f319(f227(a925),x78071),f319(f181(f926(x78073)),x78074)))
% 28.77/28.53 [7808]E(x78081,x78082)+~E(f319(f319(f156(x78083),x78084),x78081),f319(f319(f156(x78083),x78084),x78082))+~P1(f319(f129(x78083),x78084))+~P1(f319(f319(f227(a925),x78082),f319(f181(f926(x78083)),x78084)))+~P1(f319(f319(f227(a925),x78081),f319(f181(f926(x78083)),x78084)))
% 28.77/28.53 [8174]~P74(x81741)+~P1(f319(f319(f226(x81741),x81743),f2(x81741)))+P1(f319(f319(f227(x81741),f2(x81741)),x81742))+~P1(f319(f319(f226(x81741),x81744),f319(f319(f75(x81741),x81743),x81742)))+P1(f319(f319(f226(x81741),x81743),f319(f319(f283(x81741),x81744),x81742)))
% 28.77/28.53 [8175]~P74(x81751)+~P1(f319(f319(f227(x81751),x81753),f2(x81751)))+P1(f319(f319(f227(x81751),f2(x81751)),x81752))+~P1(f319(f319(f227(x81751),x81754),f319(f319(f75(x81751),x81753),x81752)))+P1(f319(f319(f227(x81751),x81753),f319(f319(f283(x81751),x81754),x81752)))
% 28.77/28.53 [8176]~P74(x81761)+~P1(f319(f319(f227(x81761),x81762),f2(x81761)))+P1(f319(f319(f227(x81761),f2(x81761)),x81762))+~P1(f319(f319(f226(x81761),x81764),f319(f319(f75(x81761),x81763),x81762)))+P1(f319(f319(f226(x81761),x81763),f319(f319(f283(x81761),x81764),x81762)))
% 28.77/28.53 [8177]~P74(x81771)+~P1(f319(f319(f227(x81771),x81772),f2(x81771)))+P1(f319(f319(f227(x81771),f2(x81771)),x81772))+~P1(f319(f319(f226(x81771),x81774),f319(f319(f283(x81771),x81773),x81772)))+P1(f319(f319(f226(x81771),x81773),f319(f319(f75(x81771),x81774),x81772)))
% 28.77/28.53 [8178]~P74(x81781)+~P1(f319(f319(f227(x81781),x81782),f2(x81781)))+P1(f319(f319(f227(x81781),f2(x81781)),x81782))+~P1(f319(f319(f227(x81781),x81784),f319(f319(f75(x81781),x81783),x81782)))+P1(f319(f319(f227(x81781),x81783),f319(f319(f283(x81781),x81784),x81782)))
% 28.77/28.53 [8179]~P74(x81791)+~P1(f319(f319(f227(x81791),x81792),f2(x81791)))+P1(f319(f319(f227(x81791),f2(x81791)),x81792))+~P1(f319(f319(f227(x81791),x81794),f319(f319(f283(x81791),x81793),x81792)))+P1(f319(f319(f227(x81791),x81793),f319(f319(f75(x81791),x81794),x81792)))
% 28.77/28.53 [8320]~P4(x83201)+~P14(x83201,x83202)+~P1(f319(f319(f226(a925),x83203),x83204))+P1(f319(f319(f226(x83201),f319(f319(f156(x83201),x83202),x83203)),f319(f319(f156(x83201),x83202),x83204)))+~P1(f319(f319(f227(a925),x83204),f319(f181(f926(x83201)),x83202)))
% 28.77/28.53 [8321]~P4(x83211)+~P14(x83211,x83212)+~P1(f319(f319(f226(a925),x83213),x83214))+P1(f319(f319(f226(x83211),f319(f319(f156(x83211),x83212),x83213)),f319(f319(f156(x83211),x83212),x83214)))+~P1(f319(f319(f227(a925),x83214),f319(f181(f926(x83211)),x83212)))
% 28.77/28.53 [8373]~P129(x83731)+~P1(f319(f319(f226(x83731),x83732),f72(x83731)))+~P1(f319(f319(f226(x83731),f2(x83731)),x83732))+~P1(f319(f319(f226(a925),x83734),x83733))+P1(f319(f319(f226(x83731),f319(f319(f236(x83731),x83732),x83733)),f319(f319(f236(x83731),x83732),x83734)))
% 28.77/28.53 [8374]~P129(x83741)+~P1(f319(f319(f227(x83741),x83742),f72(x83741)))+~P1(f319(f319(f227(x83741),f2(x83741)),x83742))+~P1(f319(f319(f227(a925),x83744),x83743))+P1(f319(f319(f227(x83741),f319(f319(f236(x83741),x83742),x83743)),f319(f319(f236(x83741),x83742),x83744)))
% 28.77/28.53 [8375]~P129(x83751)+~P1(f319(f319(f226(x83751),f2(x83751)),x83752))+~P1(f319(f319(f227(a925),f2(a925)),x83753))+~P1(f319(f319(f227(x83751),x83752),x83754))+P1(f319(f319(f227(x83751),f319(f319(f236(x83751),x83752),x83753)),f319(f319(f236(x83751),x83754),x83753)))
% 28.77/28.53 [8394]~P4(x83941)+~P14(x83941,f319(f160(x83941),x83942))+~P1(f319(f319(f226(a925),x83944),x83943))+P1(f319(f319(f226(x83941),f319(f319(f156(x83941),x83942),x83943)),f319(f319(f156(x83941),x83942),x83944)))+~P1(f319(f319(f227(a925),x83943),f319(f181(f926(x83941)),x83942)))
% 28.77/28.53 [8641]~P74(x86411)+~P1(f319(f319(f226(x86411),x86412),f2(x86411)))+~P1(f319(f319(f226(x86411),x86413),x86414))+~P1(f319(f319(f227(x86411),f2(x86411)),f319(f319(f75(x86411),x86413),x86414)))+P1(f319(f319(f226(x86411),f319(f319(f283(x86411),x86412),x86413)),f319(f319(f283(x86411),x86412),x86414)))
% 28.77/28.53 [8642]~P75(x86421)+~P1(f319(f319(f227(x86421),x86422),f2(x86421)))+~P1(f319(f319(f227(x86421),x86423),x86424))+~P1(f319(f319(f227(x86421),f2(x86421)),f319(f319(f75(x86421),x86423),x86424)))+P1(f319(f319(f227(x86421),f319(f319(f283(x86421),x86422),x86423)),f319(f319(f283(x86421),x86422),x86424)))
% 28.77/28.53 [8651]~P75(x86511)+~P1(f319(f319(f226(x86511),x86514),x86513))+~P1(f319(f319(f226(x86511),f2(x86511)),x86512))+~P1(f319(f319(f227(x86511),f2(x86511)),f319(f319(f75(x86511),x86513),x86514)))+P1(f319(f319(f226(x86511),f319(f319(f283(x86511),x86512),x86513)),f319(f319(f283(x86511),x86512),x86514)))
% 28.77/28.53 [8652]~P75(x86521)+~P1(f319(f319(f227(x86521),x86524),x86523))+~P1(f319(f319(f227(x86521),f2(x86521)),x86522))+~P1(f319(f319(f227(x86521),f2(x86521)),f319(f319(f75(x86521),x86523),x86524)))+P1(f319(f319(f227(x86521),f319(f319(f283(x86521),x86522),x86523)),f319(f319(f283(x86521),x86522),x86524)))
% 28.77/28.53 [8756]P1(f319(x87561,x87562))+~P1(f319(f55(x87564),x87562))+P1(f319(x87561,f339(x87561,x87563,x87562,x87564)))+~P1(f319(x87561,f180(f932(x87564,a923))))+~P1(f319(f319(f226(f932(x87564,a923)),x87562),x87563))
% 28.77/28.53 [8765]P1(f319(x87651,x87652))+P1(f319(f55(x87653),f339(x87651,x87654,x87652,x87653)))+~P1(f319(f55(x87653),x87652))+~P1(f319(x87651,f180(f932(x87653,a923))))+~P1(f319(f319(f226(f932(x87653,a923)),x87652),x87654))
% 28.77/28.53 [9035]E(f319(f319(f74(a1),f398(x90351,x90352,x90353,x90354)),f399(x90351,x90352,x90353,x90354)),x90354)+~P1(f319(f319(f227(a1),f2(a1)),x90353))+~P1(f319(f319(f227(a1),x90352),x90354))+~P1(f319(f319(f321(a1),x90352),x90351))+P1(f319(f319(f227(a1),x90352),f319(f319(f23(a1),x90354),x90353)))
% 28.77/28.53 [9254]~P1(f319(f319(f227(a1),f2(a1)),x92543))+~P1(f319(f319(f227(a1),x92542),x92544))+~P1(f319(f319(f321(a1),x92542),x92541))+P1(f319(f319(f321(a1),f398(x92541,x92542,x92543,x92544)),x92541))+P1(f319(f319(f227(a1),x92542),f319(f319(f23(a1),x92544),x92543)))
% 28.77/28.53 [9266]P1(f319(x92661,x92662))+~P1(f319(f55(x92663),x92662))+P1(f319(f319(f321(x92663),f340(x92661,x92664,x92662,x92663)),x92664))+~P1(f319(x92661,f180(f932(x92663,a923))))+~P1(f319(f319(f226(f932(x92663,a923)),x92662),x92664))
% 28.77/28.53 [9283]E(f319(f319(f74(a1),f385(x92831,x92832,x92833,x92834)),f386(x92831,x92832,x92833,x92834)),x92834)+~P1(f319(f319(f227(a1),f2(a1)),x92833))+~P1(f319(f319(f226(a1),x92832),x92834))+P1(f319(f319(f226(a1),x92832),f319(f319(f23(a1),x92834),x92833)))+~P1(f319(f319(f321(a1),f319(f319(f23(a1),x92832),f72(a1))),x92831))
% 28.77/28.53 [9338]~P1(f319(f319(f227(a1),f2(a1)),x93383))+~P1(f319(f319(f227(a1),x93381),x93382))+~P1(f319(f319(f321(a1),x93381),x93384))+P1(f319(f319(f321(a1),f399(x93384,x93381,x93383,x93382)),f295(a1,f72(a1),x93383)))+P1(f319(f319(f227(a1),x93381),f319(f319(f23(a1),x93382),x93383)))
% 28.77/28.53 [9364]~P79(x93642)+~E(f803(x93643,x93644,x93641,x93642),f804(x93643,x93644,x93641,x93642))+~P1(f319(f55(x93641),f805(x93643,x93644,x93641,x93642)))+E(f319(f319(f6(f932(x93641,a923),x93642),f319(f6(x93641,x93642),x93643)),x93644),f319(f319(f6(x93641,x93642),x93643),f31(f932(x93641,a923),x93644)))+~P1(f319(f55(f932(x93641,a923)),x93644))
% 28.77/28.53 [9368]~P79(x93682)+~E(f319(x93683,f807(x93683,x93684,x93681,x93682)),f2(x93682))+~P1(f319(f55(x93681),f805(x93683,x93684,x93681,x93682)))+E(f319(f319(f6(f932(x93681,a923),x93682),f319(f6(x93681,x93682),x93683)),x93684),f319(f319(f6(x93681,x93682),x93683),f31(f932(x93681,a923),x93684)))+~P1(f319(f55(f932(x93681,a923)),x93684))
% 28.77/28.53 [9434]~P1(f319(f319(f227(a1),f2(a1)),x94343))+~P1(f319(f319(f226(a1),x94342),x94344))+P1(f319(f319(f321(a1),f385(x94341,x94342,x94343,x94344)),x94341))+P1(f319(f319(f226(a1),x94342),f319(f319(f23(a1),x94344),x94343)))+~P1(f319(f319(f321(a1),f319(f319(f23(a1),x94342),f72(a1))),x94341))
% 28.77/28.53 [9478]~P1(f319(f319(f227(a1),f2(a1)),x94783))+~P1(f319(f319(f226(a1),x94781),x94782))+P1(f319(f319(f321(a1),f386(x94784,x94781,x94783,x94782)),f295(a1,f72(a1),x94783)))+P1(f319(f319(f226(a1),x94781),f319(f319(f23(a1),x94782),x94783)))+~P1(f319(f319(f321(a1),f319(f319(f23(a1),x94781),f72(a1))),x94784))
% 28.77/28.53 [9500]~P79(x95002)+~E(f803(x95003,x95004,x95001,x95002),f804(x95003,x95004,x95001,x95002))+E(f319(f319(f6(f932(x95001,a923),x95002),f319(f6(x95001,x95002),x95003)),x95004),f319(f319(f6(x95001,x95002),x95003),f31(f932(x95001,a923),x95004)))+P1(f319(f319(f321(f932(x95001,a923)),f805(x95003,x95004,x95001,x95002)),x95004))+~P1(f319(f55(f932(x95001,a923)),x95004))
% 28.77/28.53 [9505]~P79(x95052)+~E(f319(x95053,f807(x95053,x95054,x95051,x95052)),f2(x95052))+E(f319(f319(f6(f932(x95051,a923),x95052),f319(f6(x95051,x95052),x95053)),x95054),f319(f319(f6(x95051,x95052),x95053),f31(f932(x95051,a923),x95054)))+P1(f319(f319(f321(f932(x95051,a923)),f805(x95053,x95054,x95051,x95052)),x95054))+~P1(f319(f55(f932(x95051,a923)),x95054))
% 28.77/28.53 [9608]~P79(x96082)+~P1(f319(f55(x96081),f805(x96083,x96084,x96081,x96082)))+E(f319(f319(f6(f932(x96081,a923),x96082),f319(f6(x96081,x96082),x96083)),x96084),f319(f319(f6(x96081,x96082),x96083),f31(f932(x96081,a923),x96084)))+P1(f319(f319(f321(f932(x96081,a923)),f804(x96083,x96084,x96081,x96082)),x96084))+~P1(f319(f55(f932(x96081,a923)),x96084))
% 28.77/28.53 [9609]~P79(x96092)+~P1(f319(f55(x96091),f805(x96093,x96094,x96091,x96092)))+E(f319(f319(f6(f932(x96091,a923),x96092),f319(f6(x96091,x96092),x96093)),x96094),f319(f319(f6(x96091,x96092),x96093),f31(f932(x96091,a923),x96094)))+P1(f319(f319(f321(f932(x96091,a923)),f803(x96093,x96094,x96091,x96092)),x96094))+~P1(f319(f55(f932(x96091,a923)),x96094))
% 28.77/28.53 [9689]~P79(x96892)+E(f319(f319(f6(f932(x96891,a923),x96892),f319(f6(x96891,x96892),x96893)),x96894),f319(f319(f6(x96891,x96892),x96893),f31(f932(x96891,a923),x96894)))+P1(f319(f319(f321(f932(x96891,a923)),f805(x96893,x96894,x96891,x96892)),x96894))+P1(f319(f319(f321(f932(x96891,a923)),f804(x96893,x96894,x96891,x96892)),x96894))+~P1(f319(f55(f932(x96891,a923)),x96894))
% 28.77/28.53 [9690]~P79(x96902)+E(f319(f319(f6(f932(x96901,a923),x96902),f319(f6(x96901,x96902),x96903)),x96904),f319(f319(f6(x96901,x96902),x96903),f31(f932(x96901,a923),x96904)))+P1(f319(f319(f321(f932(x96901,a923)),f805(x96903,x96904,x96901,x96902)),x96904))+P1(f319(f319(f321(f932(x96901,a923)),f803(x96903,x96904,x96901,x96902)),x96904))+~P1(f319(f55(f932(x96901,a923)),x96904))
% 28.77/28.53 [9708]~P79(x97082)+P1(f319(f319(f321(x97081),f807(x97083,x97084,x97081,x97082)),f804(x97083,x97084,x97081,x97082)))+~P1(f319(f55(x97081),f805(x97083,x97084,x97081,x97082)))+E(f319(f319(f6(f932(x97081,a923),x97082),f319(f6(x97081,x97082),x97083)),x97084),f319(f319(f6(x97081,x97082),x97083),f31(f932(x97081,a923),x97084)))+~P1(f319(f55(f932(x97081,a923)),x97084))
% 28.77/28.53 [9709]~P79(x97092)+P1(f319(f319(f321(x97091),f807(x97093,x97094,x97091,x97092)),f803(x97093,x97094,x97091,x97092)))+~P1(f319(f55(x97091),f805(x97093,x97094,x97091,x97092)))+E(f319(f319(f6(f932(x97091,a923),x97092),f319(f6(x97091,x97092),x97093)),x97094),f319(f319(f6(x97091,x97092),x97093),f31(f932(x97091,a923),x97094)))+~P1(f319(f55(f932(x97091,a923)),x97094))
% 28.77/28.53 [9722]P1(f319(x97221,x97222))+~P1(f319(f319(f321(x97223),f340(x97221,x97224,x97222,x97223)),f339(x97221,x97224,x97222,x97223)))+~P1(f319(f55(x97223),x97222))+~P1(f319(x97221,f180(f932(x97223,a923))))+~P1(f319(f319(f226(f932(x97223,a923)),x97222),x97224))
% 28.77/28.53 [9759]~P79(x97592)+P1(f319(f319(f321(x97591),f807(x97593,x97594,x97591,x97592)),f804(x97593,x97594,x97591,x97592)))+E(f319(f319(f6(f932(x97591,a923),x97592),f319(f6(x97591,x97592),x97593)),x97594),f319(f319(f6(x97591,x97592),x97593),f31(f932(x97591,a923),x97594)))+P1(f319(f319(f321(f932(x97591,a923)),f805(x97593,x97594,x97591,x97592)),x97594))+~P1(f319(f55(f932(x97591,a923)),x97594))
% 28.77/28.53 [9760]~P79(x97602)+P1(f319(f319(f321(x97601),f807(x97603,x97604,x97601,x97602)),f803(x97603,x97604,x97601,x97602)))+E(f319(f319(f6(f932(x97601,a923),x97602),f319(f6(x97601,x97602),x97603)),x97604),f319(f319(f6(x97601,x97602),x97603),f31(f932(x97601,a923),x97604)))+P1(f319(f319(f321(f932(x97601,a923)),f805(x97603,x97604,x97601,x97602)),x97604))+~P1(f319(f55(f932(x97601,a923)),x97604))
% 28.77/28.53 [9942]P1(f319(x99421,x99422))+~P1(f319(f55(x99423),x99422))+~P1(f319(x99421,f319(f319(f301(x99423),f340(x99421,x99424,x99422,x99423)),f339(x99421,x99424,x99422,x99423))))+~P1(f319(x99421,f180(f932(x99423,a923))))+~P1(f319(f319(f226(f932(x99423,a923)),x99422),x99424))
% 28.77/28.53 [7943]~P74(x79431)+P1(f319(f319(f227(x79431),x79432),f2(x79431)))+~P1(f319(f319(f226(x79431),f2(x79431)),x79434))+P1(f319(f319(f227(x79431),f2(x79431)),x79432))+P1(f319(f319(f226(x79431),f319(f319(f283(x79431),x79433),x79432)),x79434))
% 28.77/28.53 [7944]~P74(x79441)+P1(f319(f319(f227(x79441),x79442),f2(x79441)))+P1(f319(f319(f227(x79441),f2(x79441)),x79442))+~P1(f319(f319(f227(x79441),f2(x79441)),x79444))+P1(f319(f319(f227(x79441),f319(f319(f283(x79441),x79443),x79442)),x79444))
% 28.77/28.53 [8161]~P6(x81611)+~P41(x81611,x81611,x81614)+~E(x81613,f88(x81611,x81614))+P1(f319(f319(f226(x81611),x81612),x81613))+~P1(f319(f319(f226(x81611),x81612),f319(x81614,f319(f319(f102(x81611),x81612),x81613))))
% 28.77/28.53 [8227]~P1(f319(f319(f226(a1),x82274),f2(a1)))+~E(x82272,f319(f319(f74(a1),f319(f319(f75(a1),x82271),x82273)),x82274))+P1(f319(f319(f227(a1),f2(a1)),x82271))+~P1(f319(f319(f227(a1),x82271),x82274))+P1(f319(f43(x82272,x82271),f319(f319(f244(a1,a1),x82273),x82274)))
% 28.77/28.53 [8261]~P1(f319(x82611,x82614))+P1(f319(x82611,f435(x82612,x82611,x82613)))+~P1(f319(f319(f226(a1),f2(a1)),x82612))+~P1(f319(f319(f227(a1),f2(a1)),x82613))+P1(f319(x82611,f319(f319(f23(a1),x82614),f319(f319(f75(a1),x82612),x82613))))
% 28.77/28.53 [8262]~P1(f319(x82621,x82624))+P1(f319(x82621,f441(x82622,x82621,x82623)))+~P1(f319(f319(f226(a1),f2(a1)),x82622))+~P1(f319(f319(f227(a1),f2(a1)),x82623))+P1(f319(x82621,f319(f319(f74(a1),x82624),f319(f319(f75(a1),x82622),x82623))))
% 28.77/28.53 [8263]~P74(x82631)+P1(f319(f319(f227(x82631),x82632),f2(x82631)))+P1(f319(f319(f227(x82631),f2(x82631)),x82632))+P1(f319(f319(f226(x82631),f2(x82631)),x82633))+~P1(f319(f319(f226(x82631),f319(f319(f283(x82631),x82634),x82632)),x82633))
% 28.77/28.53 [8264]~P74(x82641)+P1(f319(f319(f227(x82641),x82642),f2(x82641)))+P1(f319(f319(f227(x82641),f2(x82641)),x82642))+P1(f319(f319(f227(x82641),f2(x82641)),x82643))+~P1(f319(f319(f227(x82641),f319(f319(f283(x82641),x82644),x82642)),x82643))
% 28.77/28.53 [8316]~E(x83161,f319(f319(f74(a1),f319(f319(f75(a1),x83162),x83163)),x83164))+~P1(f319(f319(f226(a1),f2(a1)),x83164))+~P1(f319(f319(f227(a1),f2(a1)),x83162))+~P1(f319(f319(f227(a1),x83164),x83162))+P1(f319(f43(x83161,x83162),f319(f319(f244(a1,a1),x83163),x83164)))
% 28.77/28.53 [8433]~P74(x84331)+P1(f319(f319(f227(x84331),x84332),f2(x84331)))+~P1(f319(f319(f226(x84331),f2(x84331)),x84334))+~P1(f319(f319(f226(x84331),x84333),f319(f319(f75(x84331),x84334),x84332)))+P1(f319(f319(f226(x84331),f319(f319(f283(x84331),x84333),x84332)),x84334))
% 28.77/28.53 [8434]~P74(x84341)+P1(f319(f319(f227(x84341),x84342),f2(x84341)))+~P1(f319(f319(f227(x84341),f2(x84341)),x84344))+~P1(f319(f319(f227(x84341),x84343),f319(f319(f75(x84341),x84344),x84342)))+P1(f319(f319(f227(x84341),f319(f319(f283(x84341),x84343),x84342)),x84344))
% 28.77/28.53 [8520]~P74(x85201)+P1(f319(f319(f227(x85201),x85202),f2(x85201)))+~P1(f319(f319(f226(x85201),x85203),f2(x85201)))+P1(f319(f319(f226(x85201),x85203),f319(f319(f283(x85201),x85204),x85202)))+~P1(f319(f319(f226(x85201),f319(f319(f75(x85201),x85203),x85202)),x85204))
% 28.77/28.53 [8521]~P74(x85211)+P1(f319(f319(f227(x85211),x85212),f2(x85211)))+~P1(f319(f319(f227(x85211),x85213),f2(x85211)))+P1(f319(f319(f227(x85211),x85213),f319(f319(f283(x85211),x85214),x85212)))+~P1(f319(f319(f227(x85211),f319(f319(f75(x85211),x85213),x85212)),x85214))
% 28.77/28.53 [8675]~P74(x86751)+~P1(f319(f319(f227(x86751),x86752),f2(x86751)))+P1(f319(f319(f227(x86751),f2(x86751)),x86752))+~P1(f319(f319(f226(x86751),f319(f319(f283(x86751),x86754),x86752)),x86753))+P1(f319(f319(f226(x86751),f319(f319(f75(x86751),x86753),x86752)),x86754))
% 28.77/28.53 [8676]~P74(x86761)+~P1(f319(f319(f227(x86761),x86762),f2(x86761)))+P1(f319(f319(f227(x86761),f2(x86761)),x86762))+~P1(f319(f319(f226(x86761),f319(f319(f75(x86761),x86764),x86762)),x86763))+P1(f319(f319(f226(x86761),f319(f319(f283(x86761),x86763),x86762)),x86764))
% 28.77/28.53 [8677]~P74(x86771)+~P1(f319(f319(f227(x86771),x86772),f2(x86771)))+P1(f319(f319(f227(x86771),f2(x86771)),x86772))+~P1(f319(f319(f227(x86771),f319(f319(f283(x86771),x86774),x86772)),x86773))+P1(f319(f319(f227(x86771),f319(f319(f75(x86771),x86773),x86772)),x86774))
% 28.77/28.53 [8678]~P74(x86781)+~P1(f319(f319(f227(x86781),x86782),f2(x86781)))+P1(f319(f319(f227(x86781),f2(x86781)),x86782))+~P1(f319(f319(f227(x86781),f319(f319(f75(x86781),x86784),x86782)),x86783))+P1(f319(f319(f227(x86781),f319(f319(f283(x86781),x86783),x86782)),x86784))
% 28.77/28.53 [8694]~P74(x86941)+~P1(f319(f319(f226(x86941),f2(x86941)),x86944))+P1(f319(f319(f227(x86941),f2(x86941)),x86942))+~P1(f319(f319(f226(x86941),f319(f319(f75(x86941),x86944),x86942)),x86943))+P1(f319(f319(f226(x86941),f319(f319(f283(x86941),x86943),x86942)),x86944))
% 28.77/28.53 [8695]~P74(x86951)+~P1(f319(f319(f227(x86951),f2(x86951)),x86954))+P1(f319(f319(f227(x86951),f2(x86951)),x86952))+~P1(f319(f319(f227(x86951),f319(f319(f75(x86951),x86954),x86952)),x86953))+P1(f319(f319(f227(x86951),f319(f319(f283(x86951),x86953),x86952)),x86954))
% 28.77/28.53 [8750]~P74(x87501)+~P100(x87501)+~P1(f319(f319(f227(x87501),f2(x87501)),x87504))+~P1(f319(f319(f226(x87501),f319(f319(f283(x87501),x87502),x87504)),f319(f95(x87501),x87503)))+P1(f319(f319(f226(x87501),x87502),f319(f319(f75(x87501),f319(f95(x87501),x87503)),x87504)))
% 28.77/28.53 [8751]~P74(x87511)+~P100(x87511)+~P1(f319(f319(f227(x87511),f2(x87511)),x87514))+~P1(f319(f319(f227(x87511),f319(f319(f283(x87511),x87512),x87514)),f319(f95(x87511),x87513)))+P1(f319(f319(f227(x87511),x87512),f319(f319(f75(x87511),f319(f95(x87511),x87513)),x87514)))
% 28.77/28.53 [8757]~P74(x87571)+~P100(x87571)+~P1(f319(f319(f227(x87571),f2(x87571)),x87573))+P1(f319(f319(f226(x87571),f319(f319(f283(x87571),x87572),x87573)),f319(f95(x87571),x87574)))+~P1(f319(f319(f226(x87571),x87572),f319(f319(f75(x87571),f319(f95(x87571),x87574)),x87573)))
% 28.77/28.53 [8758]~P74(x87581)+~P100(x87581)+~P1(f319(f319(f227(x87581),f2(x87581)),x87583))+P1(f319(f319(f227(x87581),f319(f319(f283(x87581),x87582),x87583)),f319(f95(x87581),x87584)))+~P1(f319(f319(f227(x87581),x87582),f319(f319(f75(x87581),f319(f95(x87581),x87584)),x87583)))
% 28.77/28.53 [8773]~P74(x87731)+~P1(f319(f319(f227(x87731),x87734),f2(x87731)))+~P1(f319(f319(f226(x87731),x87733),f319(f319(f75(x87731),x87732),x87734)))+P1(f319(f319(f226(x87731),x87732),f319(f319(f283(x87731),x87733),x87734)))+~P1(f319(f319(f226(x87731),f319(f319(f75(x87731),x87732),x87734)),x87733))
% 28.77/28.53 [8774]~P74(x87741)+~P1(f319(f319(f226(x87741),x87742),f2(x87741)))+~P1(f319(f319(f226(x87741),x87743),f319(f319(f75(x87741),x87742),x87744)))+P1(f319(f319(f226(x87741),x87742),f319(f319(f283(x87741),x87743),x87744)))+~P1(f319(f319(f226(x87741),f319(f319(f75(x87741),x87742),x87744)),x87743))
% 28.77/28.53 [8775]~P74(x87751)+~P1(f319(f319(f227(x87751),x87754),f2(x87751)))+~P1(f319(f319(f227(x87751),x87753),f319(f319(f75(x87751),x87752),x87754)))+P1(f319(f319(f227(x87751),x87752),f319(f319(f283(x87751),x87753),x87754)))+~P1(f319(f319(f227(x87751),f319(f319(f75(x87751),x87752),x87754)),x87753))
% 28.77/28.53 [8776]~P74(x87761)+~P1(f319(f319(f227(x87761),x87762),f2(x87761)))+~P1(f319(f319(f227(x87761),x87763),f319(f319(f75(x87761),x87762),x87764)))+P1(f319(f319(f227(x87761),x87762),f319(f319(f283(x87761),x87763),x87764)))+~P1(f319(f319(f227(x87761),f319(f319(f75(x87761),x87762),x87764)),x87763))
% 28.77/28.53 [8826]~P74(x88261)+~P100(x88261)+~P1(f319(f319(f227(x88261),f2(x88261)),f319(f95(x88261),x88263)))+~P1(f319(f319(f226(x88261),x88262),f319(f319(f283(x88261),x88264),f319(f95(x88261),x88263))))+P1(f319(f319(f226(x88261),f319(f319(f75(x88261),x88262),f319(f95(x88261),x88263))),x88264))
% 28.77/28.53 [8827]~P74(x88271)+~P100(x88271)+~P1(f319(f319(f227(x88271),f2(x88271)),f319(f95(x88271),x88273)))+~P1(f319(f319(f226(x88271),x88272),f319(f319(f75(x88271),x88274),f319(f95(x88271),x88273))))+P1(f319(f319(f226(x88271),f319(f319(f283(x88271),x88272),f319(f95(x88271),x88273))),x88274))
% 28.77/28.53 [8828]~P74(x88281)+~P100(x88281)+~P1(f319(f319(f227(x88281),f2(x88281)),f319(f95(x88281),x88283)))+~P1(f319(f319(f227(x88281),x88282),f319(f319(f283(x88281),x88284),f319(f95(x88281),x88283))))+P1(f319(f319(f227(x88281),f319(f319(f75(x88281),x88282),f319(f95(x88281),x88283))),x88284))
% 28.77/28.53 [8829]~P74(x88291)+~P100(x88291)+~P1(f319(f319(f227(x88291),f2(x88291)),f319(f95(x88291),x88293)))+~P1(f319(f319(f227(x88291),x88292),f319(f319(f75(x88291),x88294),f319(f95(x88291),x88293))))+P1(f319(f319(f227(x88291),f319(f319(f283(x88291),x88292),f319(f95(x88291),x88293))),x88294))
% 28.77/28.53 [8899]~P74(x88991)+~P1(f319(f319(f227(x88991),x88993),f2(x88991)))+~P1(f319(f319(f226(x88991),x88992),f319(f319(f75(x88991),x88994),x88993)))+~P1(f319(f319(f226(x88991),f319(f319(f75(x88991),x88994),x88993)),x88992))+P1(f319(f319(f226(x88991),f319(f319(f283(x88991),x88992),x88993)),x88994))
% 28.77/28.53 [8900]~P74(x89001)+~P1(f319(f319(f227(x89001),x89003),f2(x89001)))+~P1(f319(f319(f227(x89001),x89002),f319(f319(f75(x89001),x89004),x89003)))+~P1(f319(f319(f227(x89001),f319(f319(f75(x89001),x89004),x89003)),x89002))+P1(f319(f319(f227(x89001),f319(f319(f283(x89001),x89002),x89003)),x89004))
% 28.77/28.53 [8917]~P74(x89171)+~P1(f319(f319(f226(x89171),f2(x89171)),x89174))+~P1(f319(f319(f226(x89171),x89172),f319(f319(f75(x89171),x89174),x89173)))+~P1(f319(f319(f226(x89171),f319(f319(f75(x89171),x89174),x89173)),x89172))+P1(f319(f319(f226(x89171),f319(f319(f283(x89171),x89172),x89173)),x89174))
% 28.77/28.53 [8918]~P74(x89181)+~P1(f319(f319(f227(x89181),f2(x89181)),x89184))+~P1(f319(f319(f227(x89181),x89182),f319(f319(f75(x89181),x89184),x89183)))+~P1(f319(f319(f227(x89181),f319(f319(f75(x89181),x89184),x89183)),x89182))+P1(f319(f319(f227(x89181),f319(f319(f283(x89181),x89182),x89183)),x89184))
% 28.77/28.53 [8952]~P74(x89521)+~P100(x89521)+~P1(f319(f319(f227(x89521),f2(x89521)),f319(f95(x89521),x89524)))+P1(f319(f319(f226(x89521),x89522),f319(f319(f75(x89521),x89523),f319(f95(x89521),x89524))))+~P1(f319(f319(f226(x89521),f319(f319(f283(x89521),x89522),f319(f95(x89521),x89524))),x89523))
% 28.77/28.53 [8953]~P74(x89531)+~P100(x89531)+~P1(f319(f319(f227(x89531),f2(x89531)),f319(f95(x89531),x89534)))+P1(f319(f319(f226(x89531),x89532),f319(f319(f283(x89531),x89533),f319(f95(x89531),x89534))))+~P1(f319(f319(f226(x89531),f319(f319(f75(x89531),x89532),f319(f95(x89531),x89534))),x89533))
% 28.77/28.53 [8954]~P74(x89541)+~P100(x89541)+~P1(f319(f319(f227(x89541),f2(x89541)),f319(f95(x89541),x89544)))+P1(f319(f319(f227(x89541),x89542),f319(f319(f75(x89541),x89543),f319(f95(x89541),x89544))))+~P1(f319(f319(f227(x89541),f319(f319(f283(x89541),x89542),f319(f95(x89541),x89544))),x89543))
% 28.77/28.53 [8955]~P74(x89551)+~P100(x89551)+~P1(f319(f319(f227(x89551),f2(x89551)),f319(f95(x89551),x89554)))+P1(f319(f319(f227(x89551),x89552),f319(f319(f283(x89551),x89553),f319(f95(x89551),x89554))))+~P1(f319(f319(f227(x89551),f319(f319(f75(x89551),x89552),f319(f95(x89551),x89554))),x89553))
% 28.77/28.53 [9103]E(f319(f319(f23(a1),f400(x91031,x91032,x91033,x91034)),f401(x91031,x91032,x91033,x91034)),x91034)+~P1(f319(f319(f227(a1),f2(a1)),x91033))+~P1(f319(f319(f321(a1),x91032),x91031))+~P1(f319(f319(f227(a1),x91034),x91032))+P1(f319(f319(f227(a1),f319(f319(f74(a1),x91034),x91033)),x91032))
% 28.77/28.53 [9178]~P1(f319(x91781,x91782))+~P1(f319(f319(f226(a1),f2(a1)),x91783))+~P1(f319(f319(f227(a1),f2(a1)),x91784))+~P1(f319(x91781,f319(f319(f23(a1),f435(x91783,x91781,x91784)),x91784)))+P1(f319(x91781,f319(f319(f23(a1),x91782),f319(f319(f75(a1),x91783),x91784))))
% 28.77/28.53 [9179]~P1(f319(x91791,x91792))+~P1(f319(f319(f226(a1),f2(a1)),x91793))+~P1(f319(f319(f227(a1),f2(a1)),x91794))+~P1(f319(x91791,f319(f319(f74(a1),f441(x91793,x91791,x91794)),x91794)))+P1(f319(x91791,f319(f319(f74(a1),x91792),f319(f319(f75(a1),x91793),x91794))))
% 28.77/28.53 [9331]~P1(f319(f319(f227(a1),f2(a1)),x93313))+~P1(f319(f319(f321(a1),x93312),x93311))+~P1(f319(f319(f227(a1),x93314),x93312))+P1(f319(f319(f321(a1),f400(x93311,x93312,x93313,x93314)),x93311))+P1(f319(f319(f227(a1),f319(f319(f74(a1),x93314),x93313)),x93312))
% 28.77/28.53 [9351]E(f319(f319(f23(a1),f387(x93511,x93512,x93513,x93514)),f388(x93511,x93512,x93513,x93514)),x93514)+~P1(f319(f319(f227(a1),f2(a1)),x93513))+~P1(f319(f319(f226(a1),x93514),x93512))+~P1(f319(f319(f321(a1),f319(f319(f74(a1),x93512),f72(a1))),x93511))+P1(f319(f319(f226(a1),f319(f319(f74(a1),x93514),x93513)),x93512))
% 28.77/28.53 [9379]~P1(f319(f319(f227(a1),f2(a1)),x93792))+~P1(f319(f319(f321(a1),x93793),x93794))+~P1(f319(f319(f227(a1),x93791),x93793))+P1(f319(f319(f321(a1),f401(x93794,x93793,x93792,x93791)),f295(a1,f72(a1),x93792)))+P1(f319(f319(f227(a1),f319(f319(f74(a1),x93791),x93792)),x93793))
% 28.77/28.53 [9470]~P1(f319(f319(f227(a1),f2(a1)),x94703))+~P1(f319(f319(f226(a1),x94704),x94702))+P1(f319(f319(f321(a1),f387(x94701,x94702,x94703,x94704)),x94701))+~P1(f319(f319(f321(a1),f319(f319(f74(a1),x94702),f72(a1))),x94701))+P1(f319(f319(f226(a1),f319(f319(f74(a1),x94704),x94703)),x94702))
% 28.77/28.53 [9517]~P1(f319(f319(f227(a1),f2(a1)),x95172))+~P1(f319(f319(f226(a1),x95171),x95173))+P1(f319(f319(f321(a1),f388(x95174,x95173,x95172,x95171)),f295(a1,f72(a1),x95172)))+~P1(f319(f319(f321(a1),f319(f319(f74(a1),x95173),f72(a1))),x95174))+P1(f319(f319(f226(a1),f319(f319(f74(a1),x95171),x95172)),x95173))
% 28.77/28.53 [9815]~P38(x98151,x98153)+~P28(x98151,x98154)+P38(x98151,f319(f319(f102(f932(f931(x98151,x98151),a923)),x98152),x98153))+~P1(f319(f319(f226(f932(f931(x98151,x98151),a923)),x98152),f319(f243(f932(f931(x98151,x98151),a923),f932(f931(x98151,x98151),a923)),x98154)))+~P1(f319(f319(f226(f932(f931(x98151,x98151),a923)),x98153),f319(f248(f932(f931(x98151,x98151),a923),f932(f931(x98151,x98151),a923)),x98154)))
% 28.77/28.53 [10227]~P20(x102272,x102274,x102273)+E(x102271,f180(f932(x102272,a923)))+~P1(f319(f55(x102272),x102271))+P1(f319(f319(f321(x102272),f319(x102273,x102271)),x102271))+~P1(f319(f319(f321(x102272),f319(f319(x102274,f916(x102271,x102273,x102274,x102272)),f917(x102271,x102273,x102274,x102272))),f319(f319(f301(x102272),f916(x102271,x102273,x102274,x102272)),f319(f319(f301(x102272),f917(x102271,x102273,x102274,x102272)),f180(f932(x102272,a923))))))
% 28.77/28.53 [8801]~P6(x88011)+~P41(x88011,x88011,x88014)+~E(x88012,f87(x88011,x88014))+P1(f319(f319(f226(x88011),x88012),x88013))+~P1(f319(f319(f226(x88011),f319(x88014,f319(f319(f93(x88011),x88012),x88013))),x88013))
% 28.77/28.53 [8940]~P74(x89401)+~P100(x89401)+~P1(f319(f319(f227(x89401),f2(x89401)),x89403))+~P1(f319(f319(f226(x89401),f319(f95(x89401),x89402)),f319(f319(f283(x89401),x89404),x89403)))+P1(f319(f319(f226(x89401),f319(f319(f75(x89401),f319(f95(x89401),x89402)),x89403)),x89404))
% 28.77/28.53 [8941]~P74(x89411)+~P100(x89411)+~P1(f319(f319(f227(x89411),f2(x89411)),x89413))+~P1(f319(f319(f227(x89411),f319(f95(x89411),x89412)),f319(f319(f283(x89411),x89414),x89413)))+P1(f319(f319(f227(x89411),f319(f319(f75(x89411),f319(f95(x89411),x89412)),x89413)),x89414))
% 28.77/28.53 [9106]~P74(x91061)+~P100(x91061)+~P1(f319(f319(f227(x91061),f2(x91061)),x91064))+P1(f319(f319(f226(x91061),f319(f95(x91061),x91062)),f319(f319(f283(x91061),x91063),x91064)))+~P1(f319(f319(f226(x91061),f319(f319(f75(x91061),f319(f95(x91061),x91062)),x91064)),x91063))
% 28.77/28.53 [9107]~P74(x91071)+~P100(x91071)+~P1(f319(f319(f227(x91071),f2(x91071)),x91074))+P1(f319(f319(f227(x91071),f319(f95(x91071),x91072)),f319(f319(f283(x91071),x91073),x91074)))+~P1(f319(f319(f227(x91071),f319(f319(f75(x91071),f319(f95(x91071),x91072)),x91074)),x91073))
% 28.77/28.53 [10149]~P113(x101492)+~P5(x101491)+~P1(f319(f319(f226(f932(x101491,x101492)),x101493),x101494))+P1(f319(f319(f227(f932(x101491,x101492)),x101493),x101494))+~P1(f319(f50(x101491),f319(f319(f8(a923,a923,x101491),a314),f319(f319(f18(x101491,x101492,a923),f319(f319(f8(x101492,f932(x101492,a923),x101491),a316),x101493)),x101494))))
% 28.77/28.53 [5348]~P51(x53484,x53485,x53483)+E(x53481,x53482)+~P4(x53484)+~P113(x53485)+~E(f319(x53483,x53481),f319(x53483,x53482))
% 28.77/28.53 [9728]~P59(x97281,x97281,x97284)+P1(f319(f319(f321(f931(x97281,x97281)),f319(f319(f244(x97281,x97281),x97282),x97283)),f299(x97281,x97284)))+P1(f319(f319(f321(f931(x97281,x97281)),f319(f319(f244(x97281,x97281),x97283),x97282)),f299(x97281,x97284)))+~P1(f319(f319(f321(f931(x97281,x97281)),f319(f319(f244(x97281,x97281),x97285),x97282)),f299(x97281,x97284)))+~P1(f319(f319(f321(f931(x97281,x97281)),f319(f319(f244(x97281,x97281),x97285),x97283)),f299(x97281,x97284)))
% 28.77/28.53 [5832]E(x58321,f2(a925))+~E(f319(f29(x58322),x58325),x58321)+E(f319(f29(x58322),x58323),f319(a104,x58321))+~E(x58323,f319(f319(f301(x58322),x58324),x58325))+P1(f319(f319(f321(x58322),x58324),x58325))
% 28.77/28.53 [5955]~P73(x59552)+E(x59551,f2(x59552))+E(x59553,f2(x59552))+~E(f319(f319(f283(x59552),x59554),x59553),f319(f319(f283(x59552),x59555),x59551))+E(f319(f319(f75(x59552),x59554),x59551),f319(f319(f75(x59552),x59555),x59553))
% 28.77/28.53 [5956]~P73(x59562)+E(x59561,f2(x59562))+E(x59563,f2(x59562))+~E(f319(f319(f75(x59562),x59564),x59563),f319(f319(f75(x59562),x59565),x59561))+E(f319(f319(f283(x59562),x59564),x59561),f319(f319(f283(x59562),x59565),x59563))
% 28.77/28.53 [6025]~E(f319(f29(x60251),x60255),x60253)+~E(x60255,f180(f932(x60251,a923)))+E(f319(f29(x60251),x60252),f319(a104,x60253))+~E(x60252,f319(f319(f301(x60251),x60254),x60255))+P1(f319(f319(f321(x60251),x60254),x60255))
% 28.77/28.53 [6268]~P121(x62682)+~E(f319(x62683,x62685),f2(x62682))+E(f319(f319(f9(x62681,x62682),x62683),x62684),f2(x62682))+~P1(f319(f55(x62681),x62684))+~P1(f319(f319(f321(x62681),x62685),x62684))
% 28.77/28.53 [6636]~P4(x66363)+E(x66361,x66362)+~E(f319(f294(x66363,x66364),x66361),f319(f294(x66363,x66365),x66362))+~P1(f319(f319(f227(x66363),x66365),x66362))+~P1(f319(f319(f227(x66363),x66364),x66361))
% 28.77/28.53 [6637]~P4(x66373)+E(x66371,x66372)+~E(f319(f294(x66373,x66371),x66374),f319(f294(x66373,x66372),x66375))+~P1(f319(f319(f227(x66373),x66372),x66375))+~P1(f319(f319(f227(x66373),x66371),x66374))
% 28.77/28.53 [6638]~P4(x66383)+E(x66381,x66382)+~E(f319(f294(x66383,x66384),x66381),f319(f294(x66383,x66385),x66382))+~P1(f319(f319(f227(x66383),x66385),x66382))+~P1(f319(f319(f227(x66383),x66384),x66381))
% 28.77/28.53 [6639]~P4(x66393)+E(x66391,x66392)+~E(f319(f294(x66393,x66391),x66394),f319(f294(x66393,x66392),x66395))+~P1(f319(f319(f227(x66393),x66392),x66395))+~P1(f319(f319(f227(x66393),x66391),x66394))
% 28.77/28.53 [6805]~P113(x68051)+~P51(x68055,x68051,x68052)+~P4(x68055)+P1(f319(f319(f226(x68051),f319(x68052,x68053)),f319(x68052,x68054)))+~P1(f319(f319(f226(x68055),x68053),x68054))
% 28.77/28.53 [6806]~P113(x68061)+~P41(x68065,x68061,x68062)+~P113(x68065)+P1(f319(f319(f226(x68061),f319(x68062,x68063)),f319(x68062,x68064)))+~P1(f319(f319(f226(x68065),x68063),x68064))
% 28.77/28.53 [6807]~P113(x68071)+~P51(x68075,x68071,x68072)+~P4(x68075)+P1(f319(f319(f227(x68071),f319(x68072,x68073)),f319(x68072,x68074)))+~P1(f319(f319(f227(x68075),x68073),x68074))
% 28.77/28.53 [6808]~P113(x68081)+~P51(x68085,x68081,x68082)+~P113(x68085)+P1(f319(f319(f227(x68081),f319(x68082,x68083)),f319(x68082,x68084)))+~P1(f319(f319(f227(x68085),x68083),x68084))
% 28.77/28.53 [7059]~P4(x70591)+~P51(x70591,x70594,x70595)+~P113(x70594)+~P1(f319(f319(f226(x70594),f319(x70595,x70592)),f319(x70595,x70593)))+P1(f319(f319(f226(x70591),x70592),x70593))
% 28.77/28.53 [7060]~P4(x70601)+~P51(x70601,x70604,x70605)+~P113(x70604)+~P1(f319(f319(f227(x70604),f319(x70605,x70602)),f319(x70605,x70603)))+P1(f319(f319(f227(x70601),x70602),x70603))
% 28.77/28.53 [7709]~P4(x77091)+~P14(x77091,f319(f319(f126(x77091),x77094),x77095))+~P1(f319(f319(f321(x77091),x77093),f319(f164(x77091),x77095)))+~P1(f319(f319(f321(x77091),x77092),f319(f164(x77091),x77094)))+P1(f319(f319(f226(x77091),x77092),x77093))
% 28.77/28.53 [8811]~P113(x88111)+~P1(f319(f319(f227(f932(x88111,a923)),f295(x88111,x88115,x88112)),f295(x88111,x88114,x88113)))+~P1(f319(f319(f226(x88111),x88115),x88112))+P1(f319(f319(f227(x88111),x88112),x88113))+P1(f319(f319(f227(x88111),x88114),x88115))
% 28.77/28.53 [9851]~P41(f932(x98514,a923),f932(x98514,a923),x98515)+P1(f319(x98511,x98512))+~E(x98513,f87(f932(x98514,a923),x98515))+~P1(f319(x98511,f461(x98511,x98512,x98515,x98514,x98513)))+~P1(f319(f319(f321(x98514),x98512),x98513))
% 28.77/28.53 [10270]~P19(x102702,x102705,x102703)+E(x102701,f180(f932(x102702,a923)))+~E(f319(f319(x102705,f319(x102704,f342(x102701,x102704,x102703,x102705,x102702))),f319(x102704,f343(x102701,x102704,x102703,x102705,x102702))),f319(x102704,f319(f319(x102705,f342(x102701,x102704,x102703,x102705,x102702)),f343(x102701,x102704,x102703,x102705,x102702))))+E(f319(x102703,f319(f302(x102702,x102702,x102704),x102701)),f319(x102704,f319(x102703,x102701)))+~P1(f319(f55(x102702),x102701))
% 28.77/28.53 [6635]~P20(x66352,x66355,x66353)+E(x66351,f180(f932(x66352,a923)))+~P1(f319(f55(x66352),x66351))+E(f319(x66353,f319(f319(f301(x66352),x66354),x66351)),f319(f319(x66355,x66354),f319(x66353,x66351)))+P1(f319(f319(f321(x66352),x66354),x66351))
% 28.77/28.53 [7474]~P19(x74742,x74743,x74744)+E(f319(f319(x74743,f319(x74744,x74741)),f319(x74744,x74745)),f319(x74744,x74745))+E(x74741,f180(f932(x74742,a923)))+~P1(f319(f55(x74742),x74745))+~P1(f319(f319(f226(f932(x74742,a923)),x74741),x74745))
% 28.77/28.53 [7843]~P20(x78434,x78435,x78431)+E(f319(x78431,x78432),x78433)+~P1(f319(f55(x78434),x78432))+~E(f319(f319(f23(f932(x78434,a923)),x78432),f319(f319(f301(x78434),x78433),f180(f932(x78434,a923)))),f180(f932(x78434,a923)))+~P1(f319(f319(f321(x78434),x78433),x78432))
% 28.77/28.53 [8780]E(x87801,x87802)+~P9(x87803,x87804,x87805)+E(f319(f319(f93(f932(x87803,a923)),x87801),x87802),f180(f932(x87803,a923)))+~P1(f319(f319(f321(f932(x87803,a923)),x87802),f319(f319(f54(x87803),x87804),x87805)))+~P1(f319(f319(f321(f932(x87803,a923)),x87801),f319(f319(f54(x87803),x87804),x87805)))
% 28.77/28.53 [9256]~P26(x92561,x92563,x92565,x92562)+~P1(f319(f55(x92563),x92564))+~P1(f319(f55(x92561),x92562))+P1(f319(f319(f226(a925),f319(f29(x92561),x92562)),f319(f29(x92563),x92564)))+~P1(f319(f319(f226(f932(x92563,a923)),f319(f302(x92561,x92563,x92565),x92562)),x92564))
% 28.77/28.53 [9601]~P79(x96012)+~E(f319(x96013,f445(x96013,x96014,x96015,x96011,x96012)),f2(x96012))+E(f319(f319(f6(x96011,x96012),x96013),x96014),f319(f319(f6(x96011,x96012),x96013),x96015))+~P1(f319(f55(x96011),x96015))+~P1(f319(f319(f226(f932(x96011,a923)),x96014),x96015))
% 28.77/28.53 [9602]~P79(x96022)+~E(f319(x96023,f446(x96023,x96024,x96025,x96021,x96022)),f2(x96022))+E(f319(f319(f6(x96021,x96022),x96023),x96024),f319(f319(f6(x96021,x96022),x96023),x96025))+~P1(f319(f55(x96021),x96025))+~P1(f319(f319(f226(f932(x96021,a923)),x96024),x96025))
% 28.77/28.53 [9603]~P78(x96032)+~E(f319(x96033,f505(x96033,x96034,x96035,x96031,x96032)),f72(x96032))+E(f319(f319(f9(x96031,x96032),x96033),x96034),f319(f319(f9(x96031,x96032),x96033),x96035))+~P1(f319(f55(x96031),x96035))+~P1(f319(f319(f226(f932(x96031,a923)),x96034),x96035))
% 28.77/28.53 [9604]~P78(x96042)+~E(f319(x96043,f506(x96043,x96044,x96045,x96041,x96042)),f72(x96042))+E(f319(f319(f9(x96041,x96042),x96043),x96044),f319(f319(f9(x96041,x96042),x96043),x96045))+~P1(f319(f55(x96041),x96045))+~P1(f319(f319(f226(f932(x96041,a923)),x96044),x96045))
% 28.77/28.53 [10043]~P41(f932(x100431,a923),f932(x100431,a923),f319(f319(f8(f932(x100431,a923),f932(x100431,a923),f932(x100431,a923)),f254(x100431)),x100434))+~P1(f319(f319(x100434,f319(f319(f102(f932(x100431,a923)),x100435),x100433)),f462(x100435,x100432,x100434,x100431,x100433)))+~E(x100433,f88(f932(x100431,a923),f319(f319(f8(f932(x100431,a923),f932(x100431,a923),f932(x100431,a923)),f254(x100431)),x100434)))+P1(f319(f319(f321(x100431),x100432),x100433))+~P1(f319(f319(f321(x100431),x100432),x100435))
% 28.77/28.53 [10047]~P41(f932(x100471,a923),f932(x100471,a923),f319(f319(f8(f932(x100471,a923),f932(x100471,a923),f932(x100471,a923)),f254(x100471)),x100475))+~E(x100473,f88(f932(x100471,a923),f319(f319(f8(f932(x100471,a923),f932(x100471,a923),f932(x100471,a923)),f254(x100471)),x100475)))+~P1(f319(f319(f321(x100471),x100472),x100474))+P1(f319(f319(f321(x100471),f462(x100474,x100472,x100475,x100471,x100473)),x100474))+P1(f319(f319(f321(x100471),x100472),x100473))
% 28.77/28.53 [10102]~P93(x101021)+~P1(f319(f55(x101022),x101025))+~P1(f319(f319(f226(x101021),f2(x101021)),f319(x101023,f389(x101023,x101024,x101025,x101022,x101021))))+P1(f319(f319(f226(x101021),f319(f319(f6(x101022,x101021),x101023),x101024)),f319(f319(f6(x101022,x101021),x101023),x101025)))+~P1(f319(f319(f226(f932(x101022,a923)),x101024),x101025))
% 28.77/28.53 [7706]E(x77061,f2(a925))+P1(f319(x77062,x77063))+~E(x77064,f319(f319(f74(a925),f319(f319(f75(a925),x77061),x77063)),x77065))+~P1(f319(f319(f227(a925),x77065),x77061))+~P1(f319(x77062,f319(f319(f30(a925),x77064),x77061)))
% 28.77/28.53 [7781]E(x77811,f2(a925))+P1(f319(x77812,x77813))+~P1(f319(x77812,f39(a925,x77814,x77811)))+~E(x77814,f319(f319(f74(a925),f319(f319(f75(a925),x77811),x77815)),x77813))+~P1(f319(f319(f227(a925),x77813),x77811))
% 28.77/28.53 [8074]~P73(x80743)+E(f319(x80741,x80742),f2(x80743))+~P1(f319(f55(x80744),x80745))+E(f319(f319(f9(x80744,x80743),x80741),f319(f319(f23(f932(x80744,a923)),x80745),f319(f319(f301(x80744),x80742),f180(f932(x80744,a923))))),f319(f319(f9(x80744,x80743),x80741),x80745))+P1(f319(f319(f321(x80744),x80742),x80745))
% 28.77/28.53 [8474]~P79(x84741)+~P1(f319(f55(x84742),x84745))+~P1(f319(f55(x84742),x84744))+~E(f319(f319(f93(f932(x84742,a923)),x84744),x84745),f180(f932(x84742,a923)))+E(f319(f319(f74(x84741),f319(f319(f6(x84742,x84741),x84743),x84744)),f319(f319(f6(x84742,x84741),x84743),x84745)),f319(f319(f6(x84742,x84741),x84743),f319(f319(f102(f932(x84742,a923)),x84744),x84745)))
% 28.77/28.53 [8475]~P78(x84751)+~P1(f319(f55(x84752),x84755))+~P1(f319(f55(x84752),x84754))+~E(f319(f319(f93(f932(x84752,a923)),x84754),x84755),f180(f932(x84752,a923)))+E(f319(f319(f75(x84751),f319(f319(f9(x84752,x84751),x84753),x84754)),f319(f319(f9(x84752,x84751),x84753),x84755)),f319(f319(f9(x84752,x84751),x84753),f319(f319(f102(f932(x84752,a923)),x84754),x84755)))
% 28.77/28.53 [8476]~P78(x84761)+~P1(f319(f55(x84762),x84765))+~P1(f319(f55(x84762),x84764))+~E(f319(f319(f93(f932(x84762,a923)),x84764),x84765),f180(f932(x84762,a923)))+E(f319(f319(f75(x84761),f319(f319(f9(x84762,x84761),x84763),x84764)),f319(f319(f9(x84762,x84761),x84763),x84765)),f319(f319(f9(x84762,x84761),x84763),f319(f319(f102(f932(x84762,a923)),x84764),x84765)))
% 28.77/28.53 [8576]~P73(x85763)+E(f319(x85761,x85762),f2(x85763))+~P1(f319(f55(x85764),x85765))+E(f319(f319(f9(x85764,x85763),x85761),f319(f319(f23(f932(x85764,a923)),x85765),f319(f319(f301(x85764),x85762),f180(f932(x85764,a923))))),f319(f319(f283(x85763),f319(f319(f9(x85764,x85763),x85761),x85765)),f319(x85761,x85762)))+~P1(f319(f319(f321(x85764),x85762),x85765))
% 28.77/28.53 [9121]~P9(x91211,x91215,x91214)+~E(f319(f277(x91211,x91211,x91214),f319(f319(f301(x91211),x91212),f180(f932(x91211,a923)))),f319(f277(x91211,x91211,x91214),f319(f319(f301(x91211),x91213),f180(f932(x91211,a923)))))+~P1(f319(f319(f321(x91211),x91213),x91215))+~P1(f319(f319(f321(x91211),x91212),x91215))+P1(f319(f319(f321(f931(x91211,x91211)),f319(f319(f244(x91211,x91211),x91212),x91213)),x91214))
% 28.77/28.53 [9122]~P9(x91221,x91225,x91224)+~E(f319(f277(x91221,x91221,x91224),f319(f319(f301(x91221),x91222),f180(f932(x91221,a923)))),f319(f277(x91221,x91221,x91224),f319(f319(f301(x91221),x91223),f180(f932(x91221,a923)))))+~P1(f319(f319(f321(x91221),x91223),x91225))+~P1(f319(f319(f321(x91221),x91222),x91225))+P1(f319(f319(f321(f931(x91221,x91221)),f319(f319(f244(x91221,x91221),x91222),x91223)),x91224))
% 28.77/28.53 [9219]~P9(x92191,x92195,x92192)+E(f319(f277(x92191,x92191,x92192),f319(f319(f301(x92191),x92193),f180(f932(x92191,a923)))),f319(f277(x92191,x92191,x92192),f319(f319(f301(x92191),x92194),f180(f932(x92191,a923)))))+~P1(f319(f319(f321(x92191),x92194),x92195))+~P1(f319(f319(f321(x92191),x92193),x92195))+~P1(f319(f319(f321(f931(x92191,x92191)),f319(f319(f244(x92191,x92191),x92193),x92194)),x92192))
% 28.77/28.53 [9308]~P9(x93081,x93085,x93084)+~E(f319(f319(f54(x93081),f319(f319(f301(x93081),x93082),f180(f932(x93081,a923)))),x93084),f319(f319(f54(x93081),f319(f319(f301(x93081),x93083),f180(f932(x93081,a923)))),x93084))+~P1(f319(f319(f321(x93081),x93083),x93085))+~P1(f319(f319(f321(x93081),x93082),x93085))+P1(f319(f319(f321(f931(x93081,x93081)),f319(f319(f244(x93081,x93081),x93082),x93083)),x93084))
% 28.77/28.53 [9330]~P9(x93301,x93305,x93303)+E(f319(f319(f54(x93301),f319(f319(f301(x93301),x93302),f180(f932(x93301,a923)))),x93303),f319(f319(f54(x93301),f319(f319(f301(x93301),x93304),f180(f932(x93301,a923)))),x93303))+~P1(f319(f319(f321(x93301),x93304),x93305))+~P1(f319(f319(f321(x93301),x93302),x93305))+~P1(f319(f319(f321(f931(x93301,x93301)),f319(f319(f244(x93301,x93301),x93302),x93304)),x93303))
% 28.77/28.53 [9630]~P78(x96301)+~P1(f319(f55(x96302),x96305))+~P1(f319(f55(x96302),x96304))+~E(f319(f319(f93(f932(x96302,a923)),x96304),x96305),f180(f932(x96302,a923)))+E(f319(f319(f75(x96301),f319(f319(f319(f59(x96301,x96302,f75(x96301)),x96303),f72(x96301)),x96304)),f319(f319(f319(f59(x96301,x96302,f75(x96301)),x96303),f72(x96301)),x96305)),f319(f319(f319(f59(x96301,x96302,f75(x96301)),x96303),f72(x96301)),f319(f319(f102(f932(x96302,a923)),x96304),x96305)))
% 28.77/28.53 [9641]~P79(x96411)+~E(f319(x96413,f407(x96413,x96415,x96414,x96412,x96411)),f2(x96411))+~P1(f319(f55(x96412),x96414))+~P1(f319(f55(x96412),x96415))+E(f319(f319(f74(x96411),f319(f319(f6(x96412,x96411),x96413),x96414)),f319(f319(f6(x96412,x96411),x96413),x96415)),f319(f319(f6(x96412,x96411),x96413),f319(f319(f102(f932(x96412,a923)),x96414),x96415)))
% 28.77/28.53 [9642]~P79(x96421)+~E(f319(x96423,f408(x96423,x96425,x96424,x96422,x96421)),f2(x96421))+~P1(f319(f55(x96422),x96424))+~P1(f319(f55(x96422),x96425))+E(f319(f319(f74(x96421),f319(f319(f6(x96422,x96421),x96423),x96424)),f319(f319(f6(x96422,x96421),x96423),x96425)),f319(f319(f6(x96422,x96421),x96423),f319(f319(f102(f932(x96422,a923)),x96424),x96425)))
% 28.77/28.53 [9643]~P78(x96431)+~E(f319(x96433,f492(x96433,x96435,x96434,x96432,x96431)),f72(x96431))+~P1(f319(f55(x96432),x96434))+~P1(f319(f55(x96432),x96435))+E(f319(f319(f75(x96431),f319(f319(f9(x96432,x96431),x96433),x96434)),f319(f319(f9(x96432,x96431),x96433),x96435)),f319(f319(f9(x96432,x96431),x96433),f319(f319(f102(f932(x96432,a923)),x96434),x96435)))
% 28.77/28.53 [9644]~P78(x96441)+~E(f319(x96443,f493(x96443,x96445,x96444,x96442,x96441)),f72(x96441))+~P1(f319(f55(x96442),x96444))+~P1(f319(f55(x96442),x96445))+E(f319(f319(f75(x96441),f319(f319(f9(x96442,x96441),x96443),x96444)),f319(f319(f9(x96442,x96441),x96443),x96445)),f319(f319(f9(x96442,x96441),x96443),f319(f319(f102(f932(x96442,a923)),x96444),x96445)))
% 28.77/28.53 [9859]~P78(x98591)+~E(f319(x98593,f349(x98593,x98595,x98594,x98592,x98591)),f72(x98591))+~P1(f319(f55(x98592),x98594))+~P1(f319(f55(x98592),x98595))+E(f319(f319(f75(x98591),f319(f319(f319(f59(x98591,x98592,f75(x98591)),x98593),f72(x98591)),x98594)),f319(f319(f319(f59(x98591,x98592,f75(x98591)),x98593),f72(x98591)),x98595)),f319(f319(f319(f59(x98591,x98592,f75(x98591)),x98593),f72(x98591)),f319(f319(f102(f932(x98592,a923)),x98594),x98595)))
% 28.77/28.53 [9980]~P79(x99802)+E(f319(f319(f6(x99801,x99802),x99803),x99804),f319(f319(f6(x99801,x99802),x99803),x99805))+~P1(f319(f55(x99801),x99805))+~P1(f319(f319(f226(f932(x99801,a923)),x99804),x99805))+P1(f319(f319(f321(x99801),f445(x99803,x99804,x99805,x99801,x99802)),f319(f319(f23(f932(x99801,a923)),x99805),x99804)))
% 28.77/28.53 [9981]~P79(x99812)+E(f319(f319(f6(x99811,x99812),x99813),x99814),f319(f319(f6(x99811,x99812),x99813),x99815))+~P1(f319(f55(x99811),x99815))+~P1(f319(f319(f226(f932(x99811,a923)),x99814),x99815))+P1(f319(f319(f321(x99811),f446(x99813,x99814,x99815,x99811,x99812)),f319(f319(f23(f932(x99811,a923)),x99815),x99814)))
% 28.77/28.53 [9982]~P78(x99822)+E(f319(f319(f9(x99821,x99822),x99823),x99824),f319(f319(f9(x99821,x99822),x99823),x99825))+~P1(f319(f55(x99821),x99825))+~P1(f319(f319(f226(f932(x99821,a923)),x99824),x99825))+P1(f319(f319(f321(x99821),f505(x99823,x99824,x99825,x99821,x99822)),f319(f319(f23(f932(x99821,a923)),x99825),x99824)))
% 28.77/28.53 [9983]~P78(x99832)+E(f319(f319(f9(x99831,x99832),x99833),x99834),f319(f319(f9(x99831,x99832),x99833),x99835))+~P1(f319(f55(x99831),x99835))+~P1(f319(f319(f226(f932(x99831,a923)),x99834),x99835))+P1(f319(f319(f321(x99831),f506(x99833,x99834,x99835,x99831,x99832)),f319(f319(f23(f932(x99831,a923)),x99835),x99834)))
% 28.77/28.53 [10003]~P79(x100031)+~P1(f319(f55(x100032),x100034))+~P1(f319(f55(x100032),x100035))+E(f319(f319(f74(x100031),f319(f319(f6(x100032,x100031),x100033),x100034)),f319(f319(f6(x100032,x100031),x100033),x100035)),f319(f319(f6(x100032,x100031),x100033),f319(f319(f102(f932(x100032,a923)),x100034),x100035)))+P1(f319(f319(f321(x100032),f407(x100033,x100035,x100034,x100032,x100031)),f319(f319(f93(f932(x100032,a923)),x100034),x100035)))
% 28.77/28.53 [10004]~P79(x100041)+~P1(f319(f55(x100042),x100044))+~P1(f319(f55(x100042),x100045))+E(f319(f319(f74(x100041),f319(f319(f6(x100042,x100041),x100043),x100044)),f319(f319(f6(x100042,x100041),x100043),x100045)),f319(f319(f6(x100042,x100041),x100043),f319(f319(f102(f932(x100042,a923)),x100044),x100045)))+P1(f319(f319(f321(x100042),f408(x100043,x100045,x100044,x100042,x100041)),f319(f319(f93(f932(x100042,a923)),x100044),x100045)))
% 28.77/28.53 [10005]~P78(x100051)+~P1(f319(f55(x100052),x100054))+~P1(f319(f55(x100052),x100055))+E(f319(f319(f75(x100051),f319(f319(f9(x100052,x100051),x100053),x100054)),f319(f319(f9(x100052,x100051),x100053),x100055)),f319(f319(f9(x100052,x100051),x100053),f319(f319(f102(f932(x100052,a923)),x100054),x100055)))+P1(f319(f319(f321(x100052),f492(x100053,x100055,x100054,x100052,x100051)),f319(f319(f93(f932(x100052,a923)),x100054),x100055)))
% 28.77/28.53 [10006]~P78(x100061)+~P1(f319(f55(x100062),x100064))+~P1(f319(f55(x100062),x100065))+E(f319(f319(f75(x100061),f319(f319(f9(x100062,x100061),x100063),x100064)),f319(f319(f9(x100062,x100061),x100063),x100065)),f319(f319(f9(x100062,x100061),x100063),f319(f319(f102(f932(x100062,a923)),x100064),x100065)))+P1(f319(f319(f321(x100062),f493(x100063,x100065,x100064,x100062,x100061)),f319(f319(f93(f932(x100062,a923)),x100064),x100065)))
% 28.77/28.53 [10010]~P41(f932(x100103,a923),f932(x100103,a923),x100104)+P1(f319(x100101,x100102))+~E(x100105,f87(f932(x100103,a923),x100104))+~P1(f319(f319(f321(x100103),x100102),x100105))+P1(f319(f319(f321(x100103),f461(x100101,x100102,x100104,x100103,x100105)),f319(x100104,f319(f319(f93(f932(x100103,a923)),x100105),f319(f254(x100103),x100101)))))
% 28.77/28.53 [10014]~P93(x100145)+~P1(f319(f55(x100141),x100144))+P1(f319(f319(f226(x100145),f319(f319(f6(x100141,x100145),x100142),x100143)),f319(f319(f6(x100141,x100145),x100142),x100144)))+~P1(f319(f319(f226(f932(x100141,a923)),x100143),x100144))+P1(f319(f319(f321(x100141),f389(x100142,x100143,x100144,x100141,x100145)),f319(f319(f23(f932(x100141,a923)),x100144),x100143)))
% 28.77/28.53 [10061]~P78(x100611)+~P1(f319(f55(x100612),x100614))+~P1(f319(f55(x100612),x100615))+E(f319(f319(f75(x100611),f319(f319(f319(f59(x100611,x100612,f75(x100611)),x100613),f72(x100611)),x100614)),f319(f319(f319(f59(x100611,x100612,f75(x100611)),x100613),f72(x100611)),x100615)),f319(f319(f319(f59(x100611,x100612,f75(x100611)),x100613),f72(x100611)),f319(f319(f102(f932(x100612,a923)),x100614),x100615)))+P1(f319(f319(f321(x100612),f349(x100613,x100615,x100614,x100612,x100611)),f319(f319(f93(f932(x100612,a923)),x100614),x100615)))
% 28.77/28.53 [8990]~P20(x89901,x89904,x89905)+~P1(f319(f55(x89901),x89902))+E(f319(f319(f23(f932(x89901,a923)),x89902),f319(f319(f301(x89901),x89903),f180(f932(x89901,a923)))),f180(f932(x89901,a923)))+~P1(f319(f319(f321(x89901),x89903),x89902))+E(f319(f319(x89904,x89903),f319(x89905,f319(f319(f23(f932(x89901,a923)),x89902),f319(f319(f301(x89901),x89903),f180(f932(x89901,a923)))))),f319(x89905,x89902))
% 28.77/28.53 [9069]~P20(x90691,x90694,x90695)+~P1(f319(f55(x90691),x90693))+~P1(f319(f55(x90691),x90692))+E(f319(f319(f93(f932(x90691,a923)),x90692),x90693),f180(f932(x90691,a923)))+E(f319(f319(x90694,f319(x90695,f319(f319(f102(f932(x90691,a923)),x90692),x90693))),f319(x90695,f319(f319(f93(f932(x90691,a923)),x90692),x90693))),f319(f319(x90694,f319(x90695,x90692)),f319(x90695,x90693)))
% 28.77/28.53 [9257]~P41(f932(x92571,a923),f932(x92571,a923),x92574)+~E(x92573,f88(f932(x92571,a923),x92574))+P1(f319(f319(f321(x92571),x92572),x92573))+~P1(f319(f319(f321(x92571),x92572),x92575))+~P1(f319(f319(f226(f932(x92571,a923)),x92575),f319(x92574,f319(f319(f102(f932(x92571,a923)),x92575),x92573))))
% 28.77/28.53 [9646]~P1(f319(f319(f226(a1),x96464),f2(a1)))+~P1(f319(f319(f227(a1),x96463),x96465))+P1(f319(f319(f226(a1),x96461),x96462))+~P1(f319(f319(f227(a1),x96463),x96464))+~P1(f319(f319(f226(a1),f319(f319(f74(a1),f319(f319(f75(a1),x96463),x96462)),x96465)),f319(f319(f74(a1),f319(f319(f75(a1),x96463),x96461)),x96464)))
% 28.77/28.53 [9648]~P1(f319(f319(f226(a1),f2(a1)),x96485))+P1(f319(f319(f226(a1),x96481),x96482))+~P1(f319(f319(f227(a1),x96483),x96484))+~P1(f319(f319(f227(a1),x96485),x96484))+~P1(f319(f319(f226(a1),f319(f319(f74(a1),f319(f319(f75(a1),x96484),x96481)),x96485)),f319(f319(f74(a1),f319(f319(f75(a1),x96484),x96482)),x96483)))
% 28.77/28.53 [9765]~P73(x97655)+E(f319(x97651,f495(x97651,x97652,x97653,x97654,x97655)),f2(x97655))+~P1(f319(f55(x97654),x97653))+~P1(f319(f55(x97654),x97652))+E(f319(f319(f283(x97655),f319(f319(f75(x97655),f319(f319(f9(x97654,x97655),x97651),x97653)),f319(f319(f9(x97654,x97655),x97651),x97652))),f319(f319(f9(x97654,x97655),x97651),f319(f319(f93(f932(x97654,a923)),x97653),x97652))),f319(f319(f9(x97654,x97655),x97651),f319(f319(f102(f932(x97654,a923)),x97653),x97652)))
% 28.77/28.53 [10053]~P73(x100531)+~P1(f319(f55(x100532),x100534))+~P1(f319(f55(x100532),x100535))+E(f319(f319(f283(x100531),f319(f319(f75(x100531),f319(f319(f9(x100532,x100531),x100533),x100534)),f319(f319(f9(x100532,x100531),x100533),x100535))),f319(f319(f9(x100532,x100531),x100533),f319(f319(f93(f932(x100532,a923)),x100534),x100535))),f319(f319(f9(x100532,x100531),x100533),f319(f319(f102(f932(x100532,a923)),x100534),x100535)))+P1(f319(f319(f321(x100532),f495(x100533,x100535,x100534,x100532,x100531)),f319(f319(f93(f932(x100532,a923)),x100534),x100535)))
% 28.77/28.53 [9350]E(f319(f319(f126(x93501),x93502),x93503),f319(f319(f126(x93501),x93504),x93505))+~E(f319(f319(f167(x93501),f319(f181(f926(x93501)),x93504)),x93502),x93504)+~E(f319(f319(f167(x93501),f319(f181(f926(x93501)),x93502)),x93504),x93502)+~E(x93505,f319(f319(f126(x93501),f319(f319(f130(x93501),f319(f181(f926(x93501)),x93504)),x93502)),x93503))+~E(f319(f319(f126(x93501),f319(f319(f130(x93501),f319(f181(f926(x93501)),x93502)),x93504)),x93505),x93503)
% 28.77/28.53 [9763]~P4(x97632)+E(f319(f319(f140(x97631,x97632,x97633),x97634),f162(x97631,x97634,x97635)),x97635)+~P14(x97632,f319(f319(f146(x97631,x97632),x97633),x97635))+~P1(f319(f319(f321(x97631),x97634),f319(f164(x97631),x97635)))+~E(f319(f133(x97631),f319(f128(x97631,f319(f319(f8(x97632,a923,x97631),f319(a316,f319(x97633,x97634))),x97633)),x97635)),x97634)
% 28.77/28.53 [10120]~P76(x101201)+~P1(f319(f60(x101201,x101201,f75(x101201),x101202,x101203),x101205))+~P1(f319(f319(f321(x101201),x101204),x101203))+P1(f319(f319(f321(x101201),x101202),x101203))+P1(f319(f60(x101201,x101201,f75(x101201),x101204,f319(f319(f301(x101201),x101202),f319(f319(f23(f932(x101201,a923)),x101203),f319(f319(f301(x101201),x101204),f180(f932(x101201,a923)))))),x101205))
% 28.77/28.53 [10486]~P41(f932(x104861,a923),f932(x104861,a923),x104864)+~E(x104863,f88(f932(x104861,a923),x104864))+P1(f319(f319(f321(x104861),x104862),x104863))+~P1(f319(f319(f321(x104861),x104862),x104865))+~P1(f319(f319(f226(f932(x104861,a923)),x104865),f319(x104864,f87(f932(x104861,a923),f319(f319(f7(f932(x104861,a923),f932(x104861,a923),f932(x104861,a923)),f319(f319(f8(f932(x104861,a923),f932(f932(x104861,a923),f932(x104861,a923)),f932(x104861,a923)),f102(f932(x104861,a923))),f319(f319(f7(f932(x104861,a923),f932(x104861,a923),f932(x104861,a923)),f319(f319(f8(f932(x104861,a923),f932(f932(x104861,a923),f932(x104861,a923)),f932(x104861,a923)),f102(f932(x104861,a923))),x104864)),x104865))),x104863)))))
% 28.77/28.53 [7479]E(x74791,x74792)+~P26(x74794,x74795,x74793,x74796)+~E(f319(x74793,x74791),f319(x74793,x74792))+~P1(f319(f319(f321(x74794),x74792),x74796))+~P1(f319(f319(f321(x74794),x74791),x74796))
% 28.77/28.53 [7480]E(x74801,x74802)+~P26(x74804,x74805,x74803,x74806)+~E(f319(x74803,x74801),f319(x74803,x74802))+~P1(f319(f319(f321(x74804),x74802),x74806))+~P1(f319(f319(f321(x74804),x74801),x74806))
% 28.77/28.53 [7481]E(x74811,x74812)+~P26(x74814,x74815,x74813,x74816)+~E(f319(x74813,x74811),f319(x74813,x74812))+~P1(f319(f319(f321(x74814),x74812),x74816))+~P1(f319(f319(f321(x74814),x74811),x74816))
% 28.77/28.53 [7482]E(x74821,x74822)+~P26(x74824,x74825,x74823,x74826)+~E(f319(x74823,x74821),f319(x74823,x74822))+~P1(f319(f319(f321(x74824),x74822),x74826))+~P1(f319(f319(f321(x74824),x74821),x74826))
% 28.77/28.53 [6729]~P148(x67294)+E(x67291,x67292)+~E(x67295,x67296)+E(x67293,f2(x67294))+~E(f319(f319(f74(x67294),x67295),f319(f319(f75(x67294),x67293),x67291)),f319(f319(f74(x67294),x67296),f319(f319(f75(x67294),x67293),x67292)))
% 28.77/28.53 [7761]~P4(x77611)+~P6(x77611)+~P1(f319(f319(f227(x77611),x77612),f319(x77615,x77616)))+~P1(f319(f319(f321(x77613),x77616),x77614))+P1(f319(f319(f227(x77611),x77612),f319(f319(f33(x77613,x77611),x77614),x77615)))
% 28.77/28.53 [10116]~P26(x101162,x101161,x101163,x101164)+~P26(x101161,x101162,x101166,x101165)+P27(x101161,x101162,f468(x101163,x101164,x101165,x101166,x101162,x101161),x101165,x101164)+~P1(f319(f319(f226(f932(x101162,a923)),f319(f302(x101161,x101162,x101166),x101165)),x101164))+~P1(f319(f319(f226(f932(x101161,a923)),f319(f302(x101162,x101161,x101163),x101164)),x101165))
% 28.77/28.53 [8444]~P4(x84441)+~P6(x84441)+~P1(f319(f319(f227(x84441),f319(x84444,x84446)),x84445))+~P1(f319(f319(f321(x84442),x84446),x84443))+P1(f319(f319(f227(x84441),f319(f319(f34(x84442,x84441),x84443),x84444)),x84445))
% 28.77/28.53 [8701]~P21(x87012,x87015,x87016,x87011)+~P1(f319(f55(x87012),x87014))+~P1(f319(f55(x87012),x87013))+~E(f319(f319(f93(f932(x87012,a923)),x87013),x87014),f180(f932(x87012,a923)))+E(f319(x87011,f319(f319(f102(f932(x87012,a923)),x87013),x87014)),f319(f66(x87015,x87015,x87015,f319(x87011,x87013)),f319(x87011,x87014)))
% 28.77/28.53 [10332]~P78(x103321)+~E(f831(x103324,x103325,x103323,x103326,x103322,x103321),f832(x103324,x103325,x103323,x103326,x103322,x103321))+~P1(f319(f55(x103322),x103326))+E(f319(f319(f319(f59(x103321,x103322,f75(x103321)),f319(f319(f8(f932(x103323,a923),x103321,x103322),f319(f319(f59(x103321,x103323,f75(x103321)),x103324),f72(x103321))),x103325)),f72(x103321)),x103326),f319(f319(f319(f59(x103321,x103323,f75(x103321)),x103324),f72(x103321)),f319(f319(f33(x103322,f932(x103323,a923)),x103326),x103325)))+P1(f319(f319(f321(x103322),f829(x103324,x103325,x103323,x103326,x103322,x103321)),x103326))
% 28.77/28.53 [10362]~P78(x103621)+~E(f831(x103624,x103625,x103623,x103626,x103622,x103621),f832(x103624,x103625,x103623,x103626,x103622,x103621))+~P1(f319(f55(x103622),x103626))+E(f319(f319(f319(f59(x103621,x103622,f75(x103621)),f319(f319(f8(f932(x103623,a923),x103621,x103622),f319(f319(f59(x103621,x103623,f75(x103621)),x103624),f72(x103621))),x103625)),f72(x103621)),x103626),f319(f319(f319(f59(x103621,x103623,f75(x103621)),x103624),f72(x103621)),f319(f319(f33(x103622,f932(x103623,a923)),x103626),x103625)))+~P1(f319(f55(x103623),f319(x103625,f829(x103624,x103625,x103623,x103626,x103622,x103621))))
% 28.77/28.53 [10365]~P78(x103651)+~P1(f319(f55(x103652),x103656))+E(f319(f319(f319(f59(x103651,x103652,f75(x103651)),f319(f319(f8(f932(x103653,a923),x103651,x103652),f319(f319(f59(x103651,x103653,f75(x103651)),x103654),f72(x103651))),x103655)),f72(x103651)),x103656),f319(f319(f319(f59(x103651,x103653,f75(x103651)),x103654),f72(x103651)),f319(f319(f33(x103652,f932(x103653,a923)),x103656),x103655)))+P1(f319(f319(f321(x103652),f829(x103654,x103655,x103653,x103656,x103652,x103651)),x103656))+P1(f319(f319(f321(x103652),f832(x103654,x103655,x103653,x103656,x103652,x103651)),x103656))
% 28.77/28.53 [10366]~P78(x103661)+~P1(f319(f55(x103662),x103666))+E(f319(f319(f319(f59(x103661,x103662,f75(x103661)),f319(f319(f8(f932(x103663,a923),x103661,x103662),f319(f319(f59(x103661,x103663,f75(x103661)),x103664),f72(x103661))),x103665)),f72(x103661)),x103666),f319(f319(f319(f59(x103661,x103663,f75(x103661)),x103664),f72(x103661)),f319(f319(f33(x103662,f932(x103663,a923)),x103666),x103665)))+P1(f319(f319(f321(x103662),f829(x103664,x103665,x103663,x103666,x103662,x103661)),x103666))+P1(f319(f319(f321(x103662),f831(x103664,x103665,x103663,x103666,x103662,x103661)),x103666))
% 28.77/28.53 [10384]~P78(x103841)+~P1(f319(f55(x103842),x103846))+E(f319(f319(f319(f59(x103841,x103842,f75(x103841)),f319(f319(f8(f932(x103843,a923),x103841,x103842),f319(f319(f59(x103841,x103843,f75(x103841)),x103844),f72(x103841))),x103845)),f72(x103841)),x103846),f319(f319(f319(f59(x103841,x103843,f75(x103841)),x103844),f72(x103841)),f319(f319(f33(x103842,f932(x103843,a923)),x103846),x103845)))+P1(f319(f319(f321(x103842),f832(x103844,x103845,x103843,x103846,x103842,x103841)),x103846))+~P1(f319(f55(x103843),f319(x103845,f829(x103844,x103845,x103843,x103846,x103842,x103841))))
% 28.77/28.53 [10385]~P78(x103851)+~P1(f319(f55(x103852),x103856))+E(f319(f319(f319(f59(x103851,x103852,f75(x103851)),f319(f319(f8(f932(x103853,a923),x103851,x103852),f319(f319(f59(x103851,x103853,f75(x103851)),x103854),f72(x103851))),x103855)),f72(x103851)),x103856),f319(f319(f319(f59(x103851,x103853,f75(x103851)),x103854),f72(x103851)),f319(f319(f33(x103852,f932(x103853,a923)),x103856),x103855)))+P1(f319(f319(f321(x103852),f831(x103854,x103855,x103853,x103856,x103852,x103851)),x103856))+~P1(f319(f55(x103853),f319(x103855,f829(x103854,x103855,x103853,x103856,x103852,x103851))))
% 28.77/28.53 [10396]~P78(x103961)+~E(f319(f319(f93(f932(x103963,a923)),f319(x103965,f832(x103964,x103965,x103963,x103966,x103962,x103961))),f319(x103965,f831(x103964,x103965,x103963,x103966,x103962,x103961))),f180(f932(x103963,a923)))+~P1(f319(f55(x103962),x103966))+E(f319(f319(f319(f59(x103961,x103962,f75(x103961)),f319(f319(f8(f932(x103963,a923),x103961,x103962),f319(f319(f59(x103961,x103963,f75(x103961)),x103964),f72(x103961))),x103965)),f72(x103961)),x103966),f319(f319(f319(f59(x103961,x103963,f75(x103961)),x103964),f72(x103961)),f319(f319(f33(x103962,f932(x103963,a923)),x103966),x103965)))+P1(f319(f319(f321(x103962),f829(x103964,x103965,x103963,x103966,x103962,x103961)),x103966))
% 28.77/28.53 [10407]~P78(x104071)+~E(f319(f319(f93(f932(x104073,a923)),f319(x104075,f832(x104074,x104075,x104073,x104076,x104072,x104071))),f319(x104075,f831(x104074,x104075,x104073,x104076,x104072,x104071))),f180(f932(x104073,a923)))+~P1(f319(f55(x104072),x104076))+E(f319(f319(f319(f59(x104071,x104072,f75(x104071)),f319(f319(f8(f932(x104073,a923),x104071,x104072),f319(f319(f59(x104071,x104073,f75(x104071)),x104074),f72(x104071))),x104075)),f72(x104071)),x104076),f319(f319(f319(f59(x104071,x104073,f75(x104071)),x104074),f72(x104071)),f319(f319(f33(x104072,f932(x104073,a923)),x104076),x104075)))+~P1(f319(f55(x104073),f319(x104075,f829(x104074,x104075,x104073,x104076,x104072,x104071))))
% 28.77/28.53 [9441]~P123(x94411)+~P120(x94411)+~P1(f319(f319(f279(x94411),x94412),x94415))+~P1(f319(f319(f279(x94411),x94412),f319(f319(f74(x94411),x94413),x94416)))+P1(f319(f319(f279(x94411),x94412),f319(f319(f74(x94411),f319(f319(f23(x94411),x94413),f319(f319(f75(x94411),x94414),x94415))),x94416)))
% 28.77/28.53 [9442]~P123(x94421)+~P120(x94421)+~P1(f319(f319(f279(x94421),x94422),x94425))+~P1(f319(f319(f279(x94421),x94422),f319(f319(f74(x94421),x94423),x94426)))+P1(f319(f319(f279(x94421),x94422),f319(f319(f74(x94421),f319(f319(f23(x94421),x94423),f319(f319(f75(x94421),x94424),x94425))),x94426)))
% 28.77/28.53 [9634]~P123(x96341)+~P120(x96341)+~P1(f319(f319(f279(x96341),x96342),x96345))+P1(f319(f319(f279(x96341),x96342),f319(f319(f74(x96341),x96343),x96344)))+~P1(f319(f319(f279(x96341),x96342),f319(f319(f74(x96341),f319(f319(f23(x96341),x96343),f319(f319(f75(x96341),x96346),x96345))),x96344)))
% 28.77/28.53 [9635]~P123(x96351)+~P120(x96351)+~P1(f319(f319(f279(x96351),x96352),x96355))+P1(f319(f319(f279(x96351),x96352),f319(f319(f74(x96351),x96353),x96354)))+~P1(f319(f319(f279(x96351),x96352),f319(f319(f74(x96351),f319(f319(f23(x96351),x96353),f319(f319(f75(x96351),x96356),x96355))),x96354)))
% 28.77/28.53 [9039]E(x90391,x90392)+~P61(x90394,x90395,x90396,x90393,x90397)+~E(f319(x90393,x90391),f319(x90393,x90392))+~P1(f319(f319(f321(x90395),x90392),x90397))+~P1(f319(f319(f321(x90395),x90391),x90397))
% 28.77/28.53 [9762]~P27(x97621,x97622,x97623,x97625,x97627)+~P27(x97621,x97622,x97623,x97624,x97626)+P27(x97621,x97622,x97623,f319(f319(f102(f932(x97621,a923)),x97624),x97625),f319(f319(f102(f932(x97622,a923)),x97626),x97627))+~E(f319(f319(f93(f932(x97622,a923)),x97626),x97627),f180(f932(x97622,a923)))+~E(f319(f319(f93(f932(x97621,a923)),x97624),x97625),f180(f932(x97621,a923)))
% 28.77/28.53 [10374]~P1(f319(x103742,x103744))+~E(x103745,f319(f128(x103741,x103742),x103747))+E(f319(f128(x103741,x103742),x103743),f319(f319(f143(x103741),x103744),x103745))+~E(x103743,f319(f319(f126(x103741),x103746),f319(f319(f143(x103741),x103744),x103747)))+P1(f319(x103742,f769(x103745,x103744,x103743,x103742,x103741,x103746,x103747)))
% 28.77/28.53 [10375]~P1(f319(x103754,x103752))+~E(x103753,f319(f128(x103751,x103754),x103757))+E(f319(f319(f143(x103751),x103752),x103753),f319(f128(x103751,x103754),x103755))+~E(x103755,f319(f319(f126(x103751),x103756),f319(f319(f143(x103751),x103752),x103757)))+P1(f319(x103754,f768(x103755,x103754,x103753,x103752,x103751,x103756,x103757)))
% 28.77/28.53 [10420]~P1(f319(x104202,x104204))+~E(x104205,f319(f128(x104201,x104202),x104207))+E(f319(f128(x104201,x104202),x104203),f319(f319(f143(x104201),x104204),x104205))+~E(x104203,f319(f319(f126(x104201),x104206),f319(f319(f143(x104201),x104204),x104207)))+P1(f319(f319(f321(x104201),f769(x104205,x104204,x104203,x104202,x104201,x104206,x104207)),f319(f164(x104201),x104206)))
% 28.77/28.53 [10421]~P1(f319(x104214,x104212))+~E(x104213,f319(f128(x104211,x104214),x104217))+E(f319(f319(f143(x104211),x104212),x104213),f319(f128(x104211,x104214),x104215))+~E(x104215,f319(f319(f126(x104211),x104216),f319(f319(f143(x104211),x104212),x104217)))+P1(f319(f319(f321(x104211),f768(x104215,x104214,x104213,x104212,x104211,x104216,x104217)),f319(f164(x104211),x104216)))
% 28.77/28.53 [10425]~P9(x104251,x104257,x104256)+~P12(x104251,f932(x104255,a923),x104256,x104254)+P1(f319(f319(f321(x104251),f550(x104252,x104253,x104254,x104255,x104256,x104257,x104251)),x104257))+~P1(f319(f319(f321(f932(x104251,a923)),x104253),f319(f319(f54(x104251),x104257),x104256)))+P1(f319(f319(f321(f932(x104255,a923)),f319(f319(f33(x104251,f932(x104255,a923)),x104253),x104254)),x104252))
% 28.77/28.53 [10481]~P9(x104812,x104816,x104817)+~P12(x104812,f932(x104811,a923),x104817,x104814)+~P1(f319(f319(f321(f932(x104812,a923)),x104813),f319(f319(f54(x104812),x104816),x104817)))+~P1(f319(f319(f321(f932(x104811,a923)),f319(x104814,f550(x104815,x104813,x104814,x104811,x104817,x104816,x104812))),x104815))+P1(f319(f319(f321(f932(x104811,a923)),f319(f319(f33(x104812,f932(x104811,a923)),x104813),x104814)),x104815))
% 28.77/28.53 [8619]~P78(x86192)+~P26(x86191,x86195,x86198,x86194)+~E(x86193,f319(f66(x86195,x86192,x86191,x86196),x86198))+~E(x86197,f319(f302(x86191,x86195,x86198),x86194))+E(f319(f319(f9(x86191,x86192),x86193),x86194),f319(f319(f9(x86195,x86192),x86196),x86197))
% 28.77/28.53 [10485]~P78(x104852)+~P26(x104855,x104851,x104858,x104857)+~E(f319(x104856,f500(x104853,x104856,x104854,x104857,x104858,x104851,x104855,x104852)),f319(f319(f66(x104851,x104852,x104855,x104853),x104858),f500(x104853,x104856,x104854,x104857,x104858,x104851,x104855,x104852)))+~E(x104854,f319(f302(x104855,x104851,x104858),x104857))+E(f319(f319(f9(x104851,x104852),x104853),x104854),f319(f319(f9(x104855,x104852),x104856),x104857))
% 28.77/28.53 [10490]~P79(x104902)+~P26(x104901,x104905,x104908,x104904)+~E(x104907,f319(f302(x104901,x104905,x104908),x104904))+E(f319(f319(f6(x104901,x104902),x104903),x104904),f319(f319(f6(x104905,x104902),x104906),x104907))+P1(f319(f319(f321(x104901),f622(x104906,x104903,x104907,x104904,x104908,x104905,x104901,x104902)),x104904))
% 28.77/28.53 [10491]~P78(x104912)+~P26(x104911,x104915,x104918,x104914)+~E(x104917,f319(f302(x104911,x104915,x104918),x104914))+E(f319(f319(f9(x104911,x104912),x104913),x104914),f319(f319(f9(x104915,x104912),x104916),x104917))+P1(f319(f319(f321(x104911),f500(x104916,x104913,x104917,x104914,x104918,x104915,x104911,x104912)),x104914))
% 28.77/28.53 [10496]~P79(x104962)+~P26(x104965,x104961,x104968,x104967)+~E(x104964,f319(f302(x104965,x104961,x104968),x104967))+~E(f319(x104966,f622(x104963,x104966,x104964,x104967,x104968,x104961,x104965,x104962)),f319(x104963,f319(x104968,f622(x104963,x104966,x104964,x104967,x104968,x104961,x104965,x104962))))+E(f319(f319(f6(x104961,x104962),x104963),x104964),f319(f319(f6(x104965,x104962),x104966),x104967))
% 28.77/28.53 [9936]~P25(x99366,x99362,x99365,x99367,x99368,x99361)+~P1(f319(f55(x99362),x99364))+~P1(f319(f55(x99362),x99363))+~E(f319(f319(f93(f932(x99362,a923)),x99363),x99364),f180(f932(x99362,a923)))+E(f319(x99361,f319(f319(f102(f932(x99362,a923)),x99363),x99364)),f319(f319(x99365,f319(x99361,x99363)),f319(x99361,x99364)))
% 28.77/28.53 [10359]~P25(x103598,x103592,x103595,x103597,x103596,x103591)+~E(f319(x103596,f344(x103594,x103593,x103591,x103596,x103597,x103595,x103592)),x103597)+~P1(f319(f55(x103592),x103593))+~P1(f319(f55(x103592),x103594))+E(f319(x103591,f319(f319(f102(f932(x103592,a923)),x103593),x103594)),f319(f319(x103595,f319(x103591,x103593)),f319(x103591,x103594)))
% 28.77/28.53 [10432]~P25(x104328,x104322,x104325,x104327,x104326,x104321)+~P1(f319(f55(x104322),x104323))+~P1(f319(f55(x104322),x104324))+E(f319(x104321,f319(f319(f102(f932(x104322,a923)),x104323),x104324)),f319(f319(x104325,f319(x104321,x104323)),f319(x104321,x104324)))+P1(f319(f319(f321(x104322),f344(x104324,x104323,x104321,x104326,x104327,x104325,x104322)),f319(f319(f93(f932(x104322,a923)),x104323),x104324)))
% 28.77/28.53 [10107]~P9(x101074,x101078,x101075)+~P9(x101071,x101079,x101073)+~P13(x101071,x101074,f932(x101072,a923),x101073,x101075,x101077)+P12(x101071,f932(x101072,a923),x101073,f319(f319(f8(f932(x101074,f932(x101072,a923)),f932(x101072,a923),x101071),f319(f33(x101074,f932(x101072,a923)),f319(f277(x101074,x101074,x101075),f319(f319(f301(x101074),x101076),f180(f932(x101074,a923)))))),x101077))+~P1(f319(f319(f321(x101074),x101076),x101078))
% 28.77/28.53 [5632]~P4(x56323)+~P14(x56323,x56321)+E(x56321,f747(x56322,x56323))+~E(f319(f164(x56323),x56321),x56322)+~P1(f319(f55(x56323),x56322))+~P1(f319(f129(x56323),x56321))
% 28.77/28.53 [7473]P17(x74731,x74732)+~E(f319(x74732,f827(x74732)),f319(x74732,f828(x74732)))+~P1(f319(f319(x74732,f827(x74732)),f827(x74732)))+~P1(f319(f319(x74732,f827(x74732)),f828(x74732)))+~P1(f319(f319(x74732,f828(x74732)),f828(x74732)))+~P1(f319(f319(x74732,x74733),x74733))
% 28.77/28.53 [5256]~P133(x52562)+~P138(x52562)+~P150(x52562)+~P119(x52562)+E(x52561,f2(x52562))+~E(f319(f319(f236(x52562),x52561),x52563),f2(x52562))
% 28.77/28.53 [5257]~P133(x52572)+~P138(x52572)+~P150(x52572)+~P119(x52572)+~E(x52571,f2(a925))+~E(f319(f319(f236(x52572),x52573),x52571),f2(x52572))
% 28.77/28.53 [6711]~P93(x67111)+~E(x67113,f2(x67111))+~E(x67112,f2(x67111))+E(f319(f319(f74(x67111),x67112),x67113),f2(x67111))+~P1(f319(f319(f226(x67111),f2(x67111)),x67113))+~P1(f319(f319(f226(x67111),f2(x67111)),x67112))
% 28.77/28.53 [9089]E(x90891,f2(a925))+~E(x90892,f319(f319(f74(a925),f319(f319(f75(a925),f319(f243(a925,a925),x90893)),x90891)),f319(f248(a925,a925),x90893)))+P1(f319(f42(x90892,x90891),x90893))+~P1(f319(f319(f226(a925),f319(f248(a925,a925),x90893)),f2(a925)))+P1(f319(f319(f227(a925),f2(a925)),x90891))+~P1(f319(f319(f227(a925),x90891),f319(f248(a925,a925),x90893)))
% 28.77/28.53 [9108]~E(f319(f243(a925,a925),x91083),f2(a925))+~E(x91081,f319(f319(f74(a925),f319(f319(f75(a925),f319(f243(a925,a925),x91083)),x91082)),f319(f248(a925,a925),x91083)))+P1(f319(f42(x91081,x91082),x91083))+~P1(f319(f319(f226(a925),f319(f248(a925,a925),x91083)),f2(a925)))+P1(f319(f319(f227(a925),f2(a925)),x91082))+~P1(f319(f319(f227(a925),x91082),f319(f248(a925,a925),x91083)))
% 28.77/28.53 [9116]E(x91161,f2(a925))+~E(x91162,f319(f319(f74(a925),f319(f319(f75(a925),f319(f243(a925,a925),x91163)),x91161)),f319(f248(a925,a925),x91163)))+P1(f319(f42(x91162,x91161),x91163))+~P1(f319(f319(f227(a925),f2(a925)),x91161))+~P1(f319(f319(f226(a925),f2(a925)),f319(f248(a925,a925),x91163)))+~P1(f319(f319(f227(a925),f319(f248(a925,a925),x91163)),x91161))
% 28.77/28.53 [9134]~E(f319(f243(a925,a925),x91343),f2(a925))+~E(x91341,f319(f319(f74(a925),f319(f319(f75(a925),f319(f243(a925,a925),x91343)),x91342)),f319(f248(a925,a925),x91343)))+P1(f319(f42(x91341,x91342),x91343))+~P1(f319(f319(f227(a925),f2(a925)),x91342))+~P1(f319(f319(f226(a925),f2(a925)),f319(f248(a925,a925),x91343)))+~P1(f319(f319(f227(a925),f319(f248(a925,a925),x91343)),x91342))
% 28.77/28.53 [7100]~P102(x71002)+E(x71001,f180(f932(x71002,a923)))+E(x71003,f180(f932(x71002,a923)))+~P1(f319(f55(x71002),x71001))+~P1(f319(f55(x71002),x71003))+E(f10(x71002,f319(f319(f102(f932(x71002,a923)),x71003),x71001)),f319(f319(f93(x71002),f10(x71002,x71003)),f10(x71002,x71001)))
% 28.77/28.53 [7101]~P102(x71012)+E(x71011,f180(f932(x71012,a923)))+E(x71013,f180(f932(x71012,a923)))+~P1(f319(f55(x71012),x71011))+~P1(f319(f55(x71012),x71013))+E(f13(x71012,f319(f319(f102(f932(x71012,a923)),x71013),x71011)),f319(f319(f102(x71012),f13(x71012,x71013)),f13(x71012,x71011)))
% 28.77/28.53 [7102]~P4(x71022)+E(x71021,f180(f932(x71022,a923)))+E(x71023,f180(f932(x71022,a923)))+~P1(f319(f55(x71022),x71021))+~P1(f319(f55(x71022),x71023))+E(f14(x71022,f319(f319(f102(f932(x71022,a923)),x71023),x71021)),f319(f319(f224(x71022),f14(x71022,x71023)),f14(x71022,x71021)))
% 28.77/28.53 [7103]~P4(x71032)+E(x71031,f180(f932(x71032,a923)))+E(x71033,f180(f932(x71032,a923)))+~P1(f319(f55(x71032),x71031))+~P1(f319(f55(x71032),x71033))+E(f15(x71032,f319(f319(f102(f932(x71032,a923)),x71033),x71031)),f319(f319(f225(x71032),f15(x71032,x71033)),f15(x71032,x71031)))
% 28.77/28.53 [7736]~P101(x77362)+E(x77361,f180(f932(x77362,a923)))+E(x77363,f180(f932(x77362,a923)))+~P1(f319(f55(x77362),x77361))+~P1(f319(f55(x77362),x77363))+E(f319(f319(f75(x77362),f319(f57(x77362,f75(x77362)),x77363)),f319(f57(x77362,f75(x77362)),x77361)),f319(f57(x77362,f75(x77362)),f319(f319(f102(f932(x77362,a923)),x77363),x77361)))
% 28.77/28.53 [7896]~P4(x78962)+E(x78961,f180(f932(x78962,a923)))+E(x78963,f180(f932(x78962,a923)))+~P1(f319(f55(x78962),x78961))+~P1(f319(f55(x78962),x78963))+E(f319(f319(f224(x78962),f11(x78962,f224(x78962),x78963)),f11(x78962,f224(x78962),x78961)),f11(x78962,f224(x78962),f319(f319(f102(f932(x78962,a923)),x78963),x78961)))
% 28.77/28.53 [7897]~P4(x78972)+E(x78971,f180(f932(x78972,a923)))+E(x78973,f180(f932(x78972,a923)))+~P1(f319(f55(x78972),x78971))+~P1(f319(f55(x78972),x78973))+E(f319(f319(f225(x78972),f12(x78972,f225(x78972),x78973)),f12(x78972,f225(x78972),x78971)),f12(x78972,f225(x78972),f319(f319(f102(f932(x78972,a923)),x78973),x78971)))
% 28.77/28.53 [8939]~P1(f319(x89391,x89393))+P1(f319(x89391,f395(x89391,x89392)))+P1(f319(x89391,f379(x89391,x89392)))+~P1(f319(f319(f227(a1),f2(a1)),x89392))+~P1(f319(f319(f321(a1),x89393),f295(a1,f72(a1),x89392)))+P1(f319(x89391,f319(f319(f23(a1),f379(x89391,x89392)),f319(f319(f75(a1),f391(x89391,x89392)),x89392))))
% 28.77/28.53 [9247]~P1(f319(x92471,x92473))+~P1(f319(x92471,f379(x92471,x92472)))+P1(f319(x92471,f395(x92471,x92472)))+~P1(f319(f319(f227(a1),f2(a1)),x92472))+~P1(f319(f319(f321(a1),x92473),f295(a1,f72(a1),x92472)))+~P1(f319(x92471,f319(f319(f23(a1),f379(x92471,x92472)),f319(f319(f75(a1),f391(x92471,x92472)),x92472))))
% 28.77/28.53 [10524]~P106(x105242)+E(x105241,f180(f932(x105242,a923)))+E(x105243,f180(f932(x105242,a923)))+~P1(f319(f55(x105242),x105241))+~P1(f319(f55(x105242),x105243))+E(f10(x105242,f319(f254(x105242),f319(f319(f8(f932(x105242,a923),a923,x105242),f81(x105242)),f319(f319(f8(f932(x105242,f932(x105242,a923)),f932(x105242,a923),x105242),f319(f8(f932(x105242,a923),a923,x105242),f81(x105242))),f319(f319(f7(x105242,f932(x105242,f932(x105242,a923)),f932(x105242,f932(x105242,a923))),f319(f319(f8(f932(x105242,f932(f932(x105242,a923),f932(x105242,a923))),f932(f932(x105242,f932(x105242,a923)),f932(x105242,f932(x105242,a923))),x105242),f18(x105242,f932(x105242,a923),f932(x105242,a923))),f319(f319(f8(f932(x105242,f932(x105242,f932(a923,a923))),f932(x105242,f932(f932(x105242,a923),f932(x105242,a923))),x105242),f319(f8(f932(x105242,f932(a923,a923)),f932(f932(x105242,a923),f932(x105242,a923)),x105242),f18(x105242,a923,a923))),f319(f319(f8(f932(x105242,f932(x105242,a923)),f932(x105242,f932(x105242,f932(a923,a923))),x105242),f319(f8(f932(x105242,a923),f932(x105242,f932(a923,a923)),x105242),f319(f8(a923,f932(a923,a923),x105242),a317))),f319(f319(f7(x105242,f932(x105242,f932(x105242,x105242)),f932(x105242,f932(x105242,a923))),f319(f319(f8(f932(f932(x105242,x105242),f932(x105242,a923)),f932(f932(x105242,f932(x105242,x105242)),f932(x105242,f932(x105242,a923))),x105242),f8(f932(x105242,x105242),f932(x105242,a923),x105242)),f319(f319(f8(f932(x105242,a923),f932(f932(x105242,x105242),f932(x105242,a923)),x105242),f8(x105242,a923,x105242)),a316))),f102(x105242)))))),f319(f319(f7(x105242,f932(x105242,a923),f932(x105242,a923)),f319(f319(f8(f932(a923,a923),f932(f932(x105242,a923),f932(x105242,a923)),x105242),f8(a923,a923,x105242)),f319(f319(f8(a923,f932(a923,a923),x105242),a317),f319(f319(f7(x105242,f932(x105242,a923),a923),f321(x105242)),x105243)))),f319(f319(f7(x105242,f932(x105242,a923),a923),f321(x105242)),x105241))))))),f319(f319(f102(x105242),f10(x105242,x105243)),f10(x105242,x105241)))
% 28.77/28.53 [10525]~P106(x105252)+E(x105251,f180(f932(x105252,a923)))+E(x105253,f180(f932(x105252,a923)))+~P1(f319(f55(x105252),x105251))+~P1(f319(f55(x105252),x105253))+E(f13(x105252,f319(f254(x105252),f319(f319(f8(f932(x105252,a923),a923,x105252),f81(x105252)),f319(f319(f8(f932(x105252,f932(x105252,a923)),f932(x105252,a923),x105252),f319(f8(f932(x105252,a923),a923,x105252),f81(x105252))),f319(f319(f7(x105252,f932(x105252,f932(x105252,a923)),f932(x105252,f932(x105252,a923))),f319(f319(f8(f932(x105252,f932(f932(x105252,a923),f932(x105252,a923))),f932(f932(x105252,f932(x105252,a923)),f932(x105252,f932(x105252,a923))),x105252),f18(x105252,f932(x105252,a923),f932(x105252,a923))),f319(f319(f8(f932(x105252,f932(x105252,f932(a923,a923))),f932(x105252,f932(f932(x105252,a923),f932(x105252,a923))),x105252),f319(f8(f932(x105252,f932(a923,a923)),f932(f932(x105252,a923),f932(x105252,a923)),x105252),f18(x105252,a923,a923))),f319(f319(f8(f932(x105252,f932(x105252,a923)),f932(x105252,f932(x105252,f932(a923,a923))),x105252),f319(f8(f932(x105252,a923),f932(x105252,f932(a923,a923)),x105252),f319(f8(a923,f932(a923,a923),x105252),a317))),f319(f319(f7(x105252,f932(x105252,f932(x105252,x105252)),f932(x105252,f932(x105252,a923))),f319(f319(f8(f932(f932(x105252,x105252),f932(x105252,a923)),f932(f932(x105252,f932(x105252,x105252)),f932(x105252,f932(x105252,a923))),x105252),f8(f932(x105252,x105252),f932(x105252,a923),x105252)),f319(f319(f8(f932(x105252,a923),f932(f932(x105252,x105252),f932(x105252,a923)),x105252),f8(x105252,a923,x105252)),a316))),f93(x105252)))))),f319(f319(f7(x105252,f932(x105252,a923),f932(x105252,a923)),f319(f319(f8(f932(a923,a923),f932(f932(x105252,a923),f932(x105252,a923)),x105252),f8(a923,a923,x105252)),f319(f319(f8(a923,f932(a923,a923),x105252),a317),f319(f319(f7(x105252,f932(x105252,a923),a923),f321(x105252)),x105253)))),f319(f319(f7(x105252,f932(x105252,a923),a923),f321(x105252)),x105251))))))),f319(f319(f93(x105252),f13(x105252,x105253)),f13(x105252,x105251)))
% 28.77/28.53 [10526]~P4(x105262)+E(x105261,f180(f932(x105262,a923)))+E(x105263,f180(f932(x105262,a923)))+~P1(f319(f55(x105262),x105261))+~P1(f319(f55(x105262),x105263))+E(f12(x105262,f225(x105262),f319(f254(x105262),f319(f319(f8(f932(x105262,a923),a923,x105262),f81(x105262)),f319(f319(f8(f932(x105262,f932(x105262,a923)),f932(x105262,a923),x105262),f319(f8(f932(x105262,a923),a923,x105262),f81(x105262))),f319(f319(f7(x105262,f932(x105262,f932(x105262,a923)),f932(x105262,f932(x105262,a923))),f319(f319(f8(f932(x105262,f932(f932(x105262,a923),f932(x105262,a923))),f932(f932(x105262,f932(x105262,a923)),f932(x105262,f932(x105262,a923))),x105262),f18(x105262,f932(x105262,a923),f932(x105262,a923))),f319(f319(f8(f932(x105262,f932(x105262,f932(a923,a923))),f932(x105262,f932(f932(x105262,a923),f932(x105262,a923))),x105262),f319(f8(f932(x105262,f932(a923,a923)),f932(f932(x105262,a923),f932(x105262,a923)),x105262),f18(x105262,a923,a923))),f319(f319(f8(f932(x105262,f932(x105262,a923)),f932(x105262,f932(x105262,f932(a923,a923))),x105262),f319(f8(f932(x105262,a923),f932(x105262,f932(a923,a923)),x105262),f319(f8(a923,f932(a923,a923),x105262),a317))),f319(f319(f7(x105262,f932(x105262,f932(x105262,x105262)),f932(x105262,f932(x105262,a923))),f319(f319(f8(f932(f932(x105262,x105262),f932(x105262,a923)),f932(f932(x105262,f932(x105262,x105262)),f932(x105262,f932(x105262,a923))),x105262),f8(f932(x105262,x105262),f932(x105262,a923),x105262)),f319(f319(f8(f932(x105262,a923),f932(f932(x105262,x105262),f932(x105262,a923)),x105262),f8(x105262,a923,x105262)),a316))),f224(x105262)))))),f319(f319(f7(x105262,f932(x105262,a923),f932(x105262,a923)),f319(f319(f8(f932(a923,a923),f932(f932(x105262,a923),f932(x105262,a923)),x105262),f8(a923,a923,x105262)),f319(f319(f8(a923,f932(a923,a923),x105262),a317),f319(f319(f7(x105262,f932(x105262,a923),a923),f321(x105262)),x105263)))),f319(f319(f7(x105262,f932(x105262,a923),a923),f321(x105262)),x105261))))))),f319(f319(f224(x105262),f12(x105262,f225(x105262),x105263)),f12(x105262,f225(x105262),x105261)))
% 28.77/28.54 [10527]~P4(x105272)+E(x105271,f180(f932(x105272,a923)))+E(x105273,f180(f932(x105272,a923)))+~P1(f319(f55(x105272),x105271))+~P1(f319(f55(x105272),x105273))+E(f11(x105272,f224(x105272),f319(f254(x105272),f319(f319(f8(f932(x105272,a923),a923,x105272),f81(x105272)),f319(f319(f8(f932(x105272,f932(x105272,a923)),f932(x105272,a923),x105272),f319(f8(f932(x105272,a923),a923,x105272),f81(x105272))),f319(f319(f7(x105272,f932(x105272,f932(x105272,a923)),f932(x105272,f932(x105272,a923))),f319(f319(f8(f932(x105272,f932(f932(x105272,a923),f932(x105272,a923))),f932(f932(x105272,f932(x105272,a923)),f932(x105272,f932(x105272,a923))),x105272),f18(x105272,f932(x105272,a923),f932(x105272,a923))),f319(f319(f8(f932(x105272,f932(x105272,f932(a923,a923))),f932(x105272,f932(f932(x105272,a923),f932(x105272,a923))),x105272),f319(f8(f932(x105272,f932(a923,a923)),f932(f932(x105272,a923),f932(x105272,a923)),x105272),f18(x105272,a923,a923))),f319(f319(f8(f932(x105272,f932(x105272,a923)),f932(x105272,f932(x105272,f932(a923,a923))),x105272),f319(f8(f932(x105272,a923),f932(x105272,f932(a923,a923)),x105272),f319(f8(a923,f932(a923,a923),x105272),a317))),f319(f319(f7(x105272,f932(x105272,f932(x105272,x105272)),f932(x105272,f932(x105272,a923))),f319(f319(f8(f932(f932(x105272,x105272),f932(x105272,a923)),f932(f932(x105272,f932(x105272,x105272)),f932(x105272,f932(x105272,a923))),x105272),f8(f932(x105272,x105272),f932(x105272,a923),x105272)),f319(f319(f8(f932(x105272,a923),f932(f932(x105272,x105272),f932(x105272,a923)),x105272),f8(x105272,a923,x105272)),a316))),f225(x105272)))))),f319(f319(f7(x105272,f932(x105272,a923),f932(x105272,a923)),f319(f319(f8(f932(a923,a923),f932(f932(x105272,a923),f932(x105272,a923)),x105272),f8(a923,a923,x105272)),f319(f319(f8(a923,f932(a923,a923),x105272),a317),f319(f319(f7(x105272,f932(x105272,a923),a923),f321(x105272)),x105273)))),f319(f319(f7(x105272,f932(x105272,a923),a923),f321(x105272)),x105271))))))),f319(f319(f225(x105272),f11(x105272,f224(x105272),x105273)),f11(x105272,f224(x105272),x105271)))
% 28.77/28.54 [7429]~P129(x74293)+E(x74291,x74292)+~E(f319(f319(f236(x74293),x74291),x74294),f319(f319(f236(x74293),x74292),x74294))+~P1(f319(f319(f226(x74293),f2(x74293)),x74292))+~P1(f319(f319(f226(x74293),f2(x74293)),x74291))+~P1(f319(f319(f227(a925),f2(a925)),x74294))
% 28.77/28.54 [8248]~P74(x82481)+~P100(x82481)+P1(f319(f319(f227(x82481),x82482),f2(x82481)))+P1(f319(f319(f227(x82481),f2(x82481)),x82482))+P1(f319(f319(f226(x82481),f319(f319(f283(x82481),x82483),x82482)),f319(f95(x82481),x82484)))+~P1(f319(f319(f226(x82481),f2(x82481)),f319(f95(x82481),x82484)))
% 28.77/28.54 [8249]~P74(x82491)+~P100(x82491)+P1(f319(f319(f227(x82491),x82492),f2(x82491)))+P1(f319(f319(f227(x82491),f2(x82491)),x82492))+P1(f319(f319(f227(x82491),f319(f319(f283(x82491),x82493),x82492)),f319(f95(x82491),x82494)))+~P1(f319(f319(f227(x82491),f2(x82491)),f319(f95(x82491),x82494)))
% 28.77/28.54 [8492]~P74(x84921)+~P100(x84921)+P1(f319(f319(f227(x84921),x84922),f2(x84921)))+P1(f319(f319(f227(x84921),f2(x84921)),x84922))+~P1(f319(f319(f226(x84921),f319(f319(f283(x84921),x84924),x84922)),f319(f95(x84921),x84923)))+P1(f319(f319(f226(x84921),f2(x84921)),f319(f95(x84921),x84923)))
% 28.77/28.54 [8493]~P74(x84931)+~P100(x84931)+P1(f319(f319(f227(x84931),x84932),f2(x84931)))+P1(f319(f319(f227(x84931),f2(x84931)),x84932))+~P1(f319(f319(f227(x84931),f319(f319(f283(x84931),x84934),x84932)),f319(f95(x84931),x84933)))+P1(f319(f319(f227(x84931),f2(x84931)),f319(f95(x84931),x84933)))
% 28.77/28.54 [9388]~P1(f319(x93882,x93883))+~P1(f319(x93881,x93884))+E(f230(a925,x93881),f319(a104,f230(a925,x93882)))+P1(f319(x93882,f841(x93883,x93882,x93884,x93881)))+P1(f319(x93881,f2(a925)))+P1(f319(x93881,f319(a104,f841(x93883,x93882,x93884,x93881))))
% 28.77/28.54 [9650]~P1(f319(x96502,x96503))+~P1(f319(x96501,x96504))+E(f230(a925,x96501),f319(a104,f230(a925,x96502)))+~P1(f319(x96502,f841(x96503,x96502,x96504,x96501)))+P1(f319(x96501,f2(a925)))+~P1(f319(x96501,f319(a104,f841(x96503,x96502,x96504,x96501))))
% 28.77/28.54 [7698]~P4(x76982)+E(x76981,f180(f932(x76982,a923)))+~P1(f319(f55(x76982),x76981))+~P1(f319(f319(f321(x76982),x76984),x76981))+P1(f319(f319(f226(x76982),x76983),x76984))+~P1(f319(f319(f226(x76982),x76983),f319(f57(x76982,f224(x76982)),x76981)))
% 28.77/28.54 [7699]~P108(x76992)+E(x76991,f180(f932(x76992,a923)))+~P1(f319(f55(x76992),x76991))+~P1(f319(f319(f321(x76992),x76994),x76991))+P1(f319(f319(f226(x76992),x76993),x76994))+~P1(f319(f319(f226(x76992),x76993),f319(f57(x76992,f93(x76992)),x76991)))
% 28.77/28.54 [7700]~P4(x77002)+E(x77001,f180(f932(x77002,a923)))+~P1(f319(f55(x77002),x77001))+~P1(f319(f319(f321(x77002),x77004),x77001))+P1(f319(f319(f227(x77002),x77003),x77004))+~P1(f319(f319(f227(x77002),x77003),f319(f57(x77002,f224(x77002)),x77001)))
% 28.77/28.54 [8202]~P74(x82021)+~P100(x82021)+P1(f319(f319(f227(x82021),f319(f95(x82021),x82022)),f2(x82021)))+~P1(f319(f319(f226(x82021),x82023),f2(x82021)))+P1(f319(f319(f227(x82021),f2(x82021)),f319(f95(x82021),x82022)))+P1(f319(f319(f226(x82021),x82023),f319(f319(f283(x82021),x82024),f319(f95(x82021),x82022))))
% 28.77/28.54 [8203]~P74(x82031)+~P100(x82031)+P1(f319(f319(f227(x82031),f319(f95(x82031),x82032)),f2(x82031)))+~P1(f319(f319(f227(x82031),x82033),f2(x82031)))+P1(f319(f319(f227(x82031),f2(x82031)),f319(f95(x82031),x82032)))+P1(f319(f319(f227(x82031),x82033),f319(f319(f283(x82031),x82034),f319(f95(x82031),x82032))))
% 28.77/28.54 [8216]~P74(x82161)+~P100(x82161)+P1(f319(f319(f227(x82161),x82162),f2(x82161)))+~P1(f319(f319(f226(x82161),f319(f95(x82161),x82163)),f2(x82161)))+P1(f319(f319(f227(x82161),f2(x82161)),x82162))+P1(f319(f319(f226(x82161),f319(f95(x82161),x82163)),f319(f319(f283(x82161),x82164),x82162)))
% 28.77/28.54 [8217]~P74(x82171)+~P100(x82171)+P1(f319(f319(f227(x82171),x82172),f2(x82171)))+~P1(f319(f319(f227(x82171),f319(f95(x82171),x82173)),f2(x82171)))+P1(f319(f319(f227(x82171),f2(x82171)),x82172))+P1(f319(f319(f227(x82171),f319(f95(x82171),x82173)),f319(f319(f283(x82171),x82174),x82172)))
% 28.77/28.54 [8364]~P74(x83641)+~P100(x83641)+P1(f319(f319(f227(x83641),x83642),f2(x83641)))+P1(f319(f319(f226(x83641),f319(f95(x83641),x83643)),f2(x83641)))+P1(f319(f319(f227(x83641),f2(x83641)),x83642))+~P1(f319(f319(f226(x83641),f319(f95(x83641),x83643)),f319(f319(f283(x83641),x83644),x83642)))
% 28.77/28.54 [8365]~P74(x83651)+~P100(x83651)+P1(f319(f319(f227(x83651),x83652),f2(x83651)))+P1(f319(f319(f227(x83651),f319(f95(x83651),x83653)),f2(x83651)))+P1(f319(f319(f227(x83651),f2(x83651)),x83652))+~P1(f319(f319(f227(x83651),f319(f95(x83651),x83653)),f319(f319(f283(x83651),x83654),x83652)))
% 28.77/28.54 [8438]~P74(x84381)+~P100(x84381)+P1(f319(f319(f226(x84381),x84382),f2(x84381)))+P1(f319(f319(f227(x84381),f319(f95(x84381),x84383)),f2(x84381)))+P1(f319(f319(f227(x84381),f2(x84381)),f319(f95(x84381),x84383)))+~P1(f319(f319(f226(x84381),x84382),f319(f319(f283(x84381),x84384),f319(f95(x84381),x84383))))
% 28.77/28.54 [8439]~P74(x84391)+~P100(x84391)+P1(f319(f319(f227(x84391),x84392),f2(x84391)))+P1(f319(f319(f227(x84391),f319(f95(x84391),x84393)),f2(x84391)))+P1(f319(f319(f227(x84391),f2(x84391)),f319(f95(x84391),x84393)))+~P1(f319(f319(f227(x84391),x84392),f319(f319(f283(x84391),x84394),f319(f95(x84391),x84393))))
% 28.77/28.54 [8633]~P74(x86331)+~P100(x86331)+~P1(f319(f319(f226(x86331),x86333),f2(x86331)))+P1(f319(f319(f227(x86331),f2(x86331)),f319(f95(x86331),x86332)))+~P1(f319(f319(f226(x86331),x86334),f319(f319(f75(x86331),x86333),f319(f95(x86331),x86332))))+P1(f319(f319(f226(x86331),x86333),f319(f319(f283(x86331),x86334),f319(f95(x86331),x86332))))
% 28.77/28.54 [8634]~P74(x86341)+~P100(x86341)+~P1(f319(f319(f227(x86341),x86343),f2(x86341)))+P1(f319(f319(f227(x86341),f2(x86341)),f319(f95(x86341),x86342)))+~P1(f319(f319(f227(x86341),x86344),f319(f319(f75(x86341),x86343),f319(f95(x86341),x86342))))+P1(f319(f319(f227(x86341),x86343),f319(f319(f283(x86341),x86344),f319(f95(x86341),x86342))))
% 28.77/28.54 [8804]~P74(x88041)+~P100(x88041)+~P1(f319(f319(f227(x88041),f319(f95(x88041),x88042)),f2(x88041)))+P1(f319(f319(f227(x88041),f2(x88041)),f319(f95(x88041),x88042)))+~P1(f319(f319(f226(x88041),x88044),f319(f319(f75(x88041),x88043),f319(f95(x88041),x88042))))+P1(f319(f319(f226(x88041),x88043),f319(f319(f283(x88041),x88044),f319(f95(x88041),x88042))))
% 28.77/28.54 [8805]~P74(x88051)+~P100(x88051)+~P1(f319(f319(f227(x88051),f319(f95(x88051),x88052)),f2(x88051)))+P1(f319(f319(f227(x88051),f2(x88051)),f319(f95(x88051),x88052)))+~P1(f319(f319(f226(x88051),x88054),f319(f319(f283(x88051),x88053),f319(f95(x88051),x88052))))+P1(f319(f319(f226(x88051),x88053),f319(f319(f75(x88051),x88054),f319(f95(x88051),x88052))))
% 28.77/28.54 [8806]~P74(x88061)+~P100(x88061)+~P1(f319(f319(f227(x88061),f319(f95(x88061),x88062)),f2(x88061)))+P1(f319(f319(f227(x88061),f2(x88061)),f319(f95(x88061),x88062)))+~P1(f319(f319(f227(x88061),x88064),f319(f319(f75(x88061),x88063),f319(f95(x88061),x88062))))+P1(f319(f319(f227(x88061),x88063),f319(f319(f283(x88061),x88064),f319(f95(x88061),x88062))))
% 28.77/28.54 [8807]~P74(x88071)+~P100(x88071)+~P1(f319(f319(f227(x88071),f319(f95(x88071),x88072)),f2(x88071)))+P1(f319(f319(f227(x88071),f2(x88071)),f319(f95(x88071),x88072)))+~P1(f319(f319(f227(x88071),x88074),f319(f319(f283(x88071),x88073),f319(f95(x88071),x88072))))+P1(f319(f319(f227(x88071),x88073),f319(f319(f75(x88071),x88074),f319(f95(x88071),x88072))))
% 28.77/28.54 [7605]E(x76051,f2(a1))+E(f319(f319(f30(a1),x76052),x76051),x76053)+~P1(f319(f319(f226(a1),x76054),f2(a1)))+~E(x76052,f319(f319(f74(a1),f319(f319(f75(a1),x76051),x76053)),x76054))+P1(f319(f319(f227(a1),f2(a1)),x76051))+~P1(f319(f319(f227(a1),x76051),x76054))
% 28.77/28.54 [7621]E(f39(a1,x76212,x76211),x76213)+E(x76211,f2(a1))+~P1(f319(f319(f226(a1),x76213),f2(a1)))+~E(x76212,f319(f319(f74(a1),f319(f319(f75(a1),x76211),x76214)),x76213))+P1(f319(f319(f227(a1),f2(a1)),x76211))+~P1(f319(f319(f227(a1),x76211),x76213))
% 28.77/28.54 [7735]E(x77351,f2(a1))+E(f319(f319(f30(a1),x77352),x77351),x77353)+~E(x77352,f319(f319(f74(a1),f319(f319(f75(a1),x77351),x77353)),x77354))+~P1(f319(f319(f226(a1),f2(a1)),x77354))+~P1(f319(f319(f227(a1),f2(a1)),x77351))+~P1(f319(f319(f227(a1),x77354),x77351))
% 28.77/28.54 [7757]E(f39(a1,x77572,x77571),x77573)+E(x77571,f2(a1))+~E(x77572,f319(f319(f74(a1),f319(f319(f75(a1),x77571),x77574)),x77573))+~P1(f319(f319(f226(a1),f2(a1)),x77573))+~P1(f319(f319(f227(a1),f2(a1)),x77571))+~P1(f319(f319(f227(a1),x77573),x77571))
% 28.77/28.54 [7900]~P4(x79002)+E(x79001,f180(f932(x79002,a923)))+~P1(f319(f55(x79002),x79001))+~P1(f319(f319(f321(x79002),x79004),x79001))+~P1(f319(f319(f226(x79002),x79004),x79003))+P1(f319(f319(f226(x79002),f319(f57(x79002,f224(x79002)),x79001)),x79003))
% 28.77/28.54 [7901]~P4(x79012)+E(x79011,f180(f932(x79012,a923)))+~P1(f319(f55(x79012),x79011))+~P1(f319(f319(f227(x79012),x79014),x79013))+~P1(f319(f319(f321(x79012),x79014),x79011))+P1(f319(f319(f227(x79012),f319(f57(x79012,f224(x79012)),x79011)),x79013))
% 28.77/28.54 [8469]~P1(f319(f319(f226(a1),x84694),f2(a1)))+~E(x84691,f319(f319(f74(a1),f319(f319(f75(a1),x84692),x84693)),x84694))+~P1(f319(f319(f226(a1),f2(a1)),x84694))+~P1(f319(f319(f227(a1),x84694),x84692))+~P1(f319(f319(f227(a1),x84692),x84694))+P1(f319(f43(x84691,x84692),f319(f319(f244(a1,a1),x84693),x84694)))
% 28.77/28.54 [8595]~P74(x85951)+~P100(x85951)+P1(f319(f319(f227(x85951),f319(f95(x85951),x85952)),f2(x85951)))+~P1(f319(f319(f226(x85951),f2(x85951)),x85954))+P1(f319(f319(f227(x85951),f2(x85951)),f319(f95(x85951),x85952)))+P1(f319(f319(f226(x85951),f319(f319(f283(x85951),x85953),f319(f95(x85951),x85952))),x85954))
% 28.77/28.54 [8596]~P74(x85961)+~P100(x85961)+P1(f319(f319(f227(x85961),f319(f95(x85961),x85962)),f2(x85961)))+~P1(f319(f319(f227(x85961),f2(x85961)),x85964))+P1(f319(f319(f227(x85961),f2(x85961)),f319(f95(x85961),x85962)))+P1(f319(f319(f227(x85961),f319(f319(f283(x85961),x85963),f319(f95(x85961),x85962))),x85964))
% 28.77/28.54 [8709]~P74(x87091)+~P100(x87091)+~P1(f319(f319(f227(x87091),x87092),f2(x87091)))+P1(f319(f319(f227(x87091),f2(x87091)),x87092))+~P1(f319(f319(f226(x87091),f319(f95(x87091),x87094)),f319(f319(f283(x87091),x87093),x87092)))+P1(f319(f319(f226(x87091),x87093),f319(f319(f75(x87091),f319(f95(x87091),x87094)),x87092)))
% 28.77/28.54 [8710]~P74(x87101)+~P100(x87101)+~P1(f319(f319(f227(x87101),x87102),f2(x87101)))+P1(f319(f319(f227(x87101),f2(x87101)),x87102))+~P1(f319(f319(f227(x87101),f319(f95(x87101),x87104)),f319(f319(f283(x87101),x87103),x87102)))+P1(f319(f319(f227(x87101),x87103),f319(f319(f75(x87101),f319(f95(x87101),x87104)),x87102)))
% 28.77/28.54 [8748]~P74(x87481)+~P100(x87481)+~P1(f319(f319(f227(x87481),x87482),f2(x87481)))+P1(f319(f319(f227(x87481),f2(x87481)),x87482))+P1(f319(f319(f226(x87481),f319(f95(x87481),x87483)),f319(f319(f283(x87481),x87484),x87482)))+~P1(f319(f319(f226(x87481),x87484),f319(f319(f75(x87481),f319(f95(x87481),x87483)),x87482)))
% 28.77/28.54 [8749]~P74(x87491)+~P100(x87491)+~P1(f319(f319(f227(x87491),x87492),f2(x87491)))+P1(f319(f319(f227(x87491),f2(x87491)),x87492))+P1(f319(f319(f227(x87491),f319(f95(x87491),x87493)),f319(f319(f283(x87491),x87494),x87492)))+~P1(f319(f319(f227(x87491),x87494),f319(f319(f75(x87491),f319(f95(x87491),x87493)),x87492)))
% 28.77/28.54 [8844]~P74(x88441)+~P100(x88441)+P1(f319(f319(f227(x88441),f319(f95(x88441),x88443)),f2(x88441)))+P1(f319(f319(f226(x88441),f2(x88441)),x88442))+P1(f319(f319(f227(x88441),f2(x88441)),f319(f95(x88441),x88443)))+~P1(f319(f319(f226(x88441),f319(f319(f283(x88441),x88444),f319(f95(x88441),x88443))),x88442))
% 28.77/28.54 [8845]~P74(x88451)+~P100(x88451)+P1(f319(f319(f227(x88451),f319(f95(x88451),x88453)),f2(x88451)))+P1(f319(f319(f227(x88451),f2(x88451)),x88452))+P1(f319(f319(f227(x88451),f2(x88451)),f319(f95(x88451),x88453)))+~P1(f319(f319(f227(x88451),f319(f319(f283(x88451),x88454),f319(f95(x88451),x88453))),x88452))
% 28.77/28.54 [8896]~P74(x88961)+~P100(x88961)+~P1(f319(f319(f226(x88961),f319(f95(x88961),x88963)),f2(x88961)))+P1(f319(f319(f227(x88961),f2(x88961)),x88962))+P1(f319(f319(f226(x88961),f319(f95(x88961),x88963)),f319(f319(f283(x88961),x88964),x88962)))+~P1(f319(f319(f226(x88961),x88964),f319(f319(f75(x88961),f319(f95(x88961),x88963)),x88962)))
% 28.77/28.54 [8897]~P74(x88971)+~P100(x88971)+~P1(f319(f319(f227(x88971),f319(f95(x88971),x88973)),f2(x88971)))+P1(f319(f319(f227(x88971),f2(x88971)),x88972))+P1(f319(f319(f227(x88971),f319(f95(x88971),x88973)),f319(f319(f283(x88971),x88974),x88972)))+~P1(f319(f319(f227(x88971),x88974),f319(f319(f75(x88971),f319(f95(x88971),x88973)),x88972)))
% 28.77/28.54 [8905]~P74(x89051)+~P100(x89051)+P1(f319(f319(f227(x89051),x89052),f2(x89051)))+P1(f319(f319(f226(x89051),f319(f319(f283(x89051),x89053),x89052)),f319(f95(x89051),x89054)))+~P1(f319(f319(f226(x89051),f2(x89051)),f319(f95(x89051),x89054)))+~P1(f319(f319(f226(x89051),x89053),f319(f319(f75(x89051),f319(f95(x89051),x89054)),x89052)))
% 28.77/28.54 [8906]~P74(x89061)+~P100(x89061)+P1(f319(f319(f227(x89061),x89062),f2(x89061)))+P1(f319(f319(f227(x89061),f319(f319(f283(x89061),x89063),x89062)),f319(f95(x89061),x89064)))+~P1(f319(f319(f227(x89061),f2(x89061)),f319(f95(x89061),x89064)))+~P1(f319(f319(f227(x89061),x89063),f319(f319(f75(x89061),f319(f95(x89061),x89064)),x89062)))
% 28.77/28.54 [8926]~P74(x89261)+~P100(x89261)+P1(f319(f319(f227(x89261),f319(f95(x89261),x89262)),f2(x89261)))+~P1(f319(f319(f226(x89261),f2(x89261)),x89264))+~P1(f319(f319(f226(x89261),x89263),f319(f319(f75(x89261),x89264),f319(f95(x89261),x89262))))+P1(f319(f319(f226(x89261),f319(f319(f283(x89261),x89263),f319(f95(x89261),x89262))),x89264))
% 28.77/28.54 [8927]~P74(x89271)+~P100(x89271)+P1(f319(f319(f227(x89271),f319(f95(x89271),x89272)),f2(x89271)))+~P1(f319(f319(f227(x89271),f2(x89271)),x89274))+~P1(f319(f319(f227(x89271),x89273),f319(f319(f75(x89271),x89274),f319(f95(x89271),x89272))))+P1(f319(f319(f227(x89271),f319(f319(f283(x89271),x89273),f319(f95(x89271),x89272))),x89274))
% 28.77/28.54 [9020]~P74(x90201)+~P100(x90201)+P1(f319(f319(f227(x90201),f319(f95(x90201),x90202)),f2(x90201)))+~P1(f319(f319(f226(x90201),x90203),f2(x90201)))+P1(f319(f319(f226(x90201),x90203),f319(f319(f283(x90201),x90204),f319(f95(x90201),x90202))))+~P1(f319(f319(f226(x90201),f319(f319(f75(x90201),x90203),f319(f95(x90201),x90202))),x90204))
% 28.77/28.54 [9021]~P74(x90211)+~P100(x90211)+P1(f319(f319(f227(x90211),f319(f95(x90211),x90212)),f2(x90211)))+~P1(f319(f319(f227(x90211),x90213),f2(x90211)))+P1(f319(f319(f227(x90211),x90213),f319(f319(f283(x90211),x90214),f319(f95(x90211),x90212))))+~P1(f319(f319(f227(x90211),f319(f319(f75(x90211),x90213),f319(f95(x90211),x90212))),x90214))
% 28.77/28.54 [9139]~P74(x91391)+~P100(x91391)+~P1(f319(f319(f226(x91391),f2(x91391)),x91394))+P1(f319(f319(f227(x91391),f2(x91391)),f319(f95(x91391),x91392)))+~P1(f319(f319(f226(x91391),f319(f319(f75(x91391),x91394),f319(f95(x91391),x91392))),x91393))+P1(f319(f319(f226(x91391),f319(f319(f283(x91391),x91393),f319(f95(x91391),x91392))),x91394))
% 28.77/28.54 [9140]~P74(x91401)+~P100(x91401)+~P1(f319(f319(f227(x91401),f2(x91401)),x91404))+P1(f319(f319(f227(x91401),f2(x91401)),f319(f95(x91401),x91402)))+~P1(f319(f319(f227(x91401),f319(f319(f75(x91401),x91404),f319(f95(x91401),x91402))),x91403))+P1(f319(f319(f227(x91401),f319(f319(f283(x91401),x91403),f319(f95(x91401),x91402))),x91404))
% 28.77/28.54 [9200]~P74(x92001)+~P100(x92001)+~P1(f319(f319(f226(x92001),x92002),f2(x92001)))+P1(f319(f319(f226(x92001),x92002),f319(f319(f283(x92001),x92003),f319(f95(x92001),x92004))))+~P1(f319(f319(f226(x92001),x92003),f319(f319(f75(x92001),x92002),f319(f95(x92001),x92004))))+~P1(f319(f319(f226(x92001),f319(f319(f75(x92001),x92002),f319(f95(x92001),x92004))),x92003))
% 28.77/28.54 [9201]~P74(x92011)+~P100(x92011)+~P1(f319(f319(f227(x92011),x92012),f2(x92011)))+P1(f319(f319(f227(x92011),x92012),f319(f319(f283(x92011),x92013),f319(f95(x92011),x92014))))+~P1(f319(f319(f227(x92011),x92013),f319(f319(f75(x92011),x92012),f319(f95(x92011),x92014))))+~P1(f319(f319(f227(x92011),f319(f319(f75(x92011),x92012),f319(f95(x92011),x92014))),x92013))
% 28.77/28.54 [9229]~P74(x92291)+~P100(x92291)+~P1(f319(f319(f227(x92291),f319(f95(x92291),x92292)),f2(x92291)))+P1(f319(f319(f227(x92291),f2(x92291)),f319(f95(x92291),x92292)))+~P1(f319(f319(f226(x92291),f319(f319(f283(x92291),x92294),f319(f95(x92291),x92292))),x92293))+P1(f319(f319(f226(x92291),f319(f319(f75(x92291),x92293),f319(f95(x92291),x92292))),x92294))
% 28.77/28.54 [9230]~P74(x92301)+~P100(x92301)+~P1(f319(f319(f227(x92301),f319(f95(x92301),x92302)),f2(x92301)))+P1(f319(f319(f227(x92301),f2(x92301)),f319(f95(x92301),x92302)))+~P1(f319(f319(f226(x92301),f319(f319(f75(x92301),x92304),f319(f95(x92301),x92302))),x92303))+P1(f319(f319(f226(x92301),f319(f319(f283(x92301),x92303),f319(f95(x92301),x92302))),x92304))
% 28.77/28.54 [9231]~P74(x92311)+~P100(x92311)+~P1(f319(f319(f227(x92311),f319(f95(x92311),x92312)),f2(x92311)))+P1(f319(f319(f227(x92311),f2(x92311)),f319(f95(x92311),x92312)))+~P1(f319(f319(f227(x92311),f319(f319(f283(x92311),x92314),f319(f95(x92311),x92312))),x92313))+P1(f319(f319(f227(x92311),f319(f319(f75(x92311),x92313),f319(f95(x92311),x92312))),x92314))
% 28.77/28.54 [9232]~P74(x92321)+~P100(x92321)+~P1(f319(f319(f227(x92321),f319(f95(x92321),x92322)),f2(x92321)))+P1(f319(f319(f227(x92321),f2(x92321)),f319(f95(x92321),x92322)))+~P1(f319(f319(f227(x92321),f319(f319(f75(x92321),x92324),f319(f95(x92321),x92322))),x92323))+P1(f319(f319(f227(x92321),f319(f319(f283(x92321),x92323),f319(f95(x92321),x92322))),x92324))
% 28.77/28.54 [9309]~P74(x93091)+~P100(x93091)+~P1(f319(f319(f227(x93091),f319(f95(x93091),x93094)),f2(x93091)))+P1(f319(f319(f226(x93091),x93092),f319(f319(f283(x93091),x93093),f319(f95(x93091),x93094))))+~P1(f319(f319(f226(x93091),x93093),f319(f319(f75(x93091),x93092),f319(f95(x93091),x93094))))+~P1(f319(f319(f226(x93091),f319(f319(f75(x93091),x93092),f319(f95(x93091),x93094))),x93093))
% 28.77/28.54 [9310]~P74(x93101)+~P100(x93101)+~P1(f319(f319(f227(x93101),f319(f95(x93101),x93104)),f2(x93101)))+P1(f319(f319(f227(x93101),x93102),f319(f319(f283(x93101),x93103),f319(f95(x93101),x93104))))+~P1(f319(f319(f227(x93101),x93103),f319(f319(f75(x93101),x93102),f319(f95(x93101),x93104))))+~P1(f319(f319(f227(x93101),f319(f319(f75(x93101),x93102),f319(f95(x93101),x93104))),x93103))
% 28.77/28.54 [9355]~P74(x93551)+~P100(x93551)+~P1(f319(f319(f226(x93551),f2(x93551)),x93554))+~P1(f319(f319(f226(x93551),x93552),f319(f319(f75(x93551),x93554),f319(f95(x93551),x93553))))+~P1(f319(f319(f226(x93551),f319(f319(f75(x93551),x93554),f319(f95(x93551),x93553))),x93552))+P1(f319(f319(f226(x93551),f319(f319(f283(x93551),x93552),f319(f95(x93551),x93553))),x93554))
% 28.77/28.54 [9356]~P74(x93561)+~P100(x93561)+~P1(f319(f319(f227(x93561),f2(x93561)),x93564))+~P1(f319(f319(f227(x93561),x93562),f319(f319(f75(x93561),x93564),f319(f95(x93561),x93563))))+~P1(f319(f319(f227(x93561),f319(f319(f75(x93561),x93564),f319(f95(x93561),x93563))),x93562))+P1(f319(f319(f227(x93561),f319(f319(f283(x93561),x93562),f319(f95(x93561),x93563))),x93564))
% 28.77/28.54 [9393]~P74(x93931)+~P100(x93931)+~P1(f319(f319(f227(x93931),f319(f95(x93931),x93933)),f2(x93931)))+~P1(f319(f319(f226(x93931),x93932),f319(f319(f75(x93931),x93934),f319(f95(x93931),x93933))))+~P1(f319(f319(f226(x93931),f319(f319(f75(x93931),x93934),f319(f95(x93931),x93933))),x93932))+P1(f319(f319(f226(x93931),f319(f319(f283(x93931),x93932),f319(f95(x93931),x93933))),x93934))
% 28.77/28.54 [9394]~P74(x93941)+~P100(x93941)+~P1(f319(f319(f227(x93941),f319(f95(x93941),x93943)),f2(x93941)))+~P1(f319(f319(f227(x93941),x93942),f319(f319(f75(x93941),x93944),f319(f95(x93941),x93943))))+~P1(f319(f319(f227(x93941),f319(f319(f75(x93941),x93944),f319(f95(x93941),x93943))),x93942))+P1(f319(f319(f227(x93941),f319(f319(f283(x93941),x93942),f319(f95(x93941),x93943))),x93944))
% 28.77/28.54 [9084]~P74(x90841)+~P100(x90841)+~P1(f319(f319(f227(x90841),x90842),f2(x90841)))+~P1(f319(f319(f226(x90841),f319(f319(f283(x90841),x90844),x90842)),f319(f95(x90841),x90843)))+P1(f319(f319(f227(x90841),f2(x90841)),x90842))+P1(f319(f319(f226(x90841),f319(f319(f75(x90841),f319(f95(x90841),x90843)),x90842)),x90844))
% 28.77/28.54 [9085]~P74(x90851)+~P100(x90851)+~P1(f319(f319(f227(x90851),x90852),f2(x90851)))+~P1(f319(f319(f227(x90851),f319(f319(f283(x90851),x90854),x90852)),f319(f95(x90851),x90853)))+P1(f319(f319(f227(x90851),f2(x90851)),x90852))+P1(f319(f319(f227(x90851),f319(f319(f75(x90851),f319(f95(x90851),x90853)),x90852)),x90854))
% 28.77/28.54 [9204]~P74(x92041)+~P100(x92041)+~P1(f319(f319(f227(x92041),x92042),f2(x92041)))+P1(f319(f319(f227(x92041),f2(x92041)),x92042))+P1(f319(f319(f226(x92041),f319(f319(f283(x92041),x92043),x92042)),f319(f95(x92041),x92044)))+~P1(f319(f319(f226(x92041),f319(f319(f75(x92041),f319(f95(x92041),x92044)),x92042)),x92043))
% 28.77/28.54 [9205]~P74(x92051)+~P100(x92051)+~P1(f319(f319(f227(x92051),x92052),f2(x92051)))+P1(f319(f319(f227(x92051),f2(x92051)),x92052))+P1(f319(f319(f227(x92051),f319(f319(f283(x92051),x92053),x92052)),f319(f95(x92051),x92054)))+~P1(f319(f319(f227(x92051),f319(f319(f75(x92051),f319(f95(x92051),x92054)),x92052)),x92053))
% 28.77/28.54 [9243]~P74(x92431)+~P100(x92431)+P1(f319(f319(f227(x92431),x92432),f2(x92431)))+~P1(f319(f319(f226(x92431),f319(f95(x92431),x92433)),f2(x92431)))+P1(f319(f319(f226(x92431),f319(f95(x92431),x92433)),f319(f319(f283(x92431),x92434),x92432)))+~P1(f319(f319(f226(x92431),f319(f319(f75(x92431),f319(f95(x92431),x92433)),x92432)),x92434))
% 28.77/28.54 [9244]~P74(x92441)+~P100(x92441)+P1(f319(f319(f227(x92441),x92442),f2(x92441)))+~P1(f319(f319(f227(x92441),f319(f95(x92441),x92443)),f2(x92441)))+P1(f319(f319(f227(x92441),f319(f95(x92441),x92443)),f319(f319(f283(x92441),x92444),x92442)))+~P1(f319(f319(f227(x92441),f319(f319(f75(x92441),f319(f95(x92441),x92443)),x92442)),x92444))
% 28.77/28.54 [9260]~P74(x92601)+~P100(x92601)+P1(f319(f319(f227(x92601),f2(x92601)),x92602))+P1(f319(f319(f226(x92601),f319(f319(f283(x92601),x92603),x92602)),f319(f95(x92601),x92604)))+~P1(f319(f319(f226(x92601),f2(x92601)),f319(f95(x92601),x92604)))+~P1(f319(f319(f226(x92601),f319(f319(f75(x92601),f319(f95(x92601),x92604)),x92602)),x92603))
% 28.77/28.54 [9261]~P74(x92611)+~P100(x92611)+P1(f319(f319(f227(x92611),f2(x92611)),x92612))+P1(f319(f319(f227(x92611),f319(f319(f283(x92611),x92613),x92612)),f319(f95(x92611),x92614)))+~P1(f319(f319(f227(x92611),f2(x92611)),f319(f95(x92611),x92614)))+~P1(f319(f319(f227(x92611),f319(f319(f75(x92611),f319(f95(x92611),x92614)),x92612)),x92613))
% 28.77/28.54 [9424]~P74(x94241)+~P100(x94241)+~P1(f319(f319(f227(x94241),x94244),f2(x94241)))+P1(f319(f319(f226(x94241),f319(f95(x94241),x94242)),f319(f319(f283(x94241),x94243),x94244)))+~P1(f319(f319(f226(x94241),x94243),f319(f319(f75(x94241),f319(f95(x94241),x94242)),x94244)))+~P1(f319(f319(f226(x94241),f319(f319(f75(x94241),f319(f95(x94241),x94242)),x94244)),x94243))
% 28.77/28.54 [9425]~P74(x94251)+~P100(x94251)+~P1(f319(f319(f227(x94251),x94254),f2(x94251)))+P1(f319(f319(f227(x94251),f319(f95(x94251),x94252)),f319(f319(f283(x94251),x94253),x94254)))+~P1(f319(f319(f227(x94251),x94253),f319(f319(f75(x94251),f319(f95(x94251),x94252)),x94254)))+~P1(f319(f319(f227(x94251),f319(f319(f75(x94251),f319(f95(x94251),x94252)),x94254)),x94253))
% 28.77/28.54 [9460]~P74(x94601)+~P100(x94601)+~P1(f319(f319(f227(x94601),x94603),f2(x94601)))+P1(f319(f319(f226(x94601),f319(f319(f283(x94601),x94602),x94603)),f319(f95(x94601),x94604)))+~P1(f319(f319(f226(x94601),x94602),f319(f319(f75(x94601),f319(f95(x94601),x94604)),x94603)))+~P1(f319(f319(f226(x94601),f319(f319(f75(x94601),f319(f95(x94601),x94604)),x94603)),x94602))
% 28.77/28.54 [9461]~P74(x94611)+~P100(x94611)+~P1(f319(f319(f227(x94611),x94613),f2(x94611)))+P1(f319(f319(f227(x94611),f319(f319(f283(x94611),x94612),x94613)),f319(f95(x94611),x94614)))+~P1(f319(f319(f227(x94611),x94612),f319(f319(f75(x94611),f319(f95(x94611),x94614)),x94613)))+~P1(f319(f319(f227(x94611),f319(f319(f75(x94611),f319(f95(x94611),x94614)),x94613)),x94612))
% 28.77/28.54 [9480]~P74(x94801)+~P100(x94801)+~P1(f319(f319(f226(x94801),f319(f95(x94801),x94802)),f2(x94801)))+P1(f319(f319(f226(x94801),f319(f95(x94801),x94802)),f319(f319(f283(x94801),x94803),x94804)))+~P1(f319(f319(f226(x94801),x94803),f319(f319(f75(x94801),f319(f95(x94801),x94802)),x94804)))+~P1(f319(f319(f226(x94801),f319(f319(f75(x94801),f319(f95(x94801),x94802)),x94804)),x94803))
% 28.77/28.54 [9481]~P74(x94811)+~P100(x94811)+~P1(f319(f319(f227(x94811),f319(f95(x94811),x94812)),f2(x94811)))+P1(f319(f319(f227(x94811),f319(f95(x94811),x94812)),f319(f319(f283(x94811),x94813),x94814)))+~P1(f319(f319(f227(x94811),x94813),f319(f319(f75(x94811),f319(f95(x94811),x94812)),x94814)))+~P1(f319(f319(f227(x94811),f319(f319(f75(x94811),f319(f95(x94811),x94812)),x94814)),x94813))
% 28.77/28.54 [9485]~P74(x94851)+~P100(x94851)+P1(f319(f319(f226(x94851),f319(f319(f283(x94851),x94852),x94853)),f319(f95(x94851),x94854)))+~P1(f319(f319(f226(x94851),f2(x94851)),f319(f95(x94851),x94854)))+~P1(f319(f319(f226(x94851),x94852),f319(f319(f75(x94851),f319(f95(x94851),x94854)),x94853)))+~P1(f319(f319(f226(x94851),f319(f319(f75(x94851),f319(f95(x94851),x94854)),x94853)),x94852))
% 28.77/28.54 [9486]~P74(x94861)+~P100(x94861)+P1(f319(f319(f227(x94861),f319(f319(f283(x94861),x94862),x94863)),f319(f95(x94861),x94864)))+~P1(f319(f319(f227(x94861),f2(x94861)),f319(f95(x94861),x94864)))+~P1(f319(f319(f227(x94861),x94862),f319(f319(f75(x94861),f319(f95(x94861),x94864)),x94863)))+~P1(f319(f319(f227(x94861),f319(f319(f75(x94861),f319(f95(x94861),x94864)),x94863)),x94862))
% 28.77/28.54 [6285]~P121(x62852)+~P138(x62852)+~E(f319(x62853,x62855),f2(x62852))+E(f319(f319(f9(x62851,x62852),x62853),x62854),f2(x62852))+~P1(f319(f55(x62851),x62854))+~P1(f319(f319(f321(x62851),x62855),x62854))
% 28.77/28.54 [8638]~P113(x86381)+P1(f319(f319(f227(f932(x86381,a923)),f295(x86381,x86382,x86383)),f295(x86381,x86384,x86385)))+~P1(f319(f319(f226(x86381),x86384),x86382))+~P1(f319(f319(f226(x86381),x86384),x86385))+~P1(f319(f319(f226(x86381),x86383),x86385))+~P1(f319(f319(f227(x86381),x86383),x86385))
% 28.77/28.54 [8639]~P113(x86391)+P1(f319(f319(f227(f932(x86391,a923)),f295(x86391,x86392,x86393)),f295(x86391,x86394,x86395)))+~P1(f319(f319(f226(x86391),x86393),x86395))+~P1(f319(f319(f226(x86391),x86394),x86395))+~P1(f319(f319(f226(x86391),x86394),x86392))+~P1(f319(f319(f227(x86391),x86394),x86392))
% 28.77/28.54 [9512]P63(x95122,x95123,x95124,x95121)+E(x95121,f180(f932(x95122,a923)))+~P1(f319(f55(x95122),x95124))+~P1(f319(f55(x95122),x95121))+~P1(f319(f319(x95123,f561(x95121,x95124,x95123,x95122)),x95125))+~P1(f319(f319(f321(x95122),x95125),x95121))
% 28.77/28.54 [9513]P63(x95132,x95133,x95134,x95131)+E(x95131,f180(f932(x95132,a923)))+~P1(f319(f55(x95132),x95134))+~P1(f319(f55(x95132),x95131))+~P1(f319(f319(x95133,f817(x95133,x95131,x95134,x95132)),x95135))+~P1(f319(f319(f321(x95132),x95135),x95131))
% 28.77/28.54 [9514]P63(x95142,x95143,x95144,x95141)+E(x95141,f180(f932(x95142,a923)))+~P1(f319(f55(x95142),x95144))+~P1(f319(f55(x95142),x95141))+~P1(f319(f319(x95143,f818(x95141,x95144,x95143,x95142)),x95145))+~P1(f319(f319(f321(x95142),x95145),x95141))
% 28.77/28.54 [9665]~E(x96653,x96655)+~P78(x96651)+~P79(x96651)+~P42(x96653)+E(f319(f319(f6(a1,x96651),x96652),x96653),f319(f319(f6(a1,x96651),x96654),x96655))+P1(f319(f319(f226(a1),f2(a1)),f447(x96652,x96654,x96653,x96655,x96651)))
% 28.77/28.54 [9666]~E(x96663,x96665)+~P78(x96661)+~P79(x96661)+~P42(x96663)+E(f319(f319(f9(a1,x96661),x96662),x96663),f319(f319(f9(a1,x96661),x96664),x96665))+P1(f319(f319(f226(a1),f2(a1)),f510(x96662,x96664,x96663,x96665,x96661)))
% 28.77/28.54 [9841]~E(x98415,x98413)+~P78(x98411)+~P79(x98411)+~P42(x98415)+~E(f319(x98412,f447(x98414,x98412,x98415,x98413,x98411)),f319(x98414,f447(x98414,x98412,x98415,x98413,x98411)))+E(f319(f319(f6(a1,x98411),x98412),x98413),f319(f319(f6(a1,x98411),x98414),x98415))
% 28.77/28.54 [9842]~E(x98425,x98423)+~P78(x98421)+~P79(x98421)+~P42(x98425)+~E(f319(x98422,f510(x98424,x98422,x98425,x98423,x98421)),f319(x98424,f510(x98424,x98422,x98425,x98423,x98421)))+E(f319(f319(f9(a1,x98421),x98422),x98423),f319(f319(f9(a1,x98421),x98424),x98425))
% 28.77/28.54 [9933]~P68(x99333)+E(f319(x99331,x99332),f2(x99333))+~E(f319(f319(f6(x99334,x99333),x99331),x99335),f2(x99333))+~P1(f319(f55(x99334),x99335))+P1(f319(f319(f321(x99334),f429(x99332,x99331,x99335,x99334,x99333)),x99335))+~P1(f319(f319(f321(x99334),x99332),x99335))
% 28.77/28.54 [10075]~P68(x100753)+E(f319(x100751,x100752),f2(x100753))+~E(f319(f319(f6(x100754,x100753),x100751),x100755),f2(x100753))+~P1(f319(f55(x100754),x100755))+~P1(f319(f319(f321(x100754),x100752),x100755))+~P1(f319(f319(f226(x100753),f2(x100753)),f319(x100751,f429(x100752,x100751,x100755,x100754,x100753))))
% 28.77/28.54 [8556]~P141(x85561)+~P1(f319(f319(f226(x85561),x85563),x85565))+~P1(f319(f319(f226(x85561),x85562),x85564))+~P1(f319(f319(f226(x85561),f2(x85561)),x85563))+~P1(f319(f319(f226(x85561),f2(x85561)),x85564))+P1(f319(f319(f226(x85561),f319(f319(f75(x85561),x85562),x85563)),f319(f319(f75(x85561),x85564),x85565)))
% 28.77/28.54 [8557]~P141(x85571)+~P1(f319(f319(f226(x85571),x85573),x85575))+~P1(f319(f319(f226(x85571),x85572),x85574))+~P1(f319(f319(f226(x85571),f2(x85571)),x85573))+~P1(f319(f319(f226(x85571),f2(x85571)),x85572))+P1(f319(f319(f226(x85571),f319(f319(f75(x85571),x85572),x85573)),f319(f319(f75(x85571),x85574),x85575)))
% 28.77/28.54 [8558]~P75(x85581)+~P1(f319(f319(f227(x85581),f2(x85581)),x85585))+~P1(f319(f319(f226(x85581),x85585),x85583))+~P1(f319(f319(f226(x85581),x85582),x85584))+~P1(f319(f319(f226(x85581),f2(x85581)),x85582))+P1(f319(f319(f226(x85581),f319(f319(f283(x85581),x85582),x85583)),f319(f319(f283(x85581),x85584),x85585)))
% 28.77/28.54 [8559]~P134(x85591)+~P1(f319(f319(f226(x85591),x85593),x85595))+~P1(f319(f319(f226(x85591),f2(x85591)),x85592))+~P1(f319(f319(f227(x85591),x85592),x85594))+~P1(f319(f319(f227(x85591),f2(x85591)),x85593))+P1(f319(f319(f227(x85591),f319(f319(f75(x85591),x85592),x85593)),f319(f319(f75(x85591),x85594),x85595)))
% 28.77/28.54 [8560]~P134(x85601)+~P1(f319(f319(f226(x85601),x85602),x85604))+~P1(f319(f319(f226(x85601),f2(x85601)),x85603))+~P1(f319(f319(f227(x85601),x85603),x85605))+~P1(f319(f319(f227(x85601),f2(x85601)),x85602))+P1(f319(f319(f227(x85601),f319(f319(f75(x85601),x85602),x85603)),f319(f319(f75(x85601),x85604),x85605)))
% 28.77/28.54 [8561]~P134(x85611)+~P1(f319(f319(f226(x85611),f2(x85611)),x85613))+~P1(f319(f319(f226(x85611),f2(x85611)),x85612))+~P1(f319(f319(f227(x85611),x85613),x85615))+~P1(f319(f319(f227(x85611),x85612),x85614))+P1(f319(f319(f227(x85611),f319(f319(f75(x85611),x85612),x85613)),f319(f319(f75(x85611),x85614),x85615)))
% 28.77/28.54 [8562]~P134(x85621)+~P1(f319(f319(f226(x85621),f2(x85621)),x85623))+~P1(f319(f319(f227(x85621),x85623),x85625))+~P1(f319(f319(f227(x85621),x85622),x85624))+~P1(f319(f319(f227(x85621),f2(x85621)),x85624))+P1(f319(f319(f227(x85621),f319(f319(f75(x85621),x85622),x85623)),f319(f319(f75(x85621),x85624),x85625)))
% 28.77/28.54 [8563]~P75(x85631)+~P1(f319(f319(f226(x85631),x85635),x85633))+~P1(f319(f319(f226(x85631),f2(x85631)),x85632))+~P1(f319(f319(f227(x85631),x85632),x85634))+~P1(f319(f319(f227(x85631),f2(x85631)),x85635))+P1(f319(f319(f227(x85631),f319(f319(f283(x85631),x85632),x85633)),f319(f319(f283(x85631),x85634),x85635)))
% 28.77/28.54 [8564]~P75(x85641)+~P1(f319(f319(f226(x85641),x85642),x85644))+~P1(f319(f319(f227(x85641),x85645),x85643))+~P1(f319(f319(f227(x85641),f2(x85641)),x85645))+~P1(f319(f319(f227(x85641),f2(x85641)),x85642))+P1(f319(f319(f227(x85641),f319(f319(f283(x85641),x85642),x85643)),f319(f319(f283(x85641),x85644),x85645)))
% 28.77/28.54 [9984]~P79(x99845)+~P89(x99845)+E(x99841,f180(f932(x99842,a923)))+~P1(f319(f55(x99842),x99841))+P1(f319(f319(f321(x99842),f350(x99843,x99844,x99841,x99842,x99845)),x99841))+P1(f319(f319(f227(x99845),f319(f319(f6(x99842,x99845),x99844),x99841)),f319(f319(f6(x99842,x99845),x99843),x99841)))
% 28.77/28.54 [10103]~P79(x101031)+~P91(x101031)+~P1(f319(f55(x101032),x101035))+~P1(f319(f319(f226(x101031),f2(x101031)),f319(x101033,f410(x101033,x101034,x101035,x101032,x101031))))+P1(f319(f319(f226(x101031),f319(f319(f6(x101032,x101031),x101033),x101034)),f319(f319(f6(x101032,x101031),x101033),x101035)))+~P1(f319(f319(f226(f932(x101032,a923)),x101034),x101035))
% 28.77/28.54 [10275]~P79(x102753)+~P89(x102753)+E(x102751,f180(f932(x102752,a923)))+~P1(f319(f55(x102752),x102751))+~P1(f319(f319(f227(x102753),f319(x102754,f350(x102755,x102754,x102751,x102752,x102753))),f319(x102755,f350(x102755,x102754,x102751,x102752,x102753))))+P1(f319(f319(f227(x102753),f319(f319(f6(x102752,x102753),x102754),x102751)),f319(f319(f6(x102752,x102753),x102755),x102751)))
% 28.77/28.54 [7282]~P19(x72822,x72825,x72824)+E(x72821,f180(f932(x72822,a923)))+E(x72823,f180(f932(x72822,a923)))+~P1(f319(f55(x72822),x72821))+~P1(f319(f55(x72822),x72823))+E(f319(x72824,f319(f319(f102(f932(x72822,a923)),x72823),x72821)),f319(f319(x72825,f319(x72824,x72823)),f319(x72824,x72821)))
% 28.77/28.54 [7867]~P152(x78671,x78674,x78673)+P1(f319(x78671,x78672))+~P1(f319(f319(f227(a1),x78674),f2(a1)))+~P1(f319(f319(f226(a1),x78675),f2(a1)))+~E(x78673,f319(f319(f74(a1),f319(f319(f75(a1),x78674),x78672)),x78675))+~P1(f319(f319(f227(a1),x78674),x78675))
% 28.77/28.54 [7868]~P151(x78681,x78684,x78683)+P1(f319(x78681,x78682))+~P1(f319(f319(f227(a1),x78684),f2(a1)))+~P1(f319(f319(f226(a1),x78682),f2(a1)))+~E(x78683,f319(f319(f74(a1),f319(f319(f75(a1),x78684),x78685)),x78682))+~P1(f319(f319(f227(a1),x78684),x78682))
% 28.77/28.54 [7910]~P152(x79101,x79104,x79103)+P1(f319(x79101,x79102))+~E(x79103,f319(f319(f74(a1),f319(f319(f75(a1),x79104),x79102)),x79105))+~P1(f319(f319(f226(a1),f2(a1)),x79105))+~P1(f319(f319(f227(a1),f2(a1)),x79104))+~P1(f319(f319(f227(a1),x79105),x79104))
% 28.77/28.54 [7911]~P151(x79111,x79114,x79113)+P1(f319(x79111,x79112))+~E(x79113,f319(f319(f74(a1),f319(f319(f75(a1),x79114),x79115)),x79112))+~P1(f319(f319(f226(a1),f2(a1)),x79112))+~P1(f319(f319(f227(a1),f2(a1)),x79114))+~P1(f319(f319(f227(a1),x79112),x79114))
% 28.77/28.54 [8852]P1(f319(f319(x88521,x88522),x88523))+~P1(f319(f319(x88521,f319(f319(f30(a1),x88524),x88525)),f39(a1,x88524,x88525)))+~P1(f319(f319(f227(a1),x88525),f2(a1)))+~P1(f319(f319(f226(a1),x88523),f2(a1)))+~E(x88524,f319(f319(f74(a1),f319(f319(f75(a1),x88525),x88522)),x88523))+~P1(f319(f319(f227(a1),x88525),x88523))
% 28.77/28.54 [8861]P1(f319(f319(x88611,x88612),x88613))+~P1(f319(f319(x88611,f319(f319(f30(a1),x88614),x88615)),f39(a1,x88614,x88615)))+~E(x88614,f319(f319(f74(a1),f319(f319(f75(a1),x88615),x88612)),x88613))+~P1(f319(f319(f226(a1),f2(a1)),x88613))+~P1(f319(f319(f227(a1),f2(a1)),x88615))+~P1(f319(f319(f227(a1),x88613),x88615))
% 28.77/28.54 [9124]E(x91241,x91242)+~P60(x91243,x91245,x91244)+~P1(f319(f319(f321(x91243),x91242),x91245))+~P1(f319(f319(f321(x91243),x91241),x91245))+P1(f319(f319(f321(f931(x91243,x91243)),f319(f319(f244(x91243,x91243),x91241),x91242)),x91244))+P1(f319(f319(f321(f931(x91243,x91243)),f319(f319(f244(x91243,x91243),x91242),x91241)),x91244))
% 28.77/28.54 [9956]~P113(x99561)+~P113(x99562)+~P41(x99562,x99561,x99563)+~P1(f319(f319(f226(x99562),x99565),f806(x99564,x99563,x99562,x99561,x99565)))+E(f230(x99561,f319(f319(f7(x99561,f932(x99561,a923),a923),f321(x99561)),f319(f302(x99562,x99561,x99563),x99564))),f319(x99563,f230(x99562,f319(f319(f7(x99562,f932(x99562,a923),a923),f321(x99562)),x99564))))+~P1(f319(f319(f321(x99562),x99565),x99564))
% 28.77/28.54 [10015]~P79(x100155)+~P91(x100155)+~P1(f319(f55(x100151),x100154))+P1(f319(f319(f226(x100155),f319(f319(f6(x100151,x100155),x100152),x100153)),f319(f319(f6(x100151,x100155),x100152),x100154)))+~P1(f319(f319(f226(f932(x100151,a923)),x100153),x100154))+P1(f319(f319(f321(x100151),f410(x100152,x100153,x100154,x100151,x100155)),f319(f319(f23(f932(x100151,a923)),x100154),x100153)))
% 28.77/28.54 [10031]~P113(x100311)+~P113(x100312)+~P41(x100312,x100311,x100313)+E(f230(x100311,f319(f319(f7(x100311,f932(x100311,a923),a923),f321(x100311)),f319(f302(x100312,x100311,x100313),x100314))),f319(x100313,f230(x100312,f319(f319(f7(x100312,f932(x100312,a923),a923),f321(x100312)),x100314))))+~P1(f319(f319(f321(x100312),x100315),x100314))+P1(f319(f319(f321(x100312),f806(x100314,x100313,x100312,x100311,x100315)),x100314))
% 28.77/28.54 [10111]E(x101111,f180(f932(x101112,a923)))+~P1(f319(f55(x101112),x101113))+~P1(f319(f55(x101112),x101111))+P1(f319(f319(f321(f931(f932(x101112,a923),f932(x101112,a923))),f319(f319(f244(f932(x101112,a923),f932(x101112,a923)),x101113),x101111)),f311(x101112,x101114)))+~P1(f319(f319(f321(x101112),x101115),x101111))+~P1(f319(f319(f321(f931(x101112,x101112)),f319(f319(f244(x101112,x101112),f571(x101114,x101111,x101113,x101112)),x101115)),x101114))
% 28.77/28.54 [10112]E(x101121,f180(f932(x101122,a923)))+~P1(f319(f55(x101122),x101123))+~P1(f319(f55(x101122),x101121))+P1(f319(f319(f321(f931(f932(x101122,a923),f932(x101122,a923))),f319(f319(f244(f932(x101122,a923),f932(x101122,a923)),x101123),x101121)),f311(x101122,x101124)))+~P1(f319(f319(f321(x101122),x101125),x101121))+~P1(f319(f319(f321(f931(x101122,x101122)),f319(f319(f244(x101122,x101122),f618(x101124,x101121,x101123,x101122)),x101125)),x101124))
% 28.77/28.54 [10280]~P68(x102801)+~E(f319(f319(f6(x102805,x102801),x102802),x102806),x102804)+~P1(f319(f55(x102805),x102806))+P1(f319(f319(f321(x102805),f437(x102803,x102804,x102802,x102806,x102805,x102801)),x102806))+P1(f319(f319(f226(x102801),f319(x102802,x102803)),x102804))+~P1(f319(f319(f321(x102805),x102803),x102806))
% 28.77/28.54 [10329]~P68(x103291)+~E(f319(f319(f6(x103295,x103291),x103292),x103296),x103294)+~P1(f319(f55(x103295),x103296))+~P1(f319(f319(f321(x103295),x103293),x103296))+~P1(f319(f319(f226(x103291),f2(x103291)),f319(x103292,f437(x103293,x103294,x103292,x103296,x103295,x103291))))+P1(f319(f319(f226(x103291),f319(x103292,x103293)),x103294))
% 28.77/28.54 [10468]~E(x104685,x104688)+~E(x104684,x104687)+~P3(x104681)+~P79(x104682)+E(f319(f319(f6(x104681,x104682),x104683),f319(f294(x104681,x104684),x104685)),f319(f319(f6(x104681,x104682),x104686),f319(f294(x104681,x104687),x104688)))+P1(f319(f319(f226(x104681),x104684),f621(x104683,x104686,x104685,x104688,x104684,x104687,x104681,x104682)))
% 28.77/28.54 [10484]~E(x104847,x104844)+~E(x104848,x104845)+~P3(x104841)+~P79(x104842)+~E(f319(x104843,f621(x104846,x104843,x104848,x104845,x104847,x104844,x104841,x104842)),f319(x104846,f621(x104846,x104843,x104848,x104845,x104847,x104844,x104841,x104842)))+E(f319(f319(f6(x104841,x104842),x104843),f319(f294(x104841,x104844),x104845)),f319(f319(f6(x104841,x104842),x104846),f319(f294(x104841,x104847),x104848)))
% 28.77/28.54 [10489]~E(x104894,x104897)+~E(x104895,x104898)+~P3(x104891)+~P79(x104892)+E(f319(f319(f6(x104891,x104892),x104893),f319(f294(x104891,x104894),x104895)),f319(f319(f6(x104891,x104892),x104896),f319(f294(x104891,x104897),x104898)))+P1(f319(f319(f227(x104891),f621(x104893,x104896,x104895,x104898,x104894,x104897,x104891,x104892)),x104895))
% 28.77/28.54 [10118]~P9(x101185,x101189,x101186)+~P9(x101181,x1011810,x101183)+~P13(x101181,x101185,f932(x101182,a923),x101183,x101186,x101188)+~P1(f319(f319(f321(x101185),x101187),x101189))+~P1(f319(f319(f321(x101181),x101184),x1011810))+E(f319(f319(f33(x101181,f932(x101182,a923)),f319(f277(x101181,x101181,x101183),f319(f319(f301(x101181),x101184),f180(f932(x101181,a923))))),f319(f319(f8(f932(x101185,f932(x101182,a923)),f932(x101182,a923),x101181),f319(f33(x101185,f932(x101182,a923)),f319(f277(x101185,x101185,x101186),f319(f319(f301(x101185),x101187),f180(f932(x101185,a923)))))),x101188)),f319(f319(x101188,x101184),x101187))
% 28.77/28.54 [5803]~P4(x58033)+~P14(x58033,x58032)+~P14(x58033,x58031)+E(x58031,x58032)+~E(f319(f164(x58033),x58031),f319(f164(x58033),x58032))+~P1(f319(f129(x58033),x58032))+~P1(f319(f129(x58033),x58031))
% 28.77/28.54 [5135]~P133(x51352)+~P138(x51352)+~P150(x51352)+~P119(x51352)+~E(x51353,f2(x51352))+E(x51351,f2(a925))+E(f319(f319(f236(x51352),x51353),x51351),f2(x51352))
% 28.77/28.54 [9387]E(x93871,f2(a925))+~E(x93872,f319(f319(f74(a925),f319(f319(f75(a925),f319(f243(a925,a925),x93873)),x93871)),f319(f248(a925,a925),x93873)))+P1(f319(f42(x93872,x93871),x93873))+~P1(f319(f319(f226(a925),f319(f248(a925,a925),x93873)),f2(a925)))+~P1(f319(f319(f226(a925),f2(a925)),f319(f248(a925,a925),x93873)))+~P1(f319(f319(f227(a925),x93871),f319(f248(a925,a925),x93873)))+~P1(f319(f319(f227(a925),f319(f248(a925,a925),x93873)),x93871))
% 28.77/28.54 [9396]~E(f319(f243(a925,a925),x93963),f2(a925))+~E(x93961,f319(f319(f74(a925),f319(f319(f75(a925),f319(f243(a925,a925),x93963)),x93962)),f319(f248(a925,a925),x93963)))+P1(f319(f42(x93961,x93962),x93963))+~P1(f319(f319(f226(a925),f319(f248(a925,a925),x93963)),f2(a925)))+~P1(f319(f319(f226(a925),f2(a925)),f319(f248(a925,a925),x93963)))+~P1(f319(f319(f227(a925),x93962),f319(f248(a925,a925),x93963)))+~P1(f319(f319(f227(a925),f319(f248(a925,a925),x93963)),x93962))
% 28.77/28.54 [7747]~P102(x77472)+E(x77471,f180(f932(x77472,a923)))+E(x77473,f180(f932(x77472,a923)))+~P1(f319(f55(x77472),x77471))+~P1(f319(f55(x77472),x77473))+~E(f319(f319(f93(f932(x77472,a923)),x77473),x77471),f180(f932(x77472,a923)))+E(f10(x77472,f319(f319(f102(f932(x77472,a923)),x77473),x77471)),f319(f319(f93(x77472),f10(x77472,x77473)),f10(x77472,x77471)))
% 28.77/28.54 [7748]~P102(x77482)+E(x77481,f180(f932(x77482,a923)))+E(x77483,f180(f932(x77482,a923)))+~P1(f319(f55(x77482),x77481))+~P1(f319(f55(x77482),x77483))+~E(f319(f319(f93(f932(x77482,a923)),x77483),x77481),f180(f932(x77482,a923)))+E(f13(x77482,f319(f319(f102(f932(x77482,a923)),x77483),x77481)),f319(f319(f102(x77482),f13(x77482,x77483)),f13(x77482,x77481)))
% 28.77/28.54 [7749]~P4(x77492)+E(x77491,f180(f932(x77492,a923)))+E(x77493,f180(f932(x77492,a923)))+~P1(f319(f55(x77492),x77491))+~P1(f319(f55(x77492),x77493))+~E(f319(f319(f93(f932(x77492,a923)),x77493),x77491),f180(f932(x77492,a923)))+E(f14(x77492,f319(f319(f102(f932(x77492,a923)),x77493),x77491)),f319(f319(f224(x77492),f14(x77492,x77493)),f14(x77492,x77491)))
% 28.77/28.54 [7750]~P4(x77502)+E(x77501,f180(f932(x77502,a923)))+E(x77503,f180(f932(x77502,a923)))+~P1(f319(f55(x77502),x77501))+~P1(f319(f55(x77502),x77503))+~E(f319(f319(f93(f932(x77502,a923)),x77503),x77501),f180(f932(x77502,a923)))+E(f15(x77502,f319(f319(f102(f932(x77502,a923)),x77503),x77501)),f319(f319(f225(x77502),f15(x77502,x77503)),f15(x77502,x77501)))
% 28.77/28.54 [8223]~P76(x82232)+E(x82231,f180(f932(x82232,a923)))+E(x82233,f180(f932(x82232,a923)))+~P1(f319(f55(x82232),x82231))+~P1(f319(f55(x82232),x82233))+~E(f319(f319(f93(f932(x82232,a923)),x82233),x82231),f180(f932(x82232,a923)))+E(f319(f319(f75(x82232),f319(f57(x82232,f75(x82232)),x82233)),f319(f57(x82232,f75(x82232)),x82231)),f319(f57(x82232,f75(x82232)),f319(f319(f102(f932(x82232,a923)),x82233),x82231)))
% 28.77/28.54 [8296]~P4(x82962)+E(x82961,f180(f932(x82962,a923)))+E(x82963,f180(f932(x82962,a923)))+~P1(f319(f55(x82962),x82961))+~P1(f319(f55(x82962),x82963))+~E(f319(f319(f93(f932(x82962,a923)),x82963),x82961),f180(f932(x82962,a923)))+E(f319(f319(f224(x82962),f11(x82962,f224(x82962),x82963)),f11(x82962,f224(x82962),x82961)),f11(x82962,f224(x82962),f319(f319(f102(f932(x82962,a923)),x82963),x82961)))
% 28.77/28.54 [8297]~P4(x82972)+E(x82971,f180(f932(x82972,a923)))+E(x82973,f180(f932(x82972,a923)))+~P1(f319(f55(x82972),x82971))+~P1(f319(f55(x82972),x82973))+~E(f319(f319(f93(f932(x82972,a923)),x82973),x82971),f180(f932(x82972,a923)))+E(f319(f319(f225(x82972),f12(x82972,f225(x82972),x82973)),f12(x82972,f225(x82972),x82971)),f12(x82972,f225(x82972),f319(f319(f102(f932(x82972,a923)),x82973),x82971)))
% 28.77/28.54 [8004]E(x80041,f2(a1))+E(f319(f319(f30(a1),x80042),x80041),x80043)+~P1(f319(f319(f226(a1),x80044),f2(a1)))+~E(x80042,f319(f319(f74(a1),f319(f319(f75(a1),x80041),x80043)),x80044))+~P1(f319(f319(f226(a1),f2(a1)),x80044))+~P1(f319(f319(f227(a1),x80044),x80041))+~P1(f319(f319(f227(a1),x80041),x80044))
% 28.77/28.54 [8012]E(f39(a1,x80122,x80121),x80123)+E(x80121,f2(a1))+~P1(f319(f319(f226(a1),x80123),f2(a1)))+~E(x80122,f319(f319(f74(a1),f319(f319(f75(a1),x80121),x80124)),x80123))+~P1(f319(f319(f226(a1),f2(a1)),x80123))+~P1(f319(f319(f227(a1),x80123),x80121))+~P1(f319(f319(f227(a1),x80121),x80123))
% 28.77/28.54 [7067]~P65(x70672)+E(x70671,f2(x70672))+E(x70673,f2(x70672))+~E(f319(f319(f30(x70672),x70674),x70673),f319(f319(f30(x70672),x70675),x70671))+E(f319(f319(f75(x70672),x70674),x70671),f319(f319(f75(x70672),x70673),x70675))+~P1(f319(f319(f279(x70672),x70671),x70675))+~P1(f319(f319(f279(x70672),x70673),x70674))
% 28.77/28.54 [7068]~P65(x70682)+E(x70681,f2(x70682))+E(x70683,f2(x70682))+~E(f319(f319(f75(x70682),x70684),x70683),f319(f319(f75(x70682),x70681),x70685))+E(f319(f319(f30(x70682),x70684),x70681),f319(f319(f30(x70682),x70685),x70683))+~P1(f319(f319(f279(x70682),x70681),x70684))+~P1(f319(f319(f279(x70682),x70683),x70685))
% 28.77/28.54 [7919]~P20(x79192,x79195,x79194)+E(x79191,f180(f932(x79192,a923)))+E(x79193,f180(f932(x79192,a923)))+~P1(f319(f55(x79192),x79191))+~P1(f319(f55(x79192),x79193))+~E(f319(f319(f93(f932(x79192,a923)),x79193),x79191),f180(f932(x79192,a923)))+E(f319(x79194,f319(f319(f102(f932(x79192,a923)),x79193),x79191)),f319(f319(x79195,f319(x79194,x79193)),f319(x79194,x79191)))
% 28.77/28.54 [9637]~P26(x96373,x96371,x96375,x96374)+~P26(x96371,x96373,x96376,x96372)+E(f319(f29(x96371),x96372),f319(f29(x96373),x96374))+~P1(f319(f55(x96373),x96374))+~P1(f319(f55(x96371),x96372))+~P1(f319(f319(f226(f932(x96373,a923)),f319(f302(x96371,x96373,x96376),x96372)),x96374))+~P1(f319(f319(f226(f932(x96371,a923)),f319(f302(x96373,x96371,x96375),x96374)),x96372))
% 28.77/28.54 [9579]~P1(f319(f319(f227(a1),f319(f319(f74(a1),f319(f319(f75(a1),x95795),x95791)),x95796)),f2(a1)))+~E(f319(f319(f74(a1),f319(f319(f75(a1),x95793),x95792)),x95794),f319(f319(f74(a1),f319(f319(f75(a1),x95795),x95791)),x95796))+~P1(f319(f319(f226(a1),f2(a1)),x95796))+~P1(f319(f319(f227(a1),f2(a1)),x95795))+~P1(f319(f319(f226(a1),x95795),x95793))+~P1(f319(f319(f227(a1),x95794),x95793))+P1(f319(f319(f226(a1),x95791),x95792))
% 28.77/28.54 [9337]~E(f319(f319(f74(a1),f319(f319(f75(a1),x93373),x93371)),x93374),f319(f319(f74(a1),f319(f319(f75(a1),x93375),x93372)),x93376))+~P1(f319(f319(f226(a1),f2(a1)),x93374))+~P1(f319(f319(f227(a1),f2(a1)),x93375))+~P1(f319(f319(f226(a1),x93375),x93373))+~P1(f319(f319(f227(a1),x93376),x93375))+P1(f319(f319(f226(a1),x93371),x93372))+~P1(f319(f319(f226(a1),f2(a1)),f319(f319(f74(a1),f319(f319(f75(a1),x93375),x93372)),x93376)))
% 28.77/28.54 [9518]~P136(x95181)+~E(f319(f319(f74(x95181),x95182),x95184),f72(x95181))+~P1(f319(f319(f226(x95181),x95185),x95186))+~P1(f319(f319(f226(x95181),x95183),x95186))+~P1(f319(f319(f226(x95181),f2(x95181)),x95184))+~P1(f319(f319(f226(x95181),f2(x95181)),x95182))+P1(f319(f319(f226(x95181),f319(f319(f74(x95181),f319(f319(f75(x95181),x95182),x95183)),f319(f319(f75(x95181),x95184),x95185))),x95186))
% 28.77/28.54 [9519]~P137(x95191)+~E(f319(f319(f74(x95191),x95192),x95194),f72(x95191))+~P1(f319(f319(f226(x95191),f2(x95191)),x95194))+~P1(f319(f319(f226(x95191),f2(x95191)),x95192))+~P1(f319(f319(f227(x95191),x95195),x95196))+~P1(f319(f319(f227(x95191),x95193),x95196))+P1(f319(f319(f227(x95191),f319(f319(f74(x95191),f319(f319(f75(x95191),x95192),x95193)),f319(f319(f75(x95191),x95194),x95195))),x95196))
% 28.77/28.54 [10377]~P9(x103777,x103776,x103775)+E(x103771,x103772)+~P12(x103777,f932(x103774,a923),x103775,x103773)+E(f319(x103773,f549(x103771,x103772,x103773,x103774,x103775,x103776,x103777)),f319(x103773,f547(x103771,x103772,x103773,x103774,x103775,x103776,x103777)))+~E(f319(f319(f33(x103777,f932(x103774,a923)),x103771),x103773),f319(f319(f33(x103777,f932(x103774,a923)),x103772),x103773))+~P1(f319(f319(f321(f932(x103777,a923)),x103772),f319(f319(f54(x103777),x103776),x103775)))+~P1(f319(f319(f321(f932(x103777,a923)),x103771),f319(f319(f54(x103777),x103776),x103775)))
% 28.77/28.54 [10423]~P9(x104233,x104237,x104236)+E(x104231,x104232)+~P12(x104233,f932(x104235,a923),x104236,x104234)+~E(f319(f319(f33(x104233,f932(x104235,a923)),x104231),x104234),f319(f319(f33(x104233,f932(x104235,a923)),x104232),x104234))+P1(f319(f319(f321(x104233),f547(x104231,x104232,x104234,x104235,x104236,x104237,x104233)),x104237))+~P1(f319(f319(f321(f932(x104233,a923)),x104232),f319(f319(f54(x104233),x104237),x104236)))+~P1(f319(f319(f321(f932(x104233,a923)),x104231),f319(f319(f54(x104233),x104237),x104236)))
% 28.77/28.54 [10424]~P9(x104243,x104247,x104246)+E(x104241,x104242)+~P12(x104243,f932(x104245,a923),x104246,x104244)+~E(f319(f319(f33(x104243,f932(x104245,a923)),x104241),x104244),f319(f319(f33(x104243,f932(x104245,a923)),x104242),x104244))+P1(f319(f319(f321(x104243),f549(x104241,x104242,x104244,x104245,x104246,x104247,x104243)),x104247))+~P1(f319(f319(f321(f932(x104243,a923)),x104242),f319(f319(f54(x104243),x104247),x104246)))+~P1(f319(f319(f321(f932(x104243,a923)),x104241),f319(f319(f54(x104243),x104247),x104246)))
% 28.77/28.54 [10505]E(x105051,x105052)+~P9(x105053,x105056,x105057)+~P12(x105053,f932(x105054,a923),x105057,x105055)+~E(f319(f319(f33(x105053,f932(x105054,a923)),x105051),x105055),f319(f319(f33(x105053,f932(x105054,a923)),x105052),x105055))+~P1(f319(f319(f321(f931(x105053,x105053)),f319(f319(f244(x105053,x105053),f547(x105051,x105052,x105055,x105054,x105057,x105056,x105053)),f549(x105051,x105052,x105055,x105054,x105057,x105056,x105053))),x105057))+~P1(f319(f319(f321(f932(x105053,a923)),x105052),f319(f319(f54(x105053),x105056),x105057)))+~P1(f319(f319(f321(f932(x105053,a923)),x105051),f319(f319(f54(x105053),x105056),x105057)))
% 28.77/28.54 [9336]~P9(x93361,x93367,x93364)+~E(x93365,x93366)+~P1(f319(f319(f321(x93361),x93363),x93366))+~P1(f319(f319(f321(x93361),x93362),x93365))+~P1(f319(f319(f321(f932(x93361,a923)),x93366),f319(f319(f54(x93361),x93367),x93364)))+~P1(f319(f319(f321(f932(x93361,a923)),x93365),f319(f319(f54(x93361),x93367),x93364)))+P1(f319(f319(f321(f931(x93361,x93361)),f319(f319(f244(x93361,x93361),x93362),x93363)),x93364))
% 28.77/28.54 [9474]E(x94741,x94742)+~P9(x94743,x94744,x94745)+~P1(f319(f319(f321(x94743),x94746),x94742))+~P1(f319(f319(f321(x94743),x94747),x94741))+~P1(f319(f319(f321(f932(x94743,a923)),x94742),f319(f319(f54(x94743),x94744),x94745)))+~P1(f319(f319(f321(f932(x94743,a923)),x94741),f319(f319(f54(x94743),x94744),x94745)))+~P1(f319(f319(f321(f931(x94743,x94743)),f319(f319(f244(x94743,x94743),x94747),x94746)),x94745))
% 28.77/28.54 [9475]E(x94751,x94752)+~P9(x94753,x94754,x94755)+~P1(f319(f319(f321(x94753),x94756),x94752))+~P1(f319(f319(f321(x94753),x94757),x94751))+~P1(f319(f319(f321(f932(x94753,a923)),x94752),f319(f319(f54(x94753),x94754),x94755)))+~P1(f319(f319(f321(f932(x94753,a923)),x94751),f319(f319(f54(x94753),x94754),x94755)))+~P1(f319(f319(f321(f931(x94753,x94753)),f319(f319(f244(x94753,x94753),x94757),x94756)),x94755))
% 28.77/28.54 [10533]~P9(x105339,x105338,x105337)+~P9(x105331,x1053311,x1053310)+~P13(x105331,x105339,f932(x105336,a923),x1053310,x105337,x105335)+P1(f319(f319(f321(x105331),f551(x105332,x105333,x105334,x105335,x105336,x105337,x105338,x105339,x1053310,x1053311,x105331)),x1053311))+~P1(f319(f319(f321(f932(x105339,a923)),x105333),f319(f319(f54(x105339),x105338),x105337)))+~P1(f319(f319(f321(f932(x105331,a923)),x105334),f319(f319(f54(x105331),x1053311),x1053310)))+P1(f319(f319(f321(f932(x105336,a923)),f319(f319(f33(x105331,f932(x105336,a923)),x105334),f319(f319(f8(f932(x105339,f932(x105336,a923)),f932(x105336,a923),x105331),f319(f33(x105339,f932(x105336,a923)),x105333)),x105335))),x105332))
% 28.77/28.54 [10534]~P9(x1053411,x1053410,x105349)+~P9(x105341,x105348,x105347)+~P13(x1053411,x105341,f932(x105346,a923),x105349,x105347,x105345)+P1(f319(f319(f321(x105341),f552(x105342,x105343,x105344,x105345,x105346,x105347,x105348,x105341,x105349,x1053410,x1053411)),x105348))+~P1(f319(f319(f321(f932(x1053411,a923)),x105344),f319(f319(f54(x1053411),x1053410),x105349)))+~P1(f319(f319(f321(f932(x105341,a923)),x105343),f319(f319(f54(x105341),x105348),x105347)))+P1(f319(f319(f321(f932(x105346,a923)),f319(f319(f33(x1053411,f932(x105346,a923)),x105344),f319(f319(f8(f932(x105341,f932(x105346,a923)),f932(x105346,a923),x1053411),f319(f33(x105341,f932(x105346,a923)),x105343)),x105345))),x105342))
% 28.77/28.54 [10535]~P9(x105352,x105358,x105359)+~P9(x105354,x1053510,x1053511)+~P13(x105352,x105354,f932(x105351,a923),x105359,x1053511,x105356)+~P1(f319(f319(f321(f932(x105352,a923)),x105353),f319(f319(f54(x105352),x105358),x105359)))+~P1(f319(f319(f321(f932(x105354,a923)),x105355),f319(f319(f54(x105354),x1053510),x1053511)))+~P1(f319(f319(f321(f932(x105351,a923)),f319(f319(x105356,f551(x105357,x105355,x105353,x105356,x105351,x1053511,x1053510,x105354,x105359,x105358,x105352)),f552(x105357,x105355,x105353,x105356,x105351,x1053511,x1053510,x105354,x105359,x105358,x105352))),x105357))+P1(f319(f319(f321(f932(x105351,a923)),f319(f319(f33(x105352,f932(x105351,a923)),x105353),f319(f319(f8(f932(x105354,f932(x105351,a923)),f932(x105351,a923),x105352),f319(f33(x105354,f932(x105351,a923)),x105355)),x105356))),x105357))
% 28.77/28.54 [9372]E(x93721,x93722)+~P4(x93724)+~P26(x93723,x93724,x93725,f319(f319(f102(f932(x93723,a923)),f319(f164(x93723),x93721)),f319(f164(x93723),x93722)))+~E(f319(f164(x93723),x93721),f319(f164(x93723),x93722))+~P14(x93724,f319(f319(f146(x93723,x93724),x93725),x93722))+~P14(x93724,f319(f319(f146(x93723,x93724),x93725),x93721))+~P1(f319(f129(x93724),f319(f319(f146(x93723,x93724),x93725),x93722)))+~P1(f319(f129(x93724),f319(f319(f146(x93723,x93724),x93725),x93721)))
% 28.77/28.54 %EqnAxiom
% 28.77/28.54 [1]E(x11,x11)
% 28.77/28.54 [2]E(x22,x21)+~E(x21,x22)
% 28.77/28.54 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 28.77/28.54 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 28.77/28.54 [5]~E(x51,x52)+E(f92(x51),f92(x52))
% 28.77/28.54 [6]~E(x61,x62)+E(f23(x61),f23(x62))
% 28.77/28.54 [7]~E(x71,x72)+E(f180(x71),f180(x72))
% 28.77/28.54 [8]~E(x81,x82)+E(f319(x81,x83),f319(x82,x83))
% 28.77/28.54 [9]~E(x91,x92)+E(f319(x93,x91),f319(x93,x92))
% 28.77/28.54 [10]~E(x101,x102)+E(f93(x101),f93(x102))
% 28.77/28.54 [11]~E(x111,x112)+E(f224(x111),f224(x112))
% 28.77/28.54 [12]~E(x121,x122)+E(f102(x121),f102(x122))
% 28.77/28.54 [13]~E(x131,x132)+E(f225(x131),f225(x132))
% 28.77/28.54 [14]~E(x141,x142)+E(f94(x141),f94(x142))
% 28.77/28.54 [15]~E(x151,x152)+E(f25(x151),f25(x152))
% 28.77/28.54 [16]~E(x161,x162)+E(f78(x161),f78(x162))
% 28.77/28.54 [17]~E(x171,x172)+E(f321(x171),f321(x172))
% 28.77/28.54 [18]~E(x181,x182)+E(f226(x181),f226(x182))
% 28.77/28.54 [19]~E(x191,x192)+E(f932(x191,x193),f932(x192,x193))
% 28.77/28.54 [20]~E(x201,x202)+E(f932(x203,x201),f932(x203,x202))
% 28.77/28.54 [21]~E(x211,x212)+E(f72(x211),f72(x212))
% 28.77/28.54 [22]~E(x221,x222)+E(f552(x221,x223,x224,x225,x226,x227,x228,x229,x2210,x2211,x2212),f552(x222,x223,x224,x225,x226,x227,x228,x229,x2210,x2211,x2212))
% 28.77/28.54 [23]~E(x231,x232)+E(f552(x233,x231,x234,x235,x236,x237,x238,x239,x2310,x2311,x2312),f552(x233,x232,x234,x235,x236,x237,x238,x239,x2310,x2311,x2312))
% 28.77/28.54 [24]~E(x241,x242)+E(f552(x243,x244,x241,x245,x246,x247,x248,x249,x2410,x2411,x2412),f552(x243,x244,x242,x245,x246,x247,x248,x249,x2410,x2411,x2412))
% 28.77/28.54 [25]~E(x251,x252)+E(f552(x253,x254,x255,x251,x256,x257,x258,x259,x2510,x2511,x2512),f552(x253,x254,x255,x252,x256,x257,x258,x259,x2510,x2511,x2512))
% 28.77/28.54 [26]~E(x261,x262)+E(f552(x263,x264,x265,x266,x261,x267,x268,x269,x2610,x2611,x2612),f552(x263,x264,x265,x266,x262,x267,x268,x269,x2610,x2611,x2612))
% 28.77/28.54 [27]~E(x271,x272)+E(f552(x273,x274,x275,x276,x277,x271,x278,x279,x2710,x2711,x2712),f552(x273,x274,x275,x276,x277,x272,x278,x279,x2710,x2711,x2712))
% 28.77/28.54 [28]~E(x281,x282)+E(f552(x283,x284,x285,x286,x287,x288,x281,x289,x2810,x2811,x2812),f552(x283,x284,x285,x286,x287,x288,x282,x289,x2810,x2811,x2812))
% 28.77/28.54 [29]~E(x291,x292)+E(f552(x293,x294,x295,x296,x297,x298,x299,x291,x2910,x2911,x2912),f552(x293,x294,x295,x296,x297,x298,x299,x292,x2910,x2911,x2912))
% 28.77/28.54 [30]~E(x301,x302)+E(f552(x303,x304,x305,x306,x307,x308,x309,x3010,x301,x3011,x3012),f552(x303,x304,x305,x306,x307,x308,x309,x3010,x302,x3011,x3012))
% 28.77/28.54 [31]~E(x311,x312)+E(f552(x313,x314,x315,x316,x317,x318,x319,x3110,x3111,x311,x3112),f552(x313,x314,x315,x316,x317,x318,x319,x3110,x3111,x312,x3112))
% 28.77/28.54 [32]~E(x321,x322)+E(f552(x323,x324,x325,x326,x327,x328,x329,x3210,x3211,x3212,x321),f552(x323,x324,x325,x326,x327,x328,x329,x3210,x3211,x3212,x322))
% 28.77/28.54 [33]~E(x331,x332)+E(f7(x331,x333,x334),f7(x332,x333,x334))
% 28.77/28.54 [34]~E(x341,x342)+E(f7(x343,x341,x344),f7(x343,x342,x344))
% 28.77/28.54 [35]~E(x351,x352)+E(f7(x353,x354,x351),f7(x353,x354,x352))
% 28.77/28.54 [36]~E(x361,x362)+E(f4(x361),f4(x362))
% 28.77/28.54 [37]~E(x371,x372)+E(f551(x371,x373,x374,x375,x376,x377,x378,x379,x3710,x3711,x3712),f551(x372,x373,x374,x375,x376,x377,x378,x379,x3710,x3711,x3712))
% 28.77/28.54 [38]~E(x381,x382)+E(f551(x383,x381,x384,x385,x386,x387,x388,x389,x3810,x3811,x3812),f551(x383,x382,x384,x385,x386,x387,x388,x389,x3810,x3811,x3812))
% 28.77/28.54 [39]~E(x391,x392)+E(f551(x393,x394,x391,x395,x396,x397,x398,x399,x3910,x3911,x3912),f551(x393,x394,x392,x395,x396,x397,x398,x399,x3910,x3911,x3912))
% 28.77/28.54 [40]~E(x401,x402)+E(f551(x403,x404,x405,x401,x406,x407,x408,x409,x4010,x4011,x4012),f551(x403,x404,x405,x402,x406,x407,x408,x409,x4010,x4011,x4012))
% 28.77/28.54 [41]~E(x411,x412)+E(f551(x413,x414,x415,x416,x411,x417,x418,x419,x4110,x4111,x4112),f551(x413,x414,x415,x416,x412,x417,x418,x419,x4110,x4111,x4112))
% 28.77/28.54 [42]~E(x421,x422)+E(f551(x423,x424,x425,x426,x427,x421,x428,x429,x4210,x4211,x4212),f551(x423,x424,x425,x426,x427,x422,x428,x429,x4210,x4211,x4212))
% 28.77/28.54 [43]~E(x431,x432)+E(f551(x433,x434,x435,x436,x437,x438,x431,x439,x4310,x4311,x4312),f551(x433,x434,x435,x436,x437,x438,x432,x439,x4310,x4311,x4312))
% 28.77/28.54 [44]~E(x441,x442)+E(f551(x443,x444,x445,x446,x447,x448,x449,x441,x4410,x4411,x4412),f551(x443,x444,x445,x446,x447,x448,x449,x442,x4410,x4411,x4412))
% 28.77/28.54 [45]~E(x451,x452)+E(f551(x453,x454,x455,x456,x457,x458,x459,x4510,x451,x4511,x4512),f551(x453,x454,x455,x456,x457,x458,x459,x4510,x452,x4511,x4512))
% 28.77/28.54 [46]~E(x461,x462)+E(f551(x463,x464,x465,x466,x467,x468,x469,x4610,x4611,x461,x4612),f551(x463,x464,x465,x466,x467,x468,x469,x4610,x4611,x462,x4612))
% 28.77/28.54 [47]~E(x471,x472)+E(f551(x473,x474,x475,x476,x477,x478,x479,x4710,x4711,x4712,x471),f551(x473,x474,x475,x476,x477,x478,x479,x4710,x4711,x4712,x472))
% 28.77/28.54 [48]~E(x481,x482)+E(f146(x481,x483),f146(x482,x483))
% 28.77/28.54 [49]~E(x491,x492)+E(f146(x493,x491),f146(x493,x492))
% 28.77/28.54 [50]~E(x501,x502)+E(f103(x501),f103(x502))
% 28.77/28.54 [51]~E(x511,x512)+E(f32(x511,x513),f32(x512,x513))
% 28.77/28.54 [52]~E(x521,x522)+E(f32(x523,x521),f32(x523,x522))
% 28.77/28.54 [53]~E(x531,x532)+E(f924(x531),f924(x532))
% 28.77/28.54 [54]~E(x541,x542)+E(f929(x541),f929(x542))
% 28.77/28.54 [55]~E(x551,x552)+E(f926(x551),f926(x552))
% 28.77/28.54 [56]~E(x561,x562)+E(f927(x561),f927(x562))
% 28.77/28.54 [57]~E(x571,x572)+E(f73(x571),f73(x572))
% 28.77/28.54 [58]~E(x581,x582)+E(f181(x581),f181(x582))
% 28.77/28.54 [59]~E(x591,x592)+E(f95(x591),f95(x592))
% 28.77/28.54 [60]~E(x601,x602)+E(f249(x601,x603,x604),f249(x602,x603,x604))
% 28.77/28.54 [61]~E(x611,x612)+E(f249(x613,x611,x614),f249(x613,x612,x614))
% 28.77/28.54 [62]~E(x621,x622)+E(f249(x623,x624,x621),f249(x623,x624,x622))
% 28.77/28.54 [63]~E(x631,x632)+E(f140(x631,x633,x634),f140(x632,x633,x634))
% 28.77/28.54 [64]~E(x641,x642)+E(f140(x643,x641,x644),f140(x643,x642,x644))
% 28.77/28.54 [65]~E(x651,x652)+E(f140(x653,x654,x651),f140(x653,x654,x652))
% 28.77/28.54 [66]~E(x661,x662)+E(f227(x661),f227(x662))
% 28.77/28.54 [67]~E(x671,x672)+E(f8(x671,x673,x674),f8(x672,x673,x674))
% 28.77/28.54 [68]~E(x681,x682)+E(f8(x683,x681,x684),f8(x683,x682,x684))
% 28.77/28.54 [69]~E(x691,x692)+E(f8(x693,x694,x691),f8(x693,x694,x692))
% 28.77/28.54 [70]~E(x701,x702)+E(f778(x701,x703,x704),f778(x702,x703,x704))
% 28.77/28.54 [71]~E(x711,x712)+E(f778(x713,x711,x714),f778(x713,x712,x714))
% 28.77/28.54 [72]~E(x721,x722)+E(f778(x723,x724,x721),f778(x723,x724,x722))
% 28.77/28.54 [73]~E(x731,x732)+E(f143(x731),f143(x732))
% 28.77/28.54 [74]~E(x741,x742)+E(f75(x741),f75(x742))
% 28.77/28.54 [75]~E(x751,x752)+E(f301(x751),f301(x752))
% 28.77/28.54 [76]~E(x761,x762)+E(f931(x761,x763),f931(x762,x763))
% 28.77/28.54 [77]~E(x771,x772)+E(f931(x773,x771),f931(x773,x772))
% 28.77/28.54 [78]~E(x781,x782)+E(f283(x781),f283(x782))
% 28.77/28.54 [79]~E(x791,x792)+E(f18(x791,x793,x794),f18(x792,x793,x794))
% 28.77/28.54 [80]~E(x801,x802)+E(f18(x803,x801,x804),f18(x803,x802,x804))
% 28.77/28.54 [81]~E(x811,x812)+E(f18(x813,x814,x811),f18(x813,x814,x812))
% 28.77/28.54 [82]~E(x821,x822)+E(f105(x821),f105(x822))
% 28.77/28.54 [83]~E(x831,x832)+E(f300(x831),f300(x832))
% 28.77/28.54 [84]~E(x841,x842)+E(f480(x841,x843),f480(x842,x843))
% 28.77/28.54 [85]~E(x851,x852)+E(f480(x853,x851),f480(x853,x852))
% 28.77/28.54 [86]~E(x861,x862)+E(f710(x861,x863,x864),f710(x862,x863,x864))
% 28.77/28.54 [87]~E(x871,x872)+E(f710(x873,x871,x874),f710(x873,x872,x874))
% 28.77/28.54 [88]~E(x881,x882)+E(f710(x883,x884,x881),f710(x883,x884,x882))
% 28.77/28.54 [89]~E(x891,x892)+E(f54(x891),f54(x892))
% 28.77/28.54 [90]~E(x901,x902)+E(f13(x901,x903),f13(x902,x903))
% 28.77/28.54 [91]~E(x911,x912)+E(f13(x913,x911),f13(x913,x912))
% 28.77/28.54 [92]~E(x921,x922)+E(f665(x921,x923,x924,x925),f665(x922,x923,x924,x925))
% 28.77/28.54 [93]~E(x931,x932)+E(f665(x933,x931,x934,x935),f665(x933,x932,x934,x935))
% 28.77/28.54 [94]~E(x941,x942)+E(f665(x943,x944,x941,x945),f665(x943,x944,x942,x945))
% 28.77/28.54 [95]~E(x951,x952)+E(f665(x953,x954,x955,x951),f665(x953,x954,x955,x952))
% 28.77/28.54 [96]~E(x961,x962)+E(f126(x961),f126(x962))
% 28.77/28.54 [97]~E(x971,x972)+E(f128(x971,x973),f128(x972,x973))
% 28.77/28.54 [98]~E(x981,x982)+E(f128(x983,x981),f128(x983,x982))
% 28.77/28.54 [99]~E(x991,x992)+E(f243(x991,x993),f243(x992,x993))
% 28.77/28.54 [100]~E(x1001,x1002)+E(f243(x1003,x1001),f243(x1003,x1002))
% 28.77/28.54 [101]~E(x1011,x1012)+E(f234(x1011),f234(x1012))
% 28.77/28.54 [102]~E(x1021,x1022)+E(f81(x1021),f81(x1022))
% 28.77/28.54 [103]~E(x1031,x1032)+E(f305(x1031,x1033,x1034,x1035),f305(x1032,x1033,x1034,x1035))
% 28.77/28.54 [104]~E(x1041,x1042)+E(f305(x1043,x1041,x1044,x1045),f305(x1043,x1042,x1044,x1045))
% 28.77/28.54 [105]~E(x1051,x1052)+E(f305(x1053,x1054,x1051,x1055),f305(x1053,x1054,x1052,x1055))
% 28.77/28.54 [106]~E(x1061,x1062)+E(f305(x1063,x1064,x1065,x1061),f305(x1063,x1064,x1065,x1062))
% 28.77/28.54 [107]~E(x1071,x1072)+E(f153(x1071,x1073),f153(x1072,x1073))
% 28.77/28.54 [108]~E(x1081,x1082)+E(f153(x1083,x1081),f153(x1083,x1082))
% 28.77/28.54 [109]~E(x1091,x1092)+E(f434(x1091,x1093,x1094),f434(x1092,x1093,x1094))
% 28.77/28.54 [110]~E(x1101,x1102)+E(f434(x1103,x1101,x1104),f434(x1103,x1102,x1104))
% 28.77/28.54 [111]~E(x1111,x1112)+E(f434(x1113,x1114,x1111),f434(x1113,x1114,x1112))
% 28.77/28.54 [112]~E(x1121,x1122)+E(f34(x1121,x1123),f34(x1122,x1123))
% 28.77/28.54 [113]~E(x1131,x1132)+E(f34(x1133,x1131),f34(x1133,x1132))
% 28.77/28.54 [114]~E(x1141,x1142)+E(f87(x1141,x1143),f87(x1142,x1143))
% 28.77/28.54 [115]~E(x1151,x1152)+E(f87(x1153,x1151),f87(x1153,x1152))
% 28.77/28.54 [116]~E(x1161,x1162)+E(f284(x1161,x1163),f284(x1162,x1163))
% 28.77/28.54 [117]~E(x1171,x1172)+E(f284(x1173,x1171),f284(x1173,x1172))
% 28.77/28.54 [118]~E(x1181,x1182)+E(f254(x1181),f254(x1182))
% 28.77/28.54 [119]~E(x1191,x1192)+E(f160(x1191),f160(x1192))
% 28.77/28.54 [120]~E(x1201,x1202)+E(f244(x1201,x1203),f244(x1202,x1203))
% 28.77/28.54 [121]~E(x1211,x1212)+E(f244(x1213,x1211),f244(x1213,x1212))
% 28.77/28.54 [122]~E(x1221,x1222)+E(f55(x1221),f55(x1222))
% 28.77/28.54 [123]~E(x1231,x1232)+E(f690(x1231,x1233,x1234,x1235),f690(x1232,x1233,x1234,x1235))
% 28.77/28.54 [124]~E(x1241,x1242)+E(f690(x1243,x1241,x1244,x1245),f690(x1243,x1242,x1244,x1245))
% 28.77/28.54 [125]~E(x1251,x1252)+E(f690(x1253,x1254,x1251,x1255),f690(x1253,x1254,x1252,x1255))
% 28.77/28.54 [126]~E(x1261,x1262)+E(f690(x1263,x1264,x1265,x1261),f690(x1263,x1264,x1265,x1262))
% 28.77/28.54 [127]~E(x1271,x1272)+E(f164(x1271),f164(x1272))
% 28.77/28.54 [128]~E(x1281,x1282)+E(f9(x1281,x1283),f9(x1282,x1283))
% 28.77/28.54 [129]~E(x1291,x1292)+E(f9(x1293,x1291),f9(x1293,x1292))
% 28.77/28.54 [130]~E(x1301,x1302)+E(f14(x1301,x1303),f14(x1302,x1303))
% 28.77/28.54 [131]~E(x1311,x1312)+E(f14(x1313,x1311),f14(x1313,x1312))
% 28.77/28.54 [132]~E(x1321,x1322)+E(f5(x1321),f5(x1322))
% 28.77/28.54 [133]~E(x1331,x1332)+E(f933(x1331,x1333),f933(x1332,x1333))
% 28.77/28.54 [134]~E(x1341,x1342)+E(f933(x1343,x1341),f933(x1343,x1342))
% 28.77/28.54 [135]~E(x1351,x1352)+E(f97(x1351),f97(x1352))
% 28.77/28.54 [136]~E(x1361,x1362)+E(f98(x1361),f98(x1362))
% 28.77/28.54 [137]~E(x1371,x1372)+E(f320(x1371),f320(x1372))
% 28.77/28.54 [138]~E(x1381,x1382)+E(f129(x1381),f129(x1382))
% 28.77/28.54 [139]~E(x1391,x1392)+E(f595(x1391),f595(x1392))
% 28.77/28.54 [140]~E(x1401,x1402)+E(f774(x1401,x1403,x1404),f774(x1402,x1403,x1404))
% 28.77/28.54 [141]~E(x1411,x1412)+E(f774(x1413,x1411,x1414),f774(x1413,x1412,x1414))
% 28.77/28.54 [142]~E(x1421,x1422)+E(f774(x1423,x1424,x1421),f774(x1423,x1424,x1422))
% 28.77/28.54 [143]~E(x1431,x1432)+E(f728(x1431,x1433),f728(x1432,x1433))
% 28.77/28.54 [144]~E(x1441,x1442)+E(f728(x1443,x1441),f728(x1443,x1442))
% 28.77/28.54 [145]~E(x1451,x1452)+E(f233(x1451,x1453),f233(x1452,x1453))
% 28.77/28.54 [146]~E(x1461,x1462)+E(f233(x1463,x1461),f233(x1463,x1462))
% 28.77/28.54 [147]~E(x1471,x1472)+E(f6(x1471,x1473),f6(x1472,x1473))
% 28.77/28.54 [148]~E(x1481,x1482)+E(f6(x1483,x1481),f6(x1483,x1482))
% 28.77/28.54 [149]~E(x1491,x1492)+E(f302(x1491,x1493,x1494),f302(x1492,x1493,x1494))
% 28.77/28.54 [150]~E(x1501,x1502)+E(f302(x1503,x1501,x1504),f302(x1503,x1502,x1504))
% 28.77/28.54 [151]~E(x1511,x1512)+E(f302(x1513,x1514,x1511),f302(x1513,x1514,x1512))
% 28.77/28.54 [152]~E(x1521,x1522)+E(f624(x1521,x1523,x1524,x1525,x1526),f624(x1522,x1523,x1524,x1525,x1526))
% 28.77/28.54 [153]~E(x1531,x1532)+E(f624(x1533,x1531,x1534,x1535,x1536),f624(x1533,x1532,x1534,x1535,x1536))
% 28.77/28.54 [154]~E(x1541,x1542)+E(f624(x1543,x1544,x1541,x1545,x1546),f624(x1543,x1544,x1542,x1545,x1546))
% 28.77/28.54 [155]~E(x1551,x1552)+E(f624(x1553,x1554,x1555,x1551,x1556),f624(x1553,x1554,x1555,x1552,x1556))
% 28.77/28.54 [156]~E(x1561,x1562)+E(f624(x1563,x1564,x1565,x1566,x1561),f624(x1563,x1564,x1565,x1566,x1562))
% 28.77/28.54 [157]~E(x1571,x1572)+E(f167(x1571),f167(x1572))
% 28.77/28.54 [158]~E(x1581,x1582)+E(f69(x1581),f69(x1582))
% 28.77/28.54 [159]~E(x1591,x1592)+E(f490(x1591,x1593),f490(x1592,x1593))
% 28.77/28.54 [160]~E(x1601,x1602)+E(f490(x1603,x1601),f490(x1603,x1602))
% 28.77/28.54 [161]~E(x1611,x1612)+E(f295(x1611,x1613,x1614),f295(x1612,x1613,x1614))
% 28.77/28.54 [162]~E(x1621,x1622)+E(f295(x1623,x1621,x1624),f295(x1623,x1622,x1624))
% 28.77/28.54 [163]~E(x1631,x1632)+E(f295(x1633,x1634,x1631),f295(x1633,x1634,x1632))
% 28.77/28.54 [164]~E(x1641,x1642)+E(f544(x1641,x1643,x1644),f544(x1642,x1643,x1644))
% 28.77/28.54 [165]~E(x1651,x1652)+E(f544(x1653,x1651,x1654),f544(x1653,x1652,x1654))
% 28.77/28.54 [166]~E(x1661,x1662)+E(f544(x1663,x1664,x1661),f544(x1663,x1664,x1662))
% 28.77/28.54 [167]~E(x1671,x1672)+E(f88(x1671,x1673),f88(x1672,x1673))
% 28.77/28.54 [168]~E(x1681,x1682)+E(f88(x1683,x1681),f88(x1683,x1682))
% 28.77/28.54 [169]~E(x1691,x1692)+E(f236(x1691),f236(x1692))
% 28.77/28.54 [170]~E(x1701,x1702)+E(f74(x1701),f74(x1702))
% 28.77/28.54 [171]~E(x1711,x1712)+E(f297(x1711,x1713,x1714),f297(x1712,x1713,x1714))
% 28.77/28.54 [172]~E(x1721,x1722)+E(f297(x1723,x1721,x1724),f297(x1723,x1722,x1724))
% 28.77/28.54 [173]~E(x1731,x1732)+E(f297(x1733,x1734,x1731),f297(x1733,x1734,x1732))
% 28.77/28.54 [174]~E(x1741,x1742)+E(f39(x1741,x1743,x1744),f39(x1742,x1743,x1744))
% 28.77/28.54 [175]~E(x1751,x1752)+E(f39(x1753,x1751,x1754),f39(x1753,x1752,x1754))
% 28.77/28.54 [176]~E(x1761,x1762)+E(f39(x1763,x1764,x1761),f39(x1763,x1764,x1762))
% 28.77/28.54 [177]~E(x1771,x1772)+E(f277(x1771,x1773,x1774),f277(x1772,x1773,x1774))
% 28.77/28.54 [178]~E(x1781,x1782)+E(f277(x1783,x1781,x1784),f277(x1783,x1782,x1784))
% 28.77/28.54 [179]~E(x1791,x1792)+E(f277(x1793,x1794,x1791),f277(x1793,x1794,x1792))
% 28.77/28.54 [180]~E(x1801,x1802)+E(f248(x1801,x1803),f248(x1802,x1803))
% 28.77/28.54 [181]~E(x1811,x1812)+E(f248(x1813,x1811),f248(x1813,x1812))
% 28.77/28.54 [182]~E(x1821,x1822)+E(f679(x1821,x1823,x1824),f679(x1822,x1823,x1824))
% 28.77/28.54 [183]~E(x1831,x1832)+E(f679(x1833,x1831,x1834),f679(x1833,x1832,x1834))
% 28.77/28.54 [184]~E(x1841,x1842)+E(f679(x1843,x1844,x1841),f679(x1843,x1844,x1842))
% 28.77/28.54 [185]~E(x1851,x1852)+E(f173(x1851,x1853),f173(x1852,x1853))
% 28.77/28.54 [186]~E(x1861,x1862)+E(f173(x1863,x1861),f173(x1863,x1862))
% 28.77/28.54 [187]~E(x1871,x1872)+E(f150(x1871,x1873),f150(x1872,x1873))
% 28.77/28.54 [188]~E(x1881,x1882)+E(f150(x1883,x1881),f150(x1883,x1882))
% 28.77/28.54 [189]~E(x1891,x1892)+E(f29(x1891),f29(x1892))
% 28.77/28.54 [190]~E(x1901,x1902)+E(f563(x1901,x1903,x1904,x1905),f563(x1902,x1903,x1904,x1905))
% 28.77/28.54 [191]~E(x1911,x1912)+E(f563(x1913,x1911,x1914,x1915),f563(x1913,x1912,x1914,x1915))
% 28.77/28.54 [192]~E(x1921,x1922)+E(f563(x1923,x1924,x1921,x1925),f563(x1923,x1924,x1922,x1925))
% 28.77/28.54 [193]~E(x1931,x1932)+E(f563(x1933,x1934,x1935,x1931),f563(x1933,x1934,x1935,x1932))
% 28.77/28.54 [194]~E(x1941,x1942)+E(f431(x1941),f431(x1942))
% 28.77/28.54 [195]~E(x1951,x1952)+E(f250(x1951,x1953,x1954,x1955,x1956,x1957),f250(x1952,x1953,x1954,x1955,x1956,x1957))
% 28.77/28.54 [196]~E(x1961,x1962)+E(f250(x1963,x1961,x1964,x1965,x1966,x1967),f250(x1963,x1962,x1964,x1965,x1966,x1967))
% 28.77/28.54 [197]~E(x1971,x1972)+E(f250(x1973,x1974,x1971,x1975,x1976,x1977),f250(x1973,x1974,x1972,x1975,x1976,x1977))
% 28.77/28.54 [198]~E(x1981,x1982)+E(f250(x1983,x1984,x1985,x1981,x1986,x1987),f250(x1983,x1984,x1985,x1982,x1986,x1987))
% 28.77/28.54 [199]~E(x1991,x1992)+E(f250(x1993,x1994,x1995,x1996,x1991,x1997),f250(x1993,x1994,x1995,x1996,x1992,x1997))
% 28.77/28.54 [200]~E(x2001,x2002)+E(f250(x2003,x2004,x2005,x2006,x2007,x2001),f250(x2003,x2004,x2005,x2006,x2007,x2002))
% 28.77/28.54 [201]~E(x2011,x2012)+E(f303(x2011,x2013,x2014),f303(x2012,x2013,x2014))
% 28.77/28.54 [202]~E(x2021,x2022)+E(f303(x2023,x2021,x2024),f303(x2023,x2022,x2024))
% 28.77/28.54 [203]~E(x2031,x2032)+E(f303(x2033,x2034,x2031),f303(x2033,x2034,x2032))
% 28.77/28.54 [204]~E(x2041,x2042)+E(f471(x2041,x2043,x2044),f471(x2042,x2043,x2044))
% 28.77/28.54 [205]~E(x2051,x2052)+E(f471(x2053,x2051,x2054),f471(x2053,x2052,x2054))
% 28.77/28.54 [206]~E(x2061,x2062)+E(f471(x2063,x2064,x2061),f471(x2063,x2064,x2062))
% 28.77/28.54 [207]~E(x2071,x2072)+E(f294(x2071,x2073),f294(x2072,x2073))
% 28.77/28.54 [208]~E(x2081,x2082)+E(f294(x2083,x2081),f294(x2083,x2082))
% 28.77/28.54 [209]~E(x2091,x2092)+E(f749(x2091,x2093,x2094,x2095),f749(x2092,x2093,x2094,x2095))
% 28.77/28.54 [210]~E(x2101,x2102)+E(f749(x2103,x2101,x2104,x2105),f749(x2103,x2102,x2104,x2105))
% 28.77/28.54 [211]~E(x2111,x2112)+E(f749(x2113,x2114,x2111,x2115),f749(x2113,x2114,x2112,x2115))
% 28.77/28.54 [212]~E(x2121,x2122)+E(f749(x2123,x2124,x2125,x2121),f749(x2123,x2124,x2125,x2122))
% 28.77/28.54 [213]~E(x2131,x2132)+E(f58(x2131,x2133,x2134),f58(x2132,x2133,x2134))
% 28.77/28.54 [214]~E(x2141,x2142)+E(f58(x2143,x2141,x2144),f58(x2143,x2142,x2144))
% 28.77/28.54 [215]~E(x2151,x2152)+E(f58(x2153,x2154,x2151),f58(x2153,x2154,x2152))
% 28.77/28.54 [216]~E(x2161,x2162)+E(f722(x2161,x2163,x2164,x2165,x2166),f722(x2162,x2163,x2164,x2165,x2166))
% 28.77/28.54 [217]~E(x2171,x2172)+E(f722(x2173,x2171,x2174,x2175,x2176),f722(x2173,x2172,x2174,x2175,x2176))
% 28.77/28.54 [218]~E(x2181,x2182)+E(f722(x2183,x2184,x2181,x2185,x2186),f722(x2183,x2184,x2182,x2185,x2186))
% 28.77/28.54 [219]~E(x2191,x2192)+E(f722(x2193,x2194,x2195,x2191,x2196),f722(x2193,x2194,x2195,x2192,x2196))
% 28.77/28.54 [220]~E(x2201,x2202)+E(f722(x2203,x2204,x2205,x2206,x2201),f722(x2203,x2204,x2205,x2206,x2202))
% 28.77/28.54 [221]~E(x2211,x2212)+E(f137(x2211,x2213),f137(x2212,x2213))
% 28.77/28.54 [222]~E(x2221,x2222)+E(f137(x2223,x2221),f137(x2223,x2222))
% 28.77/28.54 [223]~E(x2231,x2232)+E(f33(x2231,x2233),f33(x2232,x2233))
% 28.77/28.54 [224]~E(x2241,x2242)+E(f33(x2243,x2241),f33(x2243,x2242))
% 28.77/28.54 [225]~E(x2251,x2252)+E(f49(x2251,x2253,x2254),f49(x2252,x2253,x2254))
% 28.77/28.54 [226]~E(x2261,x2262)+E(f49(x2263,x2261,x2264),f49(x2263,x2262,x2264))
% 28.77/28.54 [227]~E(x2271,x2272)+E(f49(x2273,x2274,x2271),f49(x2273,x2274,x2272))
% 28.77/28.54 [228]~E(x2281,x2282)+E(f695(x2281,x2283,x2284),f695(x2282,x2283,x2284))
% 28.77/28.54 [229]~E(x2291,x2292)+E(f695(x2293,x2291,x2294),f695(x2293,x2292,x2294))
% 28.77/28.54 [230]~E(x2301,x2302)+E(f695(x2303,x2304,x2301),f695(x2303,x2304,x2302))
% 28.77/28.54 [231]~E(x2311,x2312)+E(f136(x2311,x2313),f136(x2312,x2313))
% 28.77/28.54 [232]~E(x2321,x2322)+E(f136(x2323,x2321),f136(x2323,x2322))
% 28.77/28.54 [233]~E(x2331,x2332)+E(f68(x2331,x2333,x2334,x2335,x2336),f68(x2332,x2333,x2334,x2335,x2336))
% 28.77/28.54 [234]~E(x2341,x2342)+E(f68(x2343,x2341,x2344,x2345,x2346),f68(x2343,x2342,x2344,x2345,x2346))
% 28.77/28.54 [235]~E(x2351,x2352)+E(f68(x2353,x2354,x2351,x2355,x2356),f68(x2353,x2354,x2352,x2355,x2356))
% 28.77/28.54 [236]~E(x2361,x2362)+E(f68(x2363,x2364,x2365,x2361,x2366),f68(x2363,x2364,x2365,x2362,x2366))
% 28.77/28.54 [237]~E(x2371,x2372)+E(f68(x2373,x2374,x2375,x2376,x2371),f68(x2373,x2374,x2375,x2376,x2372))
% 28.77/28.54 [238]~E(x2381,x2382)+E(f846(x2381,x2383,x2384,x2385),f846(x2382,x2383,x2384,x2385))
% 28.77/28.54 [239]~E(x2391,x2392)+E(f846(x2393,x2391,x2394,x2395),f846(x2393,x2392,x2394,x2395))
% 28.77/28.54 [240]~E(x2401,x2402)+E(f846(x2403,x2404,x2401,x2405),f846(x2403,x2404,x2402,x2405))
% 28.77/28.54 [241]~E(x2411,x2412)+E(f846(x2413,x2414,x2415,x2411),f846(x2413,x2414,x2415,x2412))
% 28.77/28.54 [242]~E(x2421,x2422)+E(f485(x2421,x2423,x2424),f485(x2422,x2423,x2424))
% 28.77/28.54 [243]~E(x2431,x2432)+E(f485(x2433,x2431,x2434),f485(x2433,x2432,x2434))
% 28.77/28.54 [244]~E(x2441,x2442)+E(f485(x2443,x2444,x2441),f485(x2443,x2444,x2442))
% 28.77/28.54 [245]~E(x2451,x2452)+E(f281(x2451,x2453,x2454),f281(x2452,x2453,x2454))
% 28.77/28.54 [246]~E(x2461,x2462)+E(f281(x2463,x2461,x2464),f281(x2463,x2462,x2464))
% 28.77/28.54 [247]~E(x2471,x2472)+E(f281(x2473,x2474,x2471),f281(x2473,x2474,x2472))
% 28.77/28.54 [248]~E(x2481,x2482)+E(f131(x2481,x2483),f131(x2482,x2483))
% 28.77/28.54 [249]~E(x2491,x2492)+E(f131(x2493,x2491),f131(x2493,x2492))
% 28.77/28.54 [250]~E(x2501,x2502)+E(f656(x2501,x2503,x2504),f656(x2502,x2503,x2504))
% 28.77/28.54 [251]~E(x2511,x2512)+E(f656(x2513,x2511,x2514),f656(x2513,x2512,x2514))
% 28.77/28.54 [252]~E(x2521,x2522)+E(f656(x2523,x2524,x2521),f656(x2523,x2524,x2522))
% 28.77/28.54 [253]~E(x2531,x2532)+E(f12(x2531,x2533,x2534),f12(x2532,x2533,x2534))
% 28.77/28.54 [254]~E(x2541,x2542)+E(f12(x2543,x2541,x2544),f12(x2543,x2542,x2544))
% 28.77/28.54 [255]~E(x2551,x2552)+E(f12(x2553,x2554,x2551),f12(x2553,x2554,x2552))
% 28.77/28.54 [256]~E(x2561,x2562)+E(f66(x2561,x2563,x2564,x2565),f66(x2562,x2563,x2564,x2565))
% 28.77/28.54 [257]~E(x2571,x2572)+E(f66(x2573,x2571,x2574,x2575),f66(x2573,x2572,x2574,x2575))
% 28.77/28.54 [258]~E(x2581,x2582)+E(f66(x2583,x2584,x2581,x2585),f66(x2583,x2584,x2582,x2585))
% 28.77/28.54 [259]~E(x2591,x2592)+E(f66(x2593,x2594,x2595,x2591),f66(x2593,x2594,x2595,x2592))
% 28.77/28.54 [260]~E(x2601,x2602)+E(f106(x2601,x2603),f106(x2602,x2603))
% 28.77/28.54 [261]~E(x2611,x2612)+E(f106(x2613,x2611),f106(x2613,x2612))
% 28.77/28.54 [262]~E(x2621,x2622)+E(f298(x2621,x2623,x2624),f298(x2622,x2623,x2624))
% 28.77/28.54 [263]~E(x2631,x2632)+E(f298(x2633,x2631,x2634),f298(x2633,x2632,x2634))
% 28.77/28.54 [264]~E(x2641,x2642)+E(f298(x2643,x2644,x2641),f298(x2643,x2644,x2642))
% 28.77/28.54 [265]~E(x2651,x2652)+E(f134(x2651,x2653,x2654,x2655),f134(x2652,x2653,x2654,x2655))
% 28.77/28.54 [266]~E(x2661,x2662)+E(f134(x2663,x2661,x2664,x2665),f134(x2663,x2662,x2664,x2665))
% 28.77/28.54 [267]~E(x2671,x2672)+E(f134(x2673,x2674,x2671,x2675),f134(x2673,x2674,x2672,x2675))
% 28.77/28.54 [268]~E(x2681,x2682)+E(f134(x2683,x2684,x2685,x2681),f134(x2683,x2684,x2685,x2682))
% 28.77/28.54 [269]~E(x2691,x2692)+E(f144(x2691,x2693),f144(x2692,x2693))
% 28.77/28.54 [270]~E(x2701,x2702)+E(f144(x2703,x2701),f144(x2703,x2702))
% 28.77/28.54 [271]~E(x2711,x2712)+E(f30(x2711),f30(x2712))
% 28.77/28.54 [272]~E(x2721,x2722)+E(f183(x2721),f183(x2722))
% 28.77/28.54 [273]~E(x2731,x2732)+E(f576(x2731,x2733),f576(x2732,x2733))
% 28.77/28.54 [274]~E(x2741,x2742)+E(f576(x2743,x2741),f576(x2743,x2742))
% 28.77/28.54 [275]~E(x2751,x2752)+E(f107(x2751),f107(x2752))
% 28.77/28.54 [276]~E(x2761,x2762)+E(f124(x2761,x2763),f124(x2762,x2763))
% 28.77/28.54 [277]~E(x2771,x2772)+E(f124(x2773,x2771),f124(x2773,x2772))
% 28.77/28.54 [278]~E(x2781,x2782)+E(f869(x2781,x2783,x2784),f869(x2782,x2783,x2784))
% 28.77/28.54 [279]~E(x2791,x2792)+E(f869(x2793,x2791,x2794),f869(x2793,x2792,x2794))
% 28.77/28.54 [280]~E(x2801,x2802)+E(f869(x2803,x2804,x2801),f869(x2803,x2804,x2802))
% 28.77/28.54 [281]~E(x2811,x2812)+E(f930(x2811,x2813),f930(x2812,x2813))
% 28.77/28.54 [282]~E(x2821,x2822)+E(f930(x2823,x2821),f930(x2823,x2822))
% 28.77/28.54 [283]~E(x2831,x2832)+E(f159(x2831),f159(x2832))
% 28.77/28.54 [284]~E(x2841,x2842)+E(f649(x2841,x2843,x2844,x2845),f649(x2842,x2843,x2844,x2845))
% 28.77/28.54 [285]~E(x2851,x2852)+E(f649(x2853,x2851,x2854,x2855),f649(x2853,x2852,x2854,x2855))
% 28.77/28.54 [286]~E(x2861,x2862)+E(f649(x2863,x2864,x2861,x2865),f649(x2863,x2864,x2862,x2865))
% 28.77/28.54 [287]~E(x2871,x2872)+E(f649(x2873,x2874,x2875,x2871),f649(x2873,x2874,x2875,x2872))
% 28.77/28.54 [288]~E(x2881,x2882)+E(f31(x2881,x2883),f31(x2882,x2883))
% 28.77/28.54 [289]~E(x2891,x2892)+E(f31(x2893,x2891),f31(x2893,x2892))
% 28.77/28.54 [290]~E(x2901,x2902)+E(f487(x2901,x2903,x2904),f487(x2902,x2903,x2904))
% 28.77/28.54 [291]~E(x2911,x2912)+E(f487(x2913,x2911,x2914),f487(x2913,x2912,x2914))
% 28.77/28.54 [292]~E(x2921,x2922)+E(f487(x2923,x2924,x2921),f487(x2923,x2924,x2922))
% 28.77/28.54 [293]~E(x2931,x2932)+E(f163(x2931),f163(x2932))
% 28.77/28.54 [294]~E(x2941,x2942)+E(f366(x2941,x2943),f366(x2942,x2943))
% 28.77/28.54 [295]~E(x2951,x2952)+E(f366(x2953,x2951),f366(x2953,x2952))
% 28.77/28.54 [296]~E(x2961,x2962)+E(f443(x2961,x2963,x2964),f443(x2962,x2963,x2964))
% 28.77/28.54 [297]~E(x2971,x2972)+E(f443(x2973,x2971,x2974),f443(x2973,x2972,x2974))
% 28.77/28.54 [298]~E(x2981,x2982)+E(f443(x2983,x2984,x2981),f443(x2983,x2984,x2982))
% 28.77/28.54 [299]~E(x2991,x2992)+E(f299(x2991,x2993),f299(x2992,x2993))
% 28.77/28.54 [300]~E(x3001,x3002)+E(f299(x3003,x3001),f299(x3003,x3002))
% 28.77/28.54 [301]~E(x3011,x3012)+E(f42(x3011,x3013),f42(x3012,x3013))
% 28.77/28.54 [302]~E(x3021,x3022)+E(f42(x3023,x3021),f42(x3023,x3022))
% 28.77/28.54 [303]~E(x3031,x3032)+E(f332(x3031,x3033),f332(x3032,x3033))
% 28.77/28.54 [304]~E(x3041,x3042)+E(f332(x3043,x3041),f332(x3043,x3042))
% 28.77/28.54 [305]~E(x3051,x3052)+E(f123(x3051,x3053,x3054,x3055),f123(x3052,x3053,x3054,x3055))
% 28.77/28.54 [306]~E(x3061,x3062)+E(f123(x3063,x3061,x3064,x3065),f123(x3063,x3062,x3064,x3065))
% 28.77/28.54 [307]~E(x3071,x3072)+E(f123(x3073,x3074,x3071,x3075),f123(x3073,x3074,x3072,x3075))
% 28.77/28.54 [308]~E(x3081,x3082)+E(f123(x3083,x3084,x3085,x3081),f123(x3083,x3084,x3085,x3082))
% 28.77/28.54 [309]~E(x3091,x3092)+E(f169(x3091,x3093,x3094),f169(x3092,x3093,x3094))
% 28.77/28.54 [310]~E(x3101,x3102)+E(f169(x3103,x3101,x3104),f169(x3103,x3102,x3104))
% 28.77/28.54 [311]~E(x3111,x3112)+E(f169(x3113,x3114,x3111),f169(x3113,x3114,x3112))
% 28.77/28.54 [312]~E(x3121,x3122)+E(f130(x3121),f130(x3122))
% 28.77/28.54 [313]~E(x3131,x3132)+E(f907(x3131,x3133,x3134,x3135,x3136,x3137),f907(x3132,x3133,x3134,x3135,x3136,x3137))
% 28.77/28.54 [314]~E(x3141,x3142)+E(f907(x3143,x3141,x3144,x3145,x3146,x3147),f907(x3143,x3142,x3144,x3145,x3146,x3147))
% 28.77/28.54 [315]~E(x3151,x3152)+E(f907(x3153,x3154,x3151,x3155,x3156,x3157),f907(x3153,x3154,x3152,x3155,x3156,x3157))
% 28.77/28.54 [316]~E(x3161,x3162)+E(f907(x3163,x3164,x3165,x3161,x3166,x3167),f907(x3163,x3164,x3165,x3162,x3166,x3167))
% 28.77/28.54 [317]~E(x3171,x3172)+E(f907(x3173,x3174,x3175,x3176,x3171,x3177),f907(x3173,x3174,x3175,x3176,x3172,x3177))
% 28.77/28.54 [318]~E(x3181,x3182)+E(f907(x3183,x3184,x3185,x3186,x3187,x3181),f907(x3183,x3184,x3185,x3186,x3187,x3182))
% 28.77/28.54 [319]~E(x3191,x3192)+E(f274(x3191),f274(x3192))
% 28.77/28.54 [320]~E(x3201,x3202)+E(f854(x3201,x3203,x3204,x3205,x3206,x3207,x3208,x3209),f854(x3202,x3203,x3204,x3205,x3206,x3207,x3208,x3209))
% 28.77/28.54 [321]~E(x3211,x3212)+E(f854(x3213,x3211,x3214,x3215,x3216,x3217,x3218,x3219),f854(x3213,x3212,x3214,x3215,x3216,x3217,x3218,x3219))
% 28.77/28.54 [322]~E(x3221,x3222)+E(f854(x3223,x3224,x3221,x3225,x3226,x3227,x3228,x3229),f854(x3223,x3224,x3222,x3225,x3226,x3227,x3228,x3229))
% 28.77/28.54 [323]~E(x3231,x3232)+E(f854(x3233,x3234,x3235,x3231,x3236,x3237,x3238,x3239),f854(x3233,x3234,x3235,x3232,x3236,x3237,x3238,x3239))
% 28.77/28.54 [324]~E(x3241,x3242)+E(f854(x3243,x3244,x3245,x3246,x3241,x3247,x3248,x3249),f854(x3243,x3244,x3245,x3246,x3242,x3247,x3248,x3249))
% 28.77/28.54 [325]~E(x3251,x3252)+E(f854(x3253,x3254,x3255,x3256,x3257,x3251,x3258,x3259),f854(x3253,x3254,x3255,x3256,x3257,x3252,x3258,x3259))
% 28.77/28.54 [326]~E(x3261,x3262)+E(f854(x3263,x3264,x3265,x3266,x3267,x3268,x3261,x3269),f854(x3263,x3264,x3265,x3266,x3267,x3268,x3262,x3269))
% 28.77/28.54 [327]~E(x3271,x3272)+E(f854(x3273,x3274,x3275,x3276,x3277,x3278,x3279,x3271),f854(x3273,x3274,x3275,x3276,x3277,x3278,x3279,x3272))
% 28.77/28.54 [328]~E(x3281,x3282)+E(f208(x3281,x3283),f208(x3282,x3283))
% 28.77/28.54 [329]~E(x3291,x3292)+E(f208(x3293,x3291),f208(x3293,x3292))
% 28.77/28.54 [330]~E(x3301,x3302)+E(f310(x3301,x3303),f310(x3302,x3303))
% 28.77/28.54 [331]~E(x3311,x3312)+E(f310(x3313,x3311),f310(x3313,x3312))
% 28.77/28.54 [332]~E(x3321,x3322)+E(f246(x3321,x3323),f246(x3322,x3323))
% 28.77/28.54 [333]~E(x3331,x3332)+E(f246(x3333,x3331),f246(x3333,x3332))
% 28.77/28.54 [334]~E(x3341,x3342)+E(f311(x3341,x3343),f311(x3342,x3343))
% 28.77/28.54 [335]~E(x3351,x3352)+E(f311(x3353,x3351),f311(x3353,x3352))
% 28.77/28.54 [336]~E(x3361,x3362)+E(f584(x3361,x3363,x3364,x3365,x3366),f584(x3362,x3363,x3364,x3365,x3366))
% 28.77/28.54 [337]~E(x3371,x3372)+E(f584(x3373,x3371,x3374,x3375,x3376),f584(x3373,x3372,x3374,x3375,x3376))
% 28.77/28.54 [338]~E(x3381,x3382)+E(f584(x3383,x3384,x3381,x3385,x3386),f584(x3383,x3384,x3382,x3385,x3386))
% 28.77/28.54 [339]~E(x3391,x3392)+E(f584(x3393,x3394,x3395,x3391,x3396),f584(x3393,x3394,x3395,x3392,x3396))
% 28.77/28.54 [340]~E(x3401,x3402)+E(f584(x3403,x3404,x3405,x3406,x3401),f584(x3403,x3404,x3405,x3406,x3402))
% 28.77/28.54 [341]~E(x3411,x3412)+E(f161(x3411,x3413,x3414),f161(x3412,x3413,x3414))
% 28.77/28.54 [342]~E(x3421,x3422)+E(f161(x3423,x3421,x3424),f161(x3423,x3422,x3424))
% 28.77/28.54 [343]~E(x3431,x3432)+E(f161(x3433,x3434,x3431),f161(x3433,x3434,x3432))
% 28.77/28.54 [344]~E(x3441,x3442)+E(f170(x3441,x3443),f170(x3442,x3443))
% 28.77/28.54 [345]~E(x3451,x3452)+E(f170(x3453,x3451),f170(x3453,x3452))
% 28.77/28.54 [346]~E(x3461,x3462)+E(f279(x3461),f279(x3462))
% 28.77/28.54 [347]~E(x3471,x3472)+E(f10(x3471,x3473),f10(x3472,x3473))
% 28.77/28.54 [348]~E(x3481,x3482)+E(f10(x3483,x3481),f10(x3483,x3482))
% 28.77/28.54 [349]~E(x3491,x3492)+E(f261(x3491,x3493),f261(x3492,x3493))
% 28.77/28.54 [350]~E(x3501,x3502)+E(f261(x3503,x3501),f261(x3503,x3502))
% 28.77/28.54 [351]~E(x3511,x3512)+E(f707(x3511,x3513,x3514,x3515),f707(x3512,x3513,x3514,x3515))
% 28.77/28.54 [352]~E(x3521,x3522)+E(f707(x3523,x3521,x3524,x3525),f707(x3523,x3522,x3524,x3525))
% 28.77/28.54 [353]~E(x3531,x3532)+E(f707(x3533,x3534,x3531,x3535),f707(x3533,x3534,x3532,x3535))
% 28.77/28.54 [354]~E(x3541,x3542)+E(f707(x3543,x3544,x3545,x3541),f707(x3543,x3544,x3545,x3542))
% 28.77/28.54 [355]~E(x3551,x3552)+E(f240(x3551,x3553),f240(x3552,x3553))
% 28.77/28.54 [356]~E(x3561,x3562)+E(f240(x3563,x3561),f240(x3563,x3562))
% 28.77/28.54 [357]~E(x3571,x3572)+E(f612(x3571,x3573,x3574),f612(x3572,x3573,x3574))
% 28.77/28.54 [358]~E(x3581,x3582)+E(f612(x3583,x3581,x3584),f612(x3583,x3582,x3584))
% 28.77/28.54 [359]~E(x3591,x3592)+E(f612(x3593,x3594,x3591),f612(x3593,x3594,x3592))
% 28.77/28.54 [360]~E(x3601,x3602)+E(f80(x3601,x3603),f80(x3602,x3603))
% 28.77/28.54 [361]~E(x3611,x3612)+E(f80(x3613,x3611),f80(x3613,x3612))
% 28.77/28.54 [362]~E(x3621,x3622)+E(f729(x3621,x3623),f729(x3622,x3623))
% 28.77/28.54 [363]~E(x3631,x3632)+E(f729(x3633,x3631),f729(x3633,x3632))
% 28.77/28.54 [364]~E(x3641,x3642)+E(f897(x3641,x3643,x3644,x3645,x3646,x3647,x3648),f897(x3642,x3643,x3644,x3645,x3646,x3647,x3648))
% 28.77/28.54 [365]~E(x3651,x3652)+E(f897(x3653,x3651,x3654,x3655,x3656,x3657,x3658),f897(x3653,x3652,x3654,x3655,x3656,x3657,x3658))
% 28.77/28.54 [366]~E(x3661,x3662)+E(f897(x3663,x3664,x3661,x3665,x3666,x3667,x3668),f897(x3663,x3664,x3662,x3665,x3666,x3667,x3668))
% 28.77/28.54 [367]~E(x3671,x3672)+E(f897(x3673,x3674,x3675,x3671,x3676,x3677,x3678),f897(x3673,x3674,x3675,x3672,x3676,x3677,x3678))
% 28.77/28.54 [368]~E(x3681,x3682)+E(f897(x3683,x3684,x3685,x3686,x3681,x3687,x3688),f897(x3683,x3684,x3685,x3686,x3682,x3687,x3688))
% 28.77/28.54 [369]~E(x3691,x3692)+E(f897(x3693,x3694,x3695,x3696,x3697,x3691,x3698),f897(x3693,x3694,x3695,x3696,x3697,x3692,x3698))
% 28.77/28.54 [370]~E(x3701,x3702)+E(f897(x3703,x3704,x3705,x3706,x3707,x3708,x3701),f897(x3703,x3704,x3705,x3706,x3707,x3708,x3702))
% 28.77/28.54 [371]~E(x3711,x3712)+E(f156(x3711),f156(x3712))
% 28.77/28.54 [372]~E(x3721,x3722)+E(f157(x3721),f157(x3722))
% 28.77/28.54 [373]~E(x3731,x3732)+E(f111(x3731),f111(x3732))
% 28.77/28.54 [374]~E(x3741,x3742)+E(f112(x3741,x3743),f112(x3742,x3743))
% 28.77/28.54 [375]~E(x3751,x3752)+E(f112(x3753,x3751),f112(x3753,x3752))
% 28.77/28.54 [376]~E(x3761,x3762)+E(f638(x3761,x3763,x3764,x3765,x3766),f638(x3762,x3763,x3764,x3765,x3766))
% 28.77/28.54 [377]~E(x3771,x3772)+E(f638(x3773,x3771,x3774,x3775,x3776),f638(x3773,x3772,x3774,x3775,x3776))
% 28.77/28.54 [378]~E(x3781,x3782)+E(f638(x3783,x3784,x3781,x3785,x3786),f638(x3783,x3784,x3782,x3785,x3786))
% 28.77/28.54 [379]~E(x3791,x3792)+E(f638(x3793,x3794,x3795,x3791,x3796),f638(x3793,x3794,x3795,x3792,x3796))
% 28.77/28.54 [380]~E(x3801,x3802)+E(f638(x3803,x3804,x3805,x3806,x3801),f638(x3803,x3804,x3805,x3806,x3802))
% 28.77/28.54 [381]~E(x3811,x3812)+E(f641(x3811,x3813,x3814,x3815,x3816),f641(x3812,x3813,x3814,x3815,x3816))
% 28.77/28.54 [382]~E(x3821,x3822)+E(f641(x3823,x3821,x3824,x3825,x3826),f641(x3823,x3822,x3824,x3825,x3826))
% 28.77/28.54 [383]~E(x3831,x3832)+E(f641(x3833,x3834,x3831,x3835,x3836),f641(x3833,x3834,x3832,x3835,x3836))
% 28.77/28.54 [384]~E(x3841,x3842)+E(f641(x3843,x3844,x3845,x3841,x3846),f641(x3843,x3844,x3845,x3842,x3846))
% 28.77/28.54 [385]~E(x3851,x3852)+E(f641(x3853,x3854,x3855,x3856,x3851),f641(x3853,x3854,x3855,x3856,x3852))
% 28.77/28.54 [386]~E(x3861,x3862)+E(f352(x3861),f352(x3862))
% 28.77/28.54 [387]~E(x3871,x3872)+E(f860(x3871,x3873,x3874,x3875,x3876,x3877),f860(x3872,x3873,x3874,x3875,x3876,x3877))
% 28.77/28.54 [388]~E(x3881,x3882)+E(f860(x3883,x3881,x3884,x3885,x3886,x3887),f860(x3883,x3882,x3884,x3885,x3886,x3887))
% 28.77/28.54 [389]~E(x3891,x3892)+E(f860(x3893,x3894,x3891,x3895,x3896,x3897),f860(x3893,x3894,x3892,x3895,x3896,x3897))
% 28.77/28.54 [390]~E(x3901,x3902)+E(f860(x3903,x3904,x3905,x3901,x3906,x3907),f860(x3903,x3904,x3905,x3902,x3906,x3907))
% 28.77/28.54 [391]~E(x3911,x3912)+E(f860(x3913,x3914,x3915,x3916,x3911,x3917),f860(x3913,x3914,x3915,x3916,x3912,x3917))
% 28.77/28.54 [392]~E(x3921,x3922)+E(f860(x3923,x3924,x3925,x3926,x3927,x3921),f860(x3923,x3924,x3925,x3926,x3927,x3922))
% 28.77/28.54 [393]~E(x3931,x3932)+E(f79(x3931,x3933),f79(x3932,x3933))
% 28.77/28.54 [394]~E(x3941,x3942)+E(f79(x3943,x3941),f79(x3943,x3942))
% 28.77/28.54 [395]~E(x3951,x3952)+E(f861(x3951,x3953,x3954,x3955,x3956,x3957),f861(x3952,x3953,x3954,x3955,x3956,x3957))
% 28.77/28.54 [396]~E(x3961,x3962)+E(f861(x3963,x3961,x3964,x3965,x3966,x3967),f861(x3963,x3962,x3964,x3965,x3966,x3967))
% 28.77/28.54 [397]~E(x3971,x3972)+E(f861(x3973,x3974,x3971,x3975,x3976,x3977),f861(x3973,x3974,x3972,x3975,x3976,x3977))
% 28.77/28.54 [398]~E(x3981,x3982)+E(f861(x3983,x3984,x3985,x3981,x3986,x3987),f861(x3983,x3984,x3985,x3982,x3986,x3987))
% 28.77/28.54 [399]~E(x3991,x3992)+E(f861(x3993,x3994,x3995,x3996,x3991,x3997),f861(x3993,x3994,x3995,x3996,x3992,x3997))
% 28.77/28.54 [400]~E(x4001,x4002)+E(f861(x4003,x4004,x4005,x4006,x4007,x4001),f861(x4003,x4004,x4005,x4006,x4007,x4002))
% 28.77/28.54 [401]~E(x4011,x4012)+E(f84(x4011,x4013),f84(x4012,x4013))
% 28.77/28.54 [402]~E(x4021,x4022)+E(f84(x4023,x4021),f84(x4023,x4022))
% 28.77/28.54 [403]~E(x4031,x4032)+E(f175(x4031,x4033),f175(x4032,x4033))
% 28.77/28.54 [404]~E(x4041,x4042)+E(f175(x4043,x4041),f175(x4043,x4042))
% 28.77/28.54 [405]~E(x4051,x4052)+E(f145(x4051,x4053),f145(x4052,x4053))
% 28.77/28.54 [406]~E(x4061,x4062)+E(f145(x4063,x4061),f145(x4063,x4062))
% 28.77/28.54 [407]~E(x4071,x4072)+E(f255(x4071,x4073),f255(x4072,x4073))
% 28.77/28.54 [408]~E(x4081,x4082)+E(f255(x4083,x4081),f255(x4083,x4082))
% 28.77/28.54 [409]~E(x4091,x4092)+E(f716(x4091,x4093,x4094,x4095,x4096),f716(x4092,x4093,x4094,x4095,x4096))
% 28.77/28.54 [410]~E(x4101,x4102)+E(f716(x4103,x4101,x4104,x4105,x4106),f716(x4103,x4102,x4104,x4105,x4106))
% 28.77/28.54 [411]~E(x4111,x4112)+E(f716(x4113,x4114,x4111,x4115,x4116),f716(x4113,x4114,x4112,x4115,x4116))
% 28.77/28.54 [412]~E(x4121,x4122)+E(f716(x4123,x4124,x4125,x4121,x4126),f716(x4123,x4124,x4125,x4122,x4126))
% 28.77/28.54 [413]~E(x4131,x4132)+E(f716(x4133,x4134,x4135,x4136,x4131),f716(x4133,x4134,x4135,x4136,x4132))
% 28.77/28.54 [414]~E(x4141,x4142)+E(f16(x4141,x4143),f16(x4142,x4143))
% 28.77/28.54 [415]~E(x4151,x4152)+E(f16(x4153,x4151),f16(x4153,x4152))
% 28.77/28.54 [416]~E(x4161,x4162)+E(f640(x4161,x4163,x4164,x4165),f640(x4162,x4163,x4164,x4165))
% 28.77/28.54 [417]~E(x4171,x4172)+E(f640(x4173,x4171,x4174,x4175),f640(x4173,x4172,x4174,x4175))
% 28.77/28.54 [418]~E(x4181,x4182)+E(f640(x4183,x4184,x4181,x4185),f640(x4183,x4184,x4182,x4185))
% 28.77/28.54 [419]~E(x4191,x4192)+E(f640(x4193,x4194,x4195,x4191),f640(x4193,x4194,x4195,x4192))
% 28.77/28.54 [420]~E(x4201,x4202)+E(f59(x4201,x4203,x4204),f59(x4202,x4203,x4204))
% 28.77/28.54 [421]~E(x4211,x4212)+E(f59(x4213,x4211,x4214),f59(x4213,x4212,x4214))
% 28.77/28.54 [422]~E(x4221,x4222)+E(f59(x4223,x4224,x4221),f59(x4223,x4224,x4222))
% 28.77/28.54 [423]~E(x4231,x4232)+E(f800(x4231),f800(x4232))
% 28.77/28.54 [424]~E(x4241,x4242)+E(f421(x4241,x4243,x4244,x4245),f421(x4242,x4243,x4244,x4245))
% 28.77/28.54 [425]~E(x4251,x4252)+E(f421(x4253,x4251,x4254,x4255),f421(x4253,x4252,x4254,x4255))
% 28.77/28.54 [426]~E(x4261,x4262)+E(f421(x4263,x4264,x4261,x4265),f421(x4263,x4264,x4262,x4265))
% 28.77/28.54 [427]~E(x4271,x4272)+E(f421(x4273,x4274,x4275,x4271),f421(x4273,x4274,x4275,x4272))
% 28.77/28.54 [428]~E(x4281,x4282)+E(f733(x4281,x4283,x4284),f733(x4282,x4283,x4284))
% 28.77/28.54 [429]~E(x4291,x4292)+E(f733(x4293,x4291,x4294),f733(x4293,x4292,x4294))
% 28.77/28.54 [430]~E(x4301,x4302)+E(f733(x4303,x4304,x4301),f733(x4303,x4304,x4302))
% 28.77/28.54 [431]~E(x4311,x4312)+E(f354(x4311,x4313),f354(x4312,x4313))
% 28.77/28.54 [432]~E(x4321,x4322)+E(f354(x4323,x4321),f354(x4323,x4322))
% 28.77/28.54 [433]~E(x4331,x4332)+E(f141(x4331,x4333,x4334,x4335,x4336),f141(x4332,x4333,x4334,x4335,x4336))
% 28.77/28.54 [434]~E(x4341,x4342)+E(f141(x4343,x4341,x4344,x4345,x4346),f141(x4343,x4342,x4344,x4345,x4346))
% 28.77/28.54 [435]~E(x4351,x4352)+E(f141(x4353,x4354,x4351,x4355,x4356),f141(x4353,x4354,x4352,x4355,x4356))
% 28.77/28.54 [436]~E(x4361,x4362)+E(f141(x4363,x4364,x4365,x4361,x4366),f141(x4363,x4364,x4365,x4362,x4366))
% 28.77/28.54 [437]~E(x4371,x4372)+E(f141(x4373,x4374,x4375,x4376,x4371),f141(x4373,x4374,x4375,x4376,x4372))
% 28.77/28.54 [438]~E(x4381,x4382)+E(f307(x4381,x4383),f307(x4382,x4383))
% 28.77/28.54 [439]~E(x4391,x4392)+E(f307(x4393,x4391),f307(x4393,x4392))
% 28.77/28.54 [440]~E(x4401,x4402)+E(f424(x4401,x4403,x4404,x4405,x4406),f424(x4402,x4403,x4404,x4405,x4406))
% 28.77/28.54 [441]~E(x4411,x4412)+E(f424(x4413,x4411,x4414,x4415,x4416),f424(x4413,x4412,x4414,x4415,x4416))
% 28.77/28.54 [442]~E(x4421,x4422)+E(f424(x4423,x4424,x4421,x4425,x4426),f424(x4423,x4424,x4422,x4425,x4426))
% 28.77/28.54 [443]~E(x4431,x4432)+E(f424(x4433,x4434,x4435,x4431,x4436),f424(x4433,x4434,x4435,x4432,x4436))
% 28.77/28.54 [444]~E(x4441,x4442)+E(f424(x4443,x4444,x4445,x4446,x4441),f424(x4443,x4444,x4445,x4446,x4442))
% 28.77/28.54 [445]~E(x4451,x4452)+E(f715(x4451,x4453,x4454,x4455,x4456),f715(x4452,x4453,x4454,x4455,x4456))
% 28.77/28.54 [446]~E(x4461,x4462)+E(f715(x4463,x4461,x4464,x4465,x4466),f715(x4463,x4462,x4464,x4465,x4466))
% 28.77/28.54 [447]~E(x4471,x4472)+E(f715(x4473,x4474,x4471,x4475,x4476),f715(x4473,x4474,x4472,x4475,x4476))
% 28.77/28.54 [448]~E(x4481,x4482)+E(f715(x4483,x4484,x4485,x4481,x4486),f715(x4483,x4484,x4485,x4482,x4486))
% 28.77/28.54 [449]~E(x4491,x4492)+E(f715(x4493,x4494,x4495,x4496,x4491),f715(x4493,x4494,x4495,x4496,x4492))
% 28.77/28.54 [450]~E(x4501,x4502)+E(f57(x4501,x4503),f57(x4502,x4503))
% 28.77/28.54 [451]~E(x4511,x4512)+E(f57(x4513,x4511),f57(x4513,x4512))
% 28.77/28.54 [452]~E(x4521,x4522)+E(f541(x4521,x4523,x4524),f541(x4522,x4523,x4524))
% 28.77/28.54 [453]~E(x4531,x4532)+E(f541(x4533,x4531,x4534),f541(x4533,x4532,x4534))
% 28.77/28.54 [454]~E(x4541,x4542)+E(f541(x4543,x4544,x4541),f541(x4543,x4544,x4542))
% 28.77/28.54 [455]~E(x4551,x4552)+E(f864(x4551,x4553,x4554,x4555,x4556,x4557),f864(x4552,x4553,x4554,x4555,x4556,x4557))
% 28.77/28.54 [456]~E(x4561,x4562)+E(f864(x4563,x4561,x4564,x4565,x4566,x4567),f864(x4563,x4562,x4564,x4565,x4566,x4567))
% 28.77/28.54 [457]~E(x4571,x4572)+E(f864(x4573,x4574,x4571,x4575,x4576,x4577),f864(x4573,x4574,x4572,x4575,x4576,x4577))
% 28.77/28.54 [458]~E(x4581,x4582)+E(f864(x4583,x4584,x4585,x4581,x4586,x4587),f864(x4583,x4584,x4585,x4582,x4586,x4587))
% 28.77/28.54 [459]~E(x4591,x4592)+E(f864(x4593,x4594,x4595,x4596,x4591,x4597),f864(x4593,x4594,x4595,x4596,x4592,x4597))
% 28.77/28.54 [460]~E(x4601,x4602)+E(f864(x4603,x4604,x4605,x4606,x4607,x4601),f864(x4603,x4604,x4605,x4606,x4607,x4602))
% 28.77/28.54 [461]~E(x4611,x4612)+E(f865(x4611,x4613,x4614,x4615,x4616,x4617),f865(x4612,x4613,x4614,x4615,x4616,x4617))
% 28.77/28.54 [462]~E(x4621,x4622)+E(f865(x4623,x4621,x4624,x4625,x4626,x4627),f865(x4623,x4622,x4624,x4625,x4626,x4627))
% 28.77/28.54 [463]~E(x4631,x4632)+E(f865(x4633,x4634,x4631,x4635,x4636,x4637),f865(x4633,x4634,x4632,x4635,x4636,x4637))
% 28.77/28.54 [464]~E(x4641,x4642)+E(f865(x4643,x4644,x4645,x4641,x4646,x4647),f865(x4643,x4644,x4645,x4642,x4646,x4647))
% 28.77/28.54 [465]~E(x4651,x4652)+E(f865(x4653,x4654,x4655,x4656,x4651,x4657),f865(x4653,x4654,x4655,x4656,x4652,x4657))
% 28.77/28.54 [466]~E(x4661,x4662)+E(f865(x4663,x4664,x4665,x4666,x4667,x4661),f865(x4663,x4664,x4665,x4666,x4667,x4662))
% 28.77/28.54 [467]~E(x4671,x4672)+E(f76(x4671,x4673),f76(x4672,x4673))
% 28.77/28.54 [468]~E(x4681,x4682)+E(f76(x4683,x4681),f76(x4683,x4682))
% 28.77/28.54 [469]~E(x4691,x4692)+E(f328(x4691,x4693,x4694),f328(x4692,x4693,x4694))
% 28.77/28.54 [470]~E(x4701,x4702)+E(f328(x4703,x4701,x4704),f328(x4703,x4702,x4704))
% 28.77/28.54 [471]~E(x4711,x4712)+E(f328(x4713,x4714,x4711),f328(x4713,x4714,x4712))
% 28.77/28.54 [472]~E(x4721,x4722)+E(f497(x4721,x4723,x4724,x4725,x4726,x4727,x4728),f497(x4722,x4723,x4724,x4725,x4726,x4727,x4728))
% 28.78/28.54 [473]~E(x4731,x4732)+E(f497(x4733,x4731,x4734,x4735,x4736,x4737,x4738),f497(x4733,x4732,x4734,x4735,x4736,x4737,x4738))
% 28.78/28.54 [474]~E(x4741,x4742)+E(f497(x4743,x4744,x4741,x4745,x4746,x4747,x4748),f497(x4743,x4744,x4742,x4745,x4746,x4747,x4748))
% 28.78/28.54 [475]~E(x4751,x4752)+E(f497(x4753,x4754,x4755,x4751,x4756,x4757,x4758),f497(x4753,x4754,x4755,x4752,x4756,x4757,x4758))
% 28.78/28.54 [476]~E(x4761,x4762)+E(f497(x4763,x4764,x4765,x4766,x4761,x4767,x4768),f497(x4763,x4764,x4765,x4766,x4762,x4767,x4768))
% 28.78/28.54 [477]~E(x4771,x4772)+E(f497(x4773,x4774,x4775,x4776,x4777,x4771,x4778),f497(x4773,x4774,x4775,x4776,x4777,x4772,x4778))
% 28.78/28.54 [478]~E(x4781,x4782)+E(f497(x4783,x4784,x4785,x4786,x4787,x4788,x4781),f497(x4783,x4784,x4785,x4786,x4787,x4788,x4782))
% 28.78/28.54 [479]~E(x4791,x4792)+E(f256(x4791,x4793),f256(x4792,x4793))
% 28.78/28.54 [480]~E(x4801,x4802)+E(f256(x4803,x4801),f256(x4803,x4802))
% 28.78/28.54 [481]~E(x4811,x4812)+E(f874(x4811,x4813,x4814),f874(x4812,x4813,x4814))
% 28.78/28.54 [482]~E(x4821,x4822)+E(f874(x4823,x4821,x4824),f874(x4823,x4822,x4824))
% 28.78/28.54 [483]~E(x4831,x4832)+E(f874(x4833,x4834,x4831),f874(x4833,x4834,x4832))
% 28.78/28.54 [484]~E(x4841,x4842)+E(f149(x4841,x4843),f149(x4842,x4843))
% 28.78/28.54 [485]~E(x4851,x4852)+E(f149(x4853,x4851),f149(x4853,x4852))
% 28.78/28.54 [486]~E(x4861,x4862)+E(f554(x4861),f554(x4862))
% 28.78/28.54 [487]~E(x4871,x4872)+E(f11(x4871,x4873,x4874),f11(x4872,x4873,x4874))
% 28.78/28.54 [488]~E(x4881,x4882)+E(f11(x4883,x4881,x4884),f11(x4883,x4882,x4884))
% 28.78/28.54 [489]~E(x4891,x4892)+E(f11(x4893,x4894,x4891),f11(x4893,x4894,x4892))
% 28.78/28.54 [490]~E(x4901,x4902)+E(f171(x4901,x4903),f171(x4902,x4903))
% 28.78/28.54 [491]~E(x4911,x4912)+E(f171(x4913,x4911),f171(x4913,x4912))
% 28.78/28.54 [492]~E(x4921,x4922)+E(f192(x4921),f192(x4922))
% 28.78/28.54 [493]~E(x4931,x4932)+E(f878(x4931,x4933,x4934),f878(x4932,x4933,x4934))
% 28.78/28.54 [494]~E(x4941,x4942)+E(f878(x4943,x4941,x4944),f878(x4943,x4942,x4944))
% 28.78/28.54 [495]~E(x4951,x4952)+E(f878(x4953,x4954,x4951),f878(x4953,x4954,x4952))
% 28.78/28.54 [496]~E(x4961,x4962)+E(f903(x4961,x4963),f903(x4962,x4963))
% 28.78/28.54 [497]~E(x4971,x4972)+E(f903(x4973,x4971),f903(x4973,x4972))
% 28.78/28.54 [498]~E(x4981,x4982)+E(f306(x4981),f306(x4982))
% 28.78/28.54 [499]~E(x4991,x4992)+E(f748(x4991,x4993),f748(x4992,x4993))
% 28.78/28.54 [500]~E(x5001,x5002)+E(f748(x5003,x5001),f748(x5003,x5002))
% 28.78/28.54 [501]~E(x5011,x5012)+E(f655(x5011,x5013,x5014,x5015),f655(x5012,x5013,x5014,x5015))
% 28.78/28.54 [502]~E(x5021,x5022)+E(f655(x5023,x5021,x5024,x5025),f655(x5023,x5022,x5024,x5025))
% 28.78/28.54 [503]~E(x5031,x5032)+E(f655(x5033,x5034,x5031,x5035),f655(x5033,x5034,x5032,x5035))
% 28.78/28.54 [504]~E(x5041,x5042)+E(f655(x5043,x5044,x5045,x5041),f655(x5043,x5044,x5045,x5042))
% 28.78/28.54 [505]~E(x5051,x5052)+E(f85(x5051,x5053,x5054,x5055),f85(x5052,x5053,x5054,x5055))
% 28.78/28.54 [506]~E(x5061,x5062)+E(f85(x5063,x5061,x5064,x5065),f85(x5063,x5062,x5064,x5065))
% 28.78/28.54 [507]~E(x5071,x5072)+E(f85(x5073,x5074,x5071,x5075),f85(x5073,x5074,x5072,x5075))
% 28.78/28.54 [508]~E(x5081,x5082)+E(f85(x5083,x5084,x5085,x5081),f85(x5083,x5084,x5085,x5082))
% 28.78/28.54 [509]~E(x5091,x5092)+E(f550(x5091,x5093,x5094,x5095,x5096,x5097,x5098),f550(x5092,x5093,x5094,x5095,x5096,x5097,x5098))
% 28.78/28.54 [510]~E(x5101,x5102)+E(f550(x5103,x5101,x5104,x5105,x5106,x5107,x5108),f550(x5103,x5102,x5104,x5105,x5106,x5107,x5108))
% 28.78/28.54 [511]~E(x5111,x5112)+E(f550(x5113,x5114,x5111,x5115,x5116,x5117,x5118),f550(x5113,x5114,x5112,x5115,x5116,x5117,x5118))
% 28.78/28.54 [512]~E(x5121,x5122)+E(f550(x5123,x5124,x5125,x5121,x5126,x5127,x5128),f550(x5123,x5124,x5125,x5122,x5126,x5127,x5128))
% 28.78/28.54 [513]~E(x5131,x5132)+E(f550(x5133,x5134,x5135,x5136,x5131,x5137,x5138),f550(x5133,x5134,x5135,x5136,x5132,x5137,x5138))
% 28.78/28.54 [514]~E(x5141,x5142)+E(f550(x5143,x5144,x5145,x5146,x5147,x5141,x5148),f550(x5143,x5144,x5145,x5146,x5147,x5142,x5148))
% 28.78/28.54 [515]~E(x5151,x5152)+E(f550(x5153,x5154,x5155,x5156,x5157,x5158,x5151),f550(x5153,x5154,x5155,x5156,x5157,x5158,x5152))
% 28.78/28.54 [516]~E(x5161,x5162)+E(f542(x5161,x5163,x5164),f542(x5162,x5163,x5164))
% 28.78/28.54 [517]~E(x5171,x5172)+E(f542(x5173,x5171,x5174),f542(x5173,x5172,x5174))
% 28.78/28.54 [518]~E(x5181,x5182)+E(f542(x5183,x5184,x5181),f542(x5183,x5184,x5182))
% 28.78/28.54 [519]~E(x5191,x5192)+E(f787(x5191,x5193,x5194),f787(x5192,x5193,x5194))
% 28.78/28.54 [520]~E(x5201,x5202)+E(f787(x5203,x5201,x5204),f787(x5203,x5202,x5204))
% 28.78/28.54 [521]~E(x5211,x5212)+E(f787(x5213,x5214,x5211),f787(x5213,x5214,x5212))
% 28.78/28.54 [522]~E(x5221,x5222)+E(f667(x5221,x5223,x5224,x5225,x5226,x5227),f667(x5222,x5223,x5224,x5225,x5226,x5227))
% 28.78/28.54 [523]~E(x5231,x5232)+E(f667(x5233,x5231,x5234,x5235,x5236,x5237),f667(x5233,x5232,x5234,x5235,x5236,x5237))
% 28.78/28.54 [524]~E(x5241,x5242)+E(f667(x5243,x5244,x5241,x5245,x5246,x5247),f667(x5243,x5244,x5242,x5245,x5246,x5247))
% 28.78/28.54 [525]~E(x5251,x5252)+E(f667(x5253,x5254,x5255,x5251,x5256,x5257),f667(x5253,x5254,x5255,x5252,x5256,x5257))
% 28.78/28.54 [526]~E(x5261,x5262)+E(f667(x5263,x5264,x5265,x5266,x5261,x5267),f667(x5263,x5264,x5265,x5266,x5262,x5267))
% 28.78/28.54 [527]~E(x5271,x5272)+E(f667(x5273,x5274,x5275,x5276,x5277,x5271),f667(x5273,x5274,x5275,x5276,x5277,x5272))
% 28.78/28.54 [528]~E(x5281,x5282)+E(f668(x5281,x5283,x5284,x5285,x5286,x5287),f668(x5282,x5283,x5284,x5285,x5286,x5287))
% 28.78/28.54 [529]~E(x5291,x5292)+E(f668(x5293,x5291,x5294,x5295,x5296,x5297),f668(x5293,x5292,x5294,x5295,x5296,x5297))
% 28.78/28.54 [530]~E(x5301,x5302)+E(f668(x5303,x5304,x5301,x5305,x5306,x5307),f668(x5303,x5304,x5302,x5305,x5306,x5307))
% 28.78/28.54 [531]~E(x5311,x5312)+E(f668(x5313,x5314,x5315,x5311,x5316,x5317),f668(x5313,x5314,x5315,x5312,x5316,x5317))
% 28.78/28.54 [532]~E(x5321,x5322)+E(f668(x5323,x5324,x5325,x5326,x5321,x5327),f668(x5323,x5324,x5325,x5326,x5322,x5327))
% 28.78/28.54 [533]~E(x5331,x5332)+E(f668(x5333,x5334,x5335,x5336,x5337,x5331),f668(x5333,x5334,x5335,x5336,x5337,x5332))
% 28.78/28.54 [534]~E(x5341,x5342)+E(f278(x5341,x5343),f278(x5342,x5343))
% 28.78/28.54 [535]~E(x5351,x5352)+E(f278(x5353,x5351),f278(x5353,x5352))
% 28.78/28.54 [536]~E(x5361,x5362)+E(f152(x5361,x5363),f152(x5362,x5363))
% 28.78/28.54 [537]~E(x5371,x5372)+E(f152(x5373,x5371),f152(x5373,x5372))
% 28.78/28.54 [538]~E(x5381,x5382)+E(f876(x5381,x5383,x5384),f876(x5382,x5383,x5384))
% 28.78/28.54 [539]~E(x5391,x5392)+E(f876(x5393,x5391,x5394),f876(x5393,x5392,x5394))
% 28.78/28.54 [540]~E(x5401,x5402)+E(f876(x5403,x5404,x5401),f876(x5403,x5404,x5402))
% 28.78/28.54 [541]~E(x5411,x5412)+E(f755(x5411,x5413,x5414,x5415,x5416),f755(x5412,x5413,x5414,x5415,x5416))
% 28.78/28.54 [542]~E(x5421,x5422)+E(f755(x5423,x5421,x5424,x5425,x5426),f755(x5423,x5422,x5424,x5425,x5426))
% 28.78/28.54 [543]~E(x5431,x5432)+E(f755(x5433,x5434,x5431,x5435,x5436),f755(x5433,x5434,x5432,x5435,x5436))
% 28.78/28.54 [544]~E(x5441,x5442)+E(f755(x5443,x5444,x5445,x5441,x5446),f755(x5443,x5444,x5445,x5442,x5446))
% 28.78/28.54 [545]~E(x5451,x5452)+E(f755(x5453,x5454,x5455,x5456,x5451),f755(x5453,x5454,x5455,x5456,x5452))
% 28.78/28.54 [546]~E(x5461,x5462)+E(f851(x5461,x5463,x5464,x5465,x5466,x5467,x5468),f851(x5462,x5463,x5464,x5465,x5466,x5467,x5468))
% 28.78/28.54 [547]~E(x5471,x5472)+E(f851(x5473,x5471,x5474,x5475,x5476,x5477,x5478),f851(x5473,x5472,x5474,x5475,x5476,x5477,x5478))
% 28.78/28.54 [548]~E(x5481,x5482)+E(f851(x5483,x5484,x5481,x5485,x5486,x5487,x5488),f851(x5483,x5484,x5482,x5485,x5486,x5487,x5488))
% 28.78/28.54 [549]~E(x5491,x5492)+E(f851(x5493,x5494,x5495,x5491,x5496,x5497,x5498),f851(x5493,x5494,x5495,x5492,x5496,x5497,x5498))
% 28.78/28.54 [550]~E(x5501,x5502)+E(f851(x5503,x5504,x5505,x5506,x5501,x5507,x5508),f851(x5503,x5504,x5505,x5506,x5502,x5507,x5508))
% 28.78/28.54 [551]~E(x5511,x5512)+E(f851(x5513,x5514,x5515,x5516,x5517,x5511,x5518),f851(x5513,x5514,x5515,x5516,x5517,x5512,x5518))
% 28.78/28.54 [552]~E(x5521,x5522)+E(f851(x5523,x5524,x5525,x5526,x5527,x5528,x5521),f851(x5523,x5524,x5525,x5526,x5527,x5528,x5522))
% 28.78/28.54 [553]~E(x5531,x5532)+E(f275(x5531),f275(x5532))
% 28.78/28.54 [554]~E(x5541,x5542)+E(f15(x5541,x5543),f15(x5542,x5543))
% 28.78/28.54 [555]~E(x5551,x5552)+E(f15(x5553,x5551),f15(x5553,x5552))
% 28.78/28.54 [556]~E(x5561,x5562)+E(f296(x5561),f296(x5562))
% 28.78/28.54 [557]~E(x5571,x5572)+E(f503(x5571,x5573,x5574),f503(x5572,x5573,x5574))
% 28.78/28.54 [558]~E(x5581,x5582)+E(f503(x5583,x5581,x5584),f503(x5583,x5582,x5584))
% 28.78/28.54 [559]~E(x5591,x5592)+E(f503(x5593,x5594,x5591),f503(x5593,x5594,x5592))
% 28.78/28.54 [560]~E(x5601,x5602)+E(f237(x5601,x5603,x5604),f237(x5602,x5603,x5604))
% 28.78/28.54 [561]~E(x5611,x5612)+E(f237(x5613,x5611,x5614),f237(x5613,x5612,x5614))
% 28.78/28.54 [562]~E(x5621,x5622)+E(f237(x5623,x5624,x5621),f237(x5623,x5624,x5622))
% 28.78/28.54 [563]~E(x5631,x5632)+E(f798(x5631,x5633,x5634,x5635),f798(x5632,x5633,x5634,x5635))
% 28.78/28.54 [564]~E(x5641,x5642)+E(f798(x5643,x5641,x5644,x5645),f798(x5643,x5642,x5644,x5645))
% 28.78/28.54 [565]~E(x5651,x5652)+E(f798(x5653,x5654,x5651,x5655),f798(x5653,x5654,x5652,x5655))
% 28.78/28.54 [566]~E(x5661,x5662)+E(f798(x5663,x5664,x5665,x5661),f798(x5663,x5664,x5665,x5662))
% 28.78/28.54 [567]~E(x5671,x5672)+E(f41(x5671,x5673),f41(x5672,x5673))
% 28.78/28.54 [568]~E(x5681,x5682)+E(f41(x5683,x5681),f41(x5683,x5682))
% 28.78/28.54 [569]~E(x5691,x5692)+E(f293(x5691),f293(x5692))
% 28.78/28.54 [570]~E(x5701,x5702)+E(f816(x5701,x5703,x5704),f816(x5702,x5703,x5704))
% 28.78/28.54 [571]~E(x5711,x5712)+E(f816(x5713,x5711,x5714),f816(x5713,x5712,x5714))
% 28.78/28.54 [572]~E(x5721,x5722)+E(f816(x5723,x5724,x5721),f816(x5723,x5724,x5722))
% 28.78/28.54 [573]~E(x5731,x5732)+E(f60(x5731,x5733,x5734,x5735,x5736),f60(x5732,x5733,x5734,x5735,x5736))
% 28.78/28.54 [574]~E(x5741,x5742)+E(f60(x5743,x5741,x5744,x5745,x5746),f60(x5743,x5742,x5744,x5745,x5746))
% 28.78/28.54 [575]~E(x5751,x5752)+E(f60(x5753,x5754,x5751,x5755,x5756),f60(x5753,x5754,x5752,x5755,x5756))
% 28.78/28.54 [576]~E(x5761,x5762)+E(f60(x5763,x5764,x5765,x5761,x5766),f60(x5763,x5764,x5765,x5762,x5766))
% 28.78/28.54 [577]~E(x5771,x5772)+E(f60(x5773,x5774,x5775,x5776,x5771),f60(x5773,x5774,x5775,x5776,x5772))
% 28.78/28.54 [578]~E(x5781,x5782)+E(f282(x5781,x5783,x5784,x5785),f282(x5782,x5783,x5784,x5785))
% 28.78/28.54 [579]~E(x5791,x5792)+E(f282(x5793,x5791,x5794,x5795),f282(x5793,x5792,x5794,x5795))
% 28.78/28.54 [580]~E(x5801,x5802)+E(f282(x5803,x5804,x5801,x5805),f282(x5803,x5804,x5802,x5805))
% 28.78/28.54 [581]~E(x5811,x5812)+E(f282(x5813,x5814,x5815,x5811),f282(x5813,x5814,x5815,x5812))
% 28.78/28.54 [582]~E(x5821,x5822)+E(f403(x5821,x5823,x5824,x5825),f403(x5822,x5823,x5824,x5825))
% 28.78/28.54 [583]~E(x5831,x5832)+E(f403(x5833,x5831,x5834,x5835),f403(x5833,x5832,x5834,x5835))
% 28.78/28.54 [584]~E(x5841,x5842)+E(f403(x5843,x5844,x5841,x5845),f403(x5843,x5844,x5842,x5845))
% 28.78/28.54 [585]~E(x5851,x5852)+E(f403(x5853,x5854,x5855,x5851),f403(x5853,x5854,x5855,x5852))
% 28.78/28.54 [586]~E(x5861,x5862)+E(f666(x5861,x5863,x5864,x5865,x5866,x5867),f666(x5862,x5863,x5864,x5865,x5866,x5867))
% 28.78/28.54 [587]~E(x5871,x5872)+E(f666(x5873,x5871,x5874,x5875,x5876,x5877),f666(x5873,x5872,x5874,x5875,x5876,x5877))
% 28.78/28.54 [588]~E(x5881,x5882)+E(f666(x5883,x5884,x5881,x5885,x5886,x5887),f666(x5883,x5884,x5882,x5885,x5886,x5887))
% 28.78/28.54 [589]~E(x5891,x5892)+E(f666(x5893,x5894,x5895,x5891,x5896,x5897),f666(x5893,x5894,x5895,x5892,x5896,x5897))
% 28.78/28.54 [590]~E(x5901,x5902)+E(f666(x5903,x5904,x5905,x5906,x5901,x5907),f666(x5903,x5904,x5905,x5906,x5902,x5907))
% 28.78/28.54 [591]~E(x5911,x5912)+E(f666(x5913,x5914,x5915,x5916,x5917,x5911),f666(x5913,x5914,x5915,x5916,x5917,x5912))
% 28.78/28.54 [592]~E(x5921,x5922)+E(f504(x5921,x5923,x5924),f504(x5922,x5923,x5924))
% 28.78/28.54 [593]~E(x5931,x5932)+E(f504(x5933,x5931,x5934),f504(x5933,x5932,x5934))
% 28.78/28.54 [594]~E(x5941,x5942)+E(f504(x5943,x5944,x5941),f504(x5943,x5944,x5942))
% 28.78/28.54 [595]~E(x5951,x5952)+E(f117(x5951,x5953),f117(x5952,x5953))
% 28.78/28.54 [596]~E(x5961,x5962)+E(f117(x5963,x5961),f117(x5963,x5962))
% 28.78/28.54 [597]~E(x5971,x5972)+E(f827(x5971),f827(x5972))
% 28.78/28.54 [598]~E(x5981,x5982)+E(f392(x5981,x5983,x5984,x5985,x5986),f392(x5982,x5983,x5984,x5985,x5986))
% 28.78/28.54 [599]~E(x5991,x5992)+E(f392(x5993,x5991,x5994,x5995,x5996),f392(x5993,x5992,x5994,x5995,x5996))
% 28.78/28.54 [600]~E(x6001,x6002)+E(f392(x6003,x6004,x6001,x6005,x6006),f392(x6003,x6004,x6002,x6005,x6006))
% 28.78/28.54 [601]~E(x6011,x6012)+E(f392(x6013,x6014,x6015,x6011,x6016),f392(x6013,x6014,x6015,x6012,x6016))
% 28.78/28.54 [602]~E(x6021,x6022)+E(f392(x6023,x6024,x6025,x6026,x6021),f392(x6023,x6024,x6025,x6026,x6022))
% 28.78/28.54 [603]~E(x6031,x6032)+E(f568(x6031,x6033),f568(x6032,x6033))
% 28.78/28.54 [604]~E(x6041,x6042)+E(f568(x6043,x6041),f568(x6043,x6042))
% 28.78/28.54 [605]~E(x6051,x6052)+E(f784(x6051,x6053,x6054),f784(x6052,x6053,x6054))
% 28.78/28.54 [606]~E(x6061,x6062)+E(f784(x6063,x6061,x6064),f784(x6063,x6062,x6064))
% 28.78/28.54 [607]~E(x6071,x6072)+E(f784(x6073,x6074,x6071),f784(x6073,x6074,x6072))
% 28.78/28.54 [608]~E(x6081,x6082)+E(f162(x6081,x6083,x6084),f162(x6082,x6083,x6084))
% 28.78/28.54 [609]~E(x6091,x6092)+E(f162(x6093,x6091,x6094),f162(x6093,x6092,x6094))
% 28.78/28.54 [610]~E(x6101,x6102)+E(f162(x6103,x6104,x6101),f162(x6103,x6104,x6102))
% 28.78/28.54 [611]~E(x6111,x6112)+E(f726(x6111,x6113,x6114),f726(x6112,x6113,x6114))
% 28.78/28.54 [612]~E(x6121,x6122)+E(f726(x6123,x6121,x6124),f726(x6123,x6122,x6124))
% 28.78/28.54 [613]~E(x6131,x6132)+E(f726(x6133,x6134,x6131),f726(x6133,x6134,x6132))
% 28.78/28.54 [614]~E(x6141,x6142)+E(f863(x6141,x6143,x6144,x6145,x6146,x6147,x6148,x6149),f863(x6142,x6143,x6144,x6145,x6146,x6147,x6148,x6149))
% 28.78/28.54 [615]~E(x6151,x6152)+E(f863(x6153,x6151,x6154,x6155,x6156,x6157,x6158,x6159),f863(x6153,x6152,x6154,x6155,x6156,x6157,x6158,x6159))
% 28.78/28.54 [616]~E(x6161,x6162)+E(f863(x6163,x6164,x6161,x6165,x6166,x6167,x6168,x6169),f863(x6163,x6164,x6162,x6165,x6166,x6167,x6168,x6169))
% 28.78/28.54 [617]~E(x6171,x6172)+E(f863(x6173,x6174,x6175,x6171,x6176,x6177,x6178,x6179),f863(x6173,x6174,x6175,x6172,x6176,x6177,x6178,x6179))
% 28.78/28.54 [618]~E(x6181,x6182)+E(f863(x6183,x6184,x6185,x6186,x6181,x6187,x6188,x6189),f863(x6183,x6184,x6185,x6186,x6182,x6187,x6188,x6189))
% 28.78/28.54 [619]~E(x6191,x6192)+E(f863(x6193,x6194,x6195,x6196,x6197,x6191,x6198,x6199),f863(x6193,x6194,x6195,x6196,x6197,x6192,x6198,x6199))
% 28.78/28.54 [620]~E(x6201,x6202)+E(f863(x6203,x6204,x6205,x6206,x6207,x6208,x6201,x6209),f863(x6203,x6204,x6205,x6206,x6207,x6208,x6202,x6209))
% 28.78/28.54 [621]~E(x6211,x6212)+E(f863(x6213,x6214,x6215,x6216,x6217,x6218,x6219,x6211),f863(x6213,x6214,x6215,x6216,x6217,x6218,x6219,x6212))
% 28.78/28.54 [622]~E(x6221,x6222)+E(f212(x6221,x6223,x6224,x6225),f212(x6222,x6223,x6224,x6225))
% 28.78/28.54 [623]~E(x6231,x6232)+E(f212(x6233,x6231,x6234,x6235),f212(x6233,x6232,x6234,x6235))
% 28.78/28.54 [624]~E(x6241,x6242)+E(f212(x6243,x6244,x6241,x6245),f212(x6243,x6244,x6242,x6245))
% 28.78/28.54 [625]~E(x6251,x6252)+E(f212(x6253,x6254,x6255,x6251),f212(x6253,x6254,x6255,x6252))
% 28.78/28.54 [626]~E(x6261,x6262)+E(f510(x6261,x6263,x6264,x6265,x6266),f510(x6262,x6263,x6264,x6265,x6266))
% 28.78/28.54 [627]~E(x6271,x6272)+E(f510(x6273,x6271,x6274,x6275,x6276),f510(x6273,x6272,x6274,x6275,x6276))
% 28.78/28.54 [628]~E(x6281,x6282)+E(f510(x6283,x6284,x6281,x6285,x6286),f510(x6283,x6284,x6282,x6285,x6286))
% 28.78/28.54 [629]~E(x6291,x6292)+E(f510(x6293,x6294,x6295,x6291,x6296),f510(x6293,x6294,x6295,x6292,x6296))
% 28.78/28.54 [630]~E(x6301,x6302)+E(f510(x6303,x6304,x6305,x6306,x6301),f510(x6303,x6304,x6305,x6306,x6302))
% 28.78/28.54 [631]~E(x6311,x6312)+E(f372(x6311,x6313),f372(x6312,x6313))
% 28.78/28.54 [632]~E(x6321,x6322)+E(f372(x6323,x6321),f372(x6323,x6322))
% 28.78/28.54 [633]~E(x6331,x6332)+E(f685(x6331,x6333,x6334),f685(x6332,x6333,x6334))
% 28.78/28.54 [634]~E(x6341,x6342)+E(f685(x6343,x6341,x6344),f685(x6343,x6342,x6344))
% 28.78/28.54 [635]~E(x6351,x6352)+E(f685(x6353,x6354,x6351),f685(x6353,x6354,x6352))
% 28.78/28.54 [636]~E(x6361,x6362)+E(f875(x6361,x6363,x6364),f875(x6362,x6363,x6364))
% 28.78/28.54 [637]~E(x6371,x6372)+E(f875(x6373,x6371,x6374),f875(x6373,x6372,x6374))
% 28.78/28.54 [638]~E(x6381,x6382)+E(f875(x6383,x6384,x6381),f875(x6383,x6384,x6382))
% 28.78/28.54 [639]~E(x6391,x6392)+E(f404(x6391,x6393,x6394,x6395),f404(x6392,x6393,x6394,x6395))
% 28.78/28.54 [640]~E(x6401,x6402)+E(f404(x6403,x6401,x6404,x6405),f404(x6403,x6402,x6404,x6405))
% 28.78/28.54 [641]~E(x6411,x6412)+E(f404(x6413,x6414,x6411,x6415),f404(x6413,x6414,x6412,x6415))
% 28.78/28.54 [642]~E(x6421,x6422)+E(f404(x6423,x6424,x6425,x6421),f404(x6423,x6424,x6425,x6422))
% 28.78/28.54 [643]~E(x6431,x6432)+E(f139(x6431,x6433),f139(x6432,x6433))
% 28.78/28.54 [644]~E(x6441,x6442)+E(f139(x6443,x6441),f139(x6443,x6442))
% 28.78/28.54 [645]~E(x6451,x6452)+E(f828(x6451),f828(x6452))
% 28.78/28.54 [646]~E(x6461,x6462)+E(f588(x6461,x6463),f588(x6462,x6463))
% 28.78/28.54 [647]~E(x6471,x6472)+E(f588(x6473,x6471),f588(x6473,x6472))
% 28.78/28.54 [648]~E(x6481,x6482)+E(f43(x6481,x6483),f43(x6482,x6483))
% 28.78/28.54 [649]~E(x6491,x6492)+E(f43(x6493,x6491),f43(x6493,x6492))
% 28.78/28.54 [650]~E(x6501,x6502)+E(f151(x6501,x6503),f151(x6502,x6503))
% 28.78/28.54 [651]~E(x6511,x6512)+E(f151(x6513,x6511),f151(x6513,x6512))
% 28.78/28.54 [652]~E(x6521,x6522)+E(f744(x6521,x6523,x6524,x6525),f744(x6522,x6523,x6524,x6525))
% 28.78/28.54 [653]~E(x6531,x6532)+E(f744(x6533,x6531,x6534,x6535),f744(x6533,x6532,x6534,x6535))
% 28.78/28.54 [654]~E(x6541,x6542)+E(f744(x6543,x6544,x6541,x6545),f744(x6543,x6544,x6542,x6545))
% 28.78/28.54 [655]~E(x6551,x6552)+E(f744(x6553,x6554,x6555,x6551),f744(x6553,x6554,x6555,x6552))
% 28.78/28.54 [656]~E(x6561,x6562)+E(f44(x6561,x6563),f44(x6562,x6563))
% 28.78/28.54 [657]~E(x6571,x6572)+E(f44(x6573,x6571),f44(x6573,x6572))
% 28.78/28.54 [658]~E(x6581,x6582)+E(f47(x6581,x6583),f47(x6582,x6583))
% 28.78/28.54 [659]~E(x6591,x6592)+E(f47(x6593,x6591),f47(x6593,x6592))
% 28.78/28.54 [660]~E(x6601,x6602)+E(f634(x6601,x6603,x6604),f634(x6602,x6603,x6604))
% 28.78/28.54 [661]~E(x6611,x6612)+E(f634(x6613,x6611,x6614),f634(x6613,x6612,x6614))
% 28.78/28.54 [662]~E(x6621,x6622)+E(f634(x6623,x6624,x6621),f634(x6623,x6624,x6622))
% 28.78/28.54 [663]~E(x6631,x6632)+E(f491(x6631,x6633),f491(x6632,x6633))
% 28.78/28.54 [664]~E(x6641,x6642)+E(f491(x6643,x6641),f491(x6643,x6642))
% 28.78/28.54 [665]~E(x6651,x6652)+E(f86(x6651),f86(x6652))
% 28.78/28.54 [666]~E(x6661,x6662)+E(f565(x6661,x6663),f565(x6662,x6663))
% 28.78/28.54 [667]~E(x6671,x6672)+E(f565(x6673,x6671),f565(x6673,x6672))
% 28.78/28.54 [668]~E(x6681,x6682)+E(f814(x6681,x6683,x6684),f814(x6682,x6683,x6684))
% 28.78/28.54 [669]~E(x6691,x6692)+E(f814(x6693,x6691,x6694),f814(x6693,x6692,x6694))
% 28.78/28.54 [670]~E(x6701,x6702)+E(f814(x6703,x6704,x6701),f814(x6703,x6704,x6702))
% 28.78/28.54 [671]~E(x6711,x6712)+E(f458(x6711,x6713),f458(x6712,x6713))
% 28.78/28.54 [672]~E(x6721,x6722)+E(f458(x6723,x6721),f458(x6723,x6722))
% 28.78/28.54 [673]~E(x6731,x6732)+E(f40(x6731,x6733),f40(x6732,x6733))
% 28.78/28.54 [674]~E(x6741,x6742)+E(f40(x6743,x6741),f40(x6743,x6742))
% 28.78/28.54 [675]~E(x6751,x6752)+E(f168(x6751,x6753,x6754),f168(x6752,x6753,x6754))
% 28.78/28.54 [676]~E(x6761,x6762)+E(f168(x6763,x6761,x6764),f168(x6763,x6762,x6764))
% 28.78/28.54 [677]~E(x6771,x6772)+E(f168(x6773,x6774,x6771),f168(x6773,x6774,x6772))
% 28.78/28.54 [678]~E(x6781,x6782)+E(f912(x6781,x6783,x6784,x6785,x6786),f912(x6782,x6783,x6784,x6785,x6786))
% 28.78/28.54 [679]~E(x6791,x6792)+E(f912(x6793,x6791,x6794,x6795,x6796),f912(x6793,x6792,x6794,x6795,x6796))
% 28.78/28.54 [680]~E(x6801,x6802)+E(f912(x6803,x6804,x6801,x6805,x6806),f912(x6803,x6804,x6802,x6805,x6806))
% 28.78/28.54 [681]~E(x6811,x6812)+E(f912(x6813,x6814,x6815,x6811,x6816),f912(x6813,x6814,x6815,x6812,x6816))
% 28.78/28.54 [682]~E(x6821,x6822)+E(f912(x6823,x6824,x6825,x6826,x6821),f912(x6823,x6824,x6825,x6826,x6822))
% 28.78/28.54 [683]~E(x6831,x6832)+E(f881(x6831,x6833,x6834,x6835),f881(x6832,x6833,x6834,x6835))
% 28.78/28.54 [684]~E(x6841,x6842)+E(f881(x6843,x6841,x6844,x6845),f881(x6843,x6842,x6844,x6845))
% 28.78/28.54 [685]~E(x6851,x6852)+E(f881(x6853,x6854,x6851,x6855),f881(x6853,x6854,x6852,x6855))
% 28.78/28.54 [686]~E(x6861,x6862)+E(f881(x6863,x6864,x6865,x6861),f881(x6863,x6864,x6865,x6862))
% 28.78/28.54 [687]~E(x6871,x6872)+E(f868(x6871,x6873,x6874),f868(x6872,x6873,x6874))
% 28.78/28.54 [688]~E(x6881,x6882)+E(f868(x6883,x6881,x6884),f868(x6883,x6882,x6884))
% 28.78/28.54 [689]~E(x6891,x6892)+E(f868(x6893,x6894,x6891),f868(x6893,x6894,x6892))
% 28.78/28.54 [690]~E(x6901,x6902)+E(f486(x6901,x6903,x6904),f486(x6902,x6903,x6904))
% 28.78/28.54 [691]~E(x6911,x6912)+E(f486(x6913,x6911,x6914),f486(x6913,x6912,x6914))
% 28.78/28.54 [692]~E(x6921,x6922)+E(f486(x6923,x6924,x6921),f486(x6923,x6924,x6922))
% 28.78/28.54 [693]~E(x6931,x6932)+E(f449(x6931,x6933,x6934),f449(x6932,x6933,x6934))
% 28.78/28.54 [694]~E(x6941,x6942)+E(f449(x6943,x6941,x6944),f449(x6943,x6942,x6944))
% 28.78/28.54 [695]~E(x6951,x6952)+E(f449(x6953,x6954,x6951),f449(x6953,x6954,x6952))
% 28.78/28.54 [696]~E(x6961,x6962)+E(f165(x6961,x6963,x6964),f165(x6962,x6963,x6964))
% 28.78/28.54 [697]~E(x6971,x6972)+E(f165(x6973,x6971,x6974),f165(x6973,x6972,x6974))
% 28.78/28.54 [698]~E(x6981,x6982)+E(f165(x6983,x6984,x6981),f165(x6983,x6984,x6982))
% 28.78/28.54 [699]~E(x6991,x6992)+E(f752(x6991,x6993),f752(x6992,x6993))
% 28.78/28.54 [700]~E(x7001,x7002)+E(f752(x7003,x7001),f752(x7003,x7002))
% 28.78/28.54 [701]~E(x7011,x7012)+E(f477(x7011,x7013,x7014),f477(x7012,x7013,x7014))
% 28.78/28.54 [702]~E(x7021,x7022)+E(f477(x7023,x7021,x7024),f477(x7023,x7022,x7024))
% 28.78/28.54 [703]~E(x7031,x7032)+E(f477(x7033,x7034,x7031),f477(x7033,x7034,x7032))
% 28.78/28.54 [704]~E(x7041,x7042)+E(f230(x7041,x7043),f230(x7042,x7043))
% 28.78/28.54 [705]~E(x7051,x7052)+E(f230(x7053,x7051),f230(x7053,x7052))
% 28.78/28.54 [706]~E(x7061,x7062)+E(f51(x7061),f51(x7062))
% 28.78/28.54 [707]~E(x7071,x7072)+E(f50(x7071),f50(x7072))
% 28.78/28.54 [708]~E(x7081,x7082)+E(f653(x7081,x7083,x7084,x7085,x7086,x7087,x7088),f653(x7082,x7083,x7084,x7085,x7086,x7087,x7088))
% 28.78/28.54 [709]~E(x7091,x7092)+E(f653(x7093,x7091,x7094,x7095,x7096,x7097,x7098),f653(x7093,x7092,x7094,x7095,x7096,x7097,x7098))
% 28.78/28.54 [710]~E(x7101,x7102)+E(f653(x7103,x7104,x7101,x7105,x7106,x7107,x7108),f653(x7103,x7104,x7102,x7105,x7106,x7107,x7108))
% 28.78/28.54 [711]~E(x7111,x7112)+E(f653(x7113,x7114,x7115,x7111,x7116,x7117,x7118),f653(x7113,x7114,x7115,x7112,x7116,x7117,x7118))
% 28.78/28.54 [712]~E(x7121,x7122)+E(f653(x7123,x7124,x7125,x7126,x7121,x7127,x7128),f653(x7123,x7124,x7125,x7126,x7122,x7127,x7128))
% 28.78/28.54 [713]~E(x7131,x7132)+E(f653(x7133,x7134,x7135,x7136,x7137,x7131,x7138),f653(x7133,x7134,x7135,x7136,x7137,x7132,x7138))
% 28.78/28.54 [714]~E(x7141,x7142)+E(f653(x7143,x7144,x7145,x7146,x7147,x7148,x7141),f653(x7143,x7144,x7145,x7146,x7147,x7148,x7142))
% 28.78/28.54 [715]~E(x7151,x7152)+E(f308(x7151,x7153),f308(x7152,x7153))
% 28.78/28.54 [716]~E(x7161,x7162)+E(f308(x7163,x7161),f308(x7163,x7162))
% 28.78/28.54 [717]~E(x7171,x7172)+E(f604(x7171,x7173,x7174,x7175,x7176,x7177),f604(x7172,x7173,x7174,x7175,x7176,x7177))
% 28.78/28.54 [718]~E(x7181,x7182)+E(f604(x7183,x7181,x7184,x7185,x7186,x7187),f604(x7183,x7182,x7184,x7185,x7186,x7187))
% 28.78/28.54 [719]~E(x7191,x7192)+E(f604(x7193,x7194,x7191,x7195,x7196,x7197),f604(x7193,x7194,x7192,x7195,x7196,x7197))
% 28.78/28.54 [720]~E(x7201,x7202)+E(f604(x7203,x7204,x7205,x7201,x7206,x7207),f604(x7203,x7204,x7205,x7202,x7206,x7207))
% 28.78/28.54 [721]~E(x7211,x7212)+E(f604(x7213,x7214,x7215,x7216,x7211,x7217),f604(x7213,x7214,x7215,x7216,x7212,x7217))
% 28.78/28.54 [722]~E(x7221,x7222)+E(f604(x7223,x7224,x7225,x7226,x7227,x7221),f604(x7223,x7224,x7225,x7226,x7227,x7222))
% 28.78/28.54 [723]~E(x7231,x7232)+E(f280(x7231,x7233),f280(x7232,x7233))
% 28.78/28.54 [724]~E(x7241,x7242)+E(f280(x7243,x7241),f280(x7243,x7242))
% 28.78/28.54 [725]~E(x7251,x7252)+E(f777(x7251,x7253,x7254),f777(x7252,x7253,x7254))
% 28.78/28.54 [726]~E(x7261,x7262)+E(f777(x7263,x7261,x7264),f777(x7263,x7262,x7264))
% 28.78/28.54 [727]~E(x7271,x7272)+E(f777(x7273,x7274,x7271),f777(x7273,x7274,x7272))
% 28.78/28.54 [728]~E(x7281,x7282)+E(f635(x7281,x7283,x7284,x7285,x7286),f635(x7282,x7283,x7284,x7285,x7286))
% 28.78/28.54 [729]~E(x7291,x7292)+E(f635(x7293,x7291,x7294,x7295,x7296),f635(x7293,x7292,x7294,x7295,x7296))
% 28.78/28.54 [730]~E(x7301,x7302)+E(f635(x7303,x7304,x7301,x7305,x7306),f635(x7303,x7304,x7302,x7305,x7306))
% 28.78/28.54 [731]~E(x7311,x7312)+E(f635(x7313,x7314,x7315,x7311,x7316),f635(x7313,x7314,x7315,x7312,x7316))
% 28.78/28.54 [732]~E(x7321,x7322)+E(f635(x7323,x7324,x7325,x7326,x7321),f635(x7323,x7324,x7325,x7326,x7322))
% 28.78/28.54 [733]~E(x7331,x7332)+E(f693(x7331,x7333,x7334,x7335),f693(x7332,x7333,x7334,x7335))
% 28.78/28.54 [734]~E(x7341,x7342)+E(f693(x7343,x7341,x7344,x7345),f693(x7343,x7342,x7344,x7345))
% 28.78/28.54 [735]~E(x7351,x7352)+E(f693(x7353,x7354,x7351,x7355),f693(x7353,x7354,x7352,x7355))
% 28.78/28.54 [736]~E(x7361,x7362)+E(f693(x7363,x7364,x7365,x7361),f693(x7363,x7364,x7365,x7362))
% 28.78/28.54 [737]~E(x7371,x7372)+E(f580(x7371,x7373,x7374,x7375,x7376,x7377),f580(x7372,x7373,x7374,x7375,x7376,x7377))
% 28.78/28.54 [738]~E(x7381,x7382)+E(f580(x7383,x7381,x7384,x7385,x7386,x7387),f580(x7383,x7382,x7384,x7385,x7386,x7387))
% 28.78/28.54 [739]~E(x7391,x7392)+E(f580(x7393,x7394,x7391,x7395,x7396,x7397),f580(x7393,x7394,x7392,x7395,x7396,x7397))
% 28.78/28.54 [740]~E(x7401,x7402)+E(f580(x7403,x7404,x7405,x7401,x7406,x7407),f580(x7403,x7404,x7405,x7402,x7406,x7407))
% 28.78/28.54 [741]~E(x7411,x7412)+E(f580(x7413,x7414,x7415,x7416,x7411,x7417),f580(x7413,x7414,x7415,x7416,x7412,x7417))
% 28.78/28.54 [742]~E(x7421,x7422)+E(f580(x7423,x7424,x7425,x7426,x7427,x7421),f580(x7423,x7424,x7425,x7426,x7427,x7422))
% 28.78/28.54 [743]~E(x7431,x7432)+E(f812(x7431,x7433),f812(x7432,x7433))
% 28.78/28.54 [744]~E(x7441,x7442)+E(f812(x7443,x7441),f812(x7443,x7442))
% 28.78/28.54 [745]~E(x7451,x7452)+E(f407(x7451,x7453,x7454,x7455,x7456),f407(x7452,x7453,x7454,x7455,x7456))
% 28.78/28.54 [746]~E(x7461,x7462)+E(f407(x7463,x7461,x7464,x7465,x7466),f407(x7463,x7462,x7464,x7465,x7466))
% 28.78/28.54 [747]~E(x7471,x7472)+E(f407(x7473,x7474,x7471,x7475,x7476),f407(x7473,x7474,x7472,x7475,x7476))
% 28.78/28.54 [748]~E(x7481,x7482)+E(f407(x7483,x7484,x7485,x7481,x7486),f407(x7483,x7484,x7485,x7482,x7486))
% 28.78/28.54 [749]~E(x7491,x7492)+E(f407(x7493,x7494,x7495,x7496,x7491),f407(x7493,x7494,x7495,x7496,x7492))
% 28.78/28.54 [750]~E(x7501,x7502)+E(f536(x7501,x7503,x7504),f536(x7502,x7503,x7504))
% 28.78/28.54 [751]~E(x7511,x7512)+E(f536(x7513,x7511,x7514),f536(x7513,x7512,x7514))
% 28.78/28.54 [752]~E(x7521,x7522)+E(f536(x7523,x7524,x7521),f536(x7523,x7524,x7522))
% 28.78/28.54 [753]~E(x7531,x7532)+E(f867(x7531,x7533,x7534),f867(x7532,x7533,x7534))
% 28.78/28.54 [754]~E(x7541,x7542)+E(f867(x7543,x7541,x7544),f867(x7543,x7542,x7544))
% 28.78/28.54 [755]~E(x7551,x7552)+E(f867(x7553,x7554,x7551),f867(x7553,x7554,x7552))
% 28.78/28.54 [756]~E(x7561,x7562)+E(f789(x7561,x7563,x7564,x7565),f789(x7562,x7563,x7564,x7565))
% 28.78/28.54 [757]~E(x7571,x7572)+E(f789(x7573,x7571,x7574,x7575),f789(x7573,x7572,x7574,x7575))
% 28.78/28.54 [758]~E(x7581,x7582)+E(f789(x7583,x7584,x7581,x7585),f789(x7583,x7584,x7582,x7585))
% 28.78/28.54 [759]~E(x7591,x7592)+E(f789(x7593,x7594,x7595,x7591),f789(x7593,x7594,x7595,x7592))
% 28.78/28.54 [760]~E(x7601,x7602)+E(f133(x7601),f133(x7602))
% 28.78/28.54 [761]~E(x7611,x7612)+E(f368(x7611,x7613),f368(x7612,x7613))
% 28.78/28.54 [762]~E(x7621,x7622)+E(f368(x7623,x7621),f368(x7623,x7622))
% 28.78/28.54 [763]~E(x7631,x7632)+E(f276(x7631,x7633),f276(x7632,x7633))
% 28.78/28.54 [764]~E(x7641,x7642)+E(f276(x7643,x7641),f276(x7643,x7642))
% 28.78/28.54 [765]~E(x7651,x7652)+E(f579(x7651,x7653,x7654,x7655),f579(x7652,x7653,x7654,x7655))
% 28.78/28.54 [766]~E(x7661,x7662)+E(f579(x7663,x7661,x7664,x7665),f579(x7663,x7662,x7664,x7665))
% 28.78/28.54 [767]~E(x7671,x7672)+E(f579(x7673,x7674,x7671,x7675),f579(x7673,x7674,x7672,x7675))
% 28.78/28.54 [768]~E(x7681,x7682)+E(f579(x7683,x7684,x7685,x7681),f579(x7683,x7684,x7685,x7682))
% 28.78/28.54 [769]~E(x7691,x7692)+E(f440(x7691,x7693),f440(x7692,x7693))
% 28.78/28.54 [770]~E(x7701,x7702)+E(f440(x7703,x7701),f440(x7703,x7702))
% 28.78/28.54 [771]~E(x7711,x7712)+E(f267(x7711,x7713),f267(x7712,x7713))
% 28.78/28.54 [772]~E(x7721,x7722)+E(f267(x7723,x7721),f267(x7723,x7722))
% 28.78/28.54 [773]~E(x7731,x7732)+E(f289(x7731,x7733,x7734,x7735,x7736),f289(x7732,x7733,x7734,x7735,x7736))
% 28.78/28.54 [774]~E(x7741,x7742)+E(f289(x7743,x7741,x7744,x7745,x7746),f289(x7743,x7742,x7744,x7745,x7746))
% 28.78/28.54 [775]~E(x7751,x7752)+E(f289(x7753,x7754,x7751,x7755,x7756),f289(x7753,x7754,x7752,x7755,x7756))
% 28.78/28.54 [776]~E(x7761,x7762)+E(f289(x7763,x7764,x7765,x7761,x7766),f289(x7763,x7764,x7765,x7762,x7766))
% 28.78/28.54 [777]~E(x7771,x7772)+E(f289(x7773,x7774,x7775,x7776,x7771),f289(x7773,x7774,x7775,x7776,x7772))
% 28.78/28.54 [778]~E(x7781,x7782)+E(f215(x7781,x7783,x7784,x7785,x7786),f215(x7782,x7783,x7784,x7785,x7786))
% 28.78/28.54 [779]~E(x7791,x7792)+E(f215(x7793,x7791,x7794,x7795,x7796),f215(x7793,x7792,x7794,x7795,x7796))
% 28.78/28.54 [780]~E(x7801,x7802)+E(f215(x7803,x7804,x7801,x7805,x7806),f215(x7803,x7804,x7802,x7805,x7806))
% 28.78/28.54 [781]~E(x7811,x7812)+E(f215(x7813,x7814,x7815,x7811,x7816),f215(x7813,x7814,x7815,x7812,x7816))
% 28.78/28.54 [782]~E(x7821,x7822)+E(f215(x7823,x7824,x7825,x7826,x7821),f215(x7823,x7824,x7825,x7826,x7822))
% 28.78/28.54 [783]~E(x7831,x7832)+E(f811(x7831,x7833),f811(x7832,x7833))
% 28.78/28.54 [784]~E(x7841,x7842)+E(f811(x7843,x7841),f811(x7843,x7842))
% 28.78/28.54 [785]~E(x7851,x7852)+E(f473(x7851,x7853,x7854),f473(x7852,x7853,x7854))
% 28.78/28.54 [786]~E(x7861,x7862)+E(f473(x7863,x7861,x7864),f473(x7863,x7862,x7864))
% 28.78/28.54 [787]~E(x7871,x7872)+E(f473(x7873,x7874,x7871),f473(x7873,x7874,x7872))
% 28.78/28.54 [788]~E(x7881,x7882)+E(f420(x7881,x7883,x7884),f420(x7882,x7883,x7884))
% 28.78/28.54 [789]~E(x7891,x7892)+E(f420(x7893,x7891,x7894),f420(x7893,x7892,x7894))
% 28.78/28.54 [790]~E(x7901,x7902)+E(f420(x7903,x7904,x7901),f420(x7903,x7904,x7902))
% 28.78/28.54 [791]~E(x7911,x7912)+E(f908(x7911,x7913,x7914,x7915,x7916),f908(x7912,x7913,x7914,x7915,x7916))
% 28.78/28.54 [792]~E(x7921,x7922)+E(f908(x7923,x7921,x7924,x7925,x7926),f908(x7923,x7922,x7924,x7925,x7926))
% 28.78/28.54 [793]~E(x7931,x7932)+E(f908(x7933,x7934,x7931,x7935,x7936),f908(x7933,x7934,x7932,x7935,x7936))
% 28.78/28.54 [794]~E(x7941,x7942)+E(f908(x7943,x7944,x7945,x7941,x7946),f908(x7943,x7944,x7945,x7942,x7946))
% 28.78/28.54 [795]~E(x7951,x7952)+E(f908(x7953,x7954,x7955,x7956,x7951),f908(x7953,x7954,x7955,x7956,x7952))
% 28.78/28.54 [796]~E(x7961,x7962)+E(f235(x7961,x7963,x7964),f235(x7962,x7963,x7964))
% 28.78/28.54 [797]~E(x7971,x7972)+E(f235(x7973,x7971,x7974),f235(x7973,x7972,x7974))
% 28.78/28.54 [798]~E(x7981,x7982)+E(f235(x7983,x7984,x7981),f235(x7983,x7984,x7982))
% 28.78/28.54 [799]~E(x7991,x7992)+E(f472(x7991,x7993,x7994),f472(x7992,x7993,x7994))
% 28.78/28.54 [800]~E(x8001,x8002)+E(f472(x8003,x8001,x8004),f472(x8003,x8002,x8004))
% 28.78/28.54 [801]~E(x8011,x8012)+E(f472(x8013,x8014,x8011),f472(x8013,x8014,x8012))
% 28.78/28.54 [802]~E(x8021,x8022)+E(f723(x8021,x8023,x8024),f723(x8022,x8023,x8024))
% 28.78/28.54 [803]~E(x8031,x8032)+E(f723(x8033,x8031,x8034),f723(x8033,x8032,x8034))
% 28.78/28.54 [804]~E(x8041,x8042)+E(f723(x8043,x8044,x8041),f723(x8043,x8044,x8042))
% 28.78/28.54 [805]~E(x8051,x8052)+E(f121(x8051),f121(x8052))
% 28.78/28.54 [806]~E(x8061,x8062)+E(f367(x8061,x8063),f367(x8062,x8063))
% 28.78/28.54 [807]~E(x8071,x8072)+E(f367(x8073,x8071),f367(x8073,x8072))
% 28.78/28.54 [808]~E(x8081,x8082)+E(f770(x8081,x8083,x8084,x8085,x8086),f770(x8082,x8083,x8084,x8085,x8086))
% 28.78/28.54 [809]~E(x8091,x8092)+E(f770(x8093,x8091,x8094,x8095,x8096),f770(x8093,x8092,x8094,x8095,x8096))
% 28.78/28.54 [810]~E(x8101,x8102)+E(f770(x8103,x8104,x8101,x8105,x8106),f770(x8103,x8104,x8102,x8105,x8106))
% 28.78/28.54 [811]~E(x8111,x8112)+E(f770(x8113,x8114,x8115,x8111,x8116),f770(x8113,x8114,x8115,x8112,x8116))
% 28.78/28.54 [812]~E(x8121,x8122)+E(f770(x8123,x8124,x8125,x8126,x8121),f770(x8123,x8124,x8125,x8126,x8122))
% 28.78/28.54 [813]~E(x8131,x8132)+E(f664(x8131,x8133,x8134,x8135,x8136),f664(x8132,x8133,x8134,x8135,x8136))
% 28.78/28.54 [814]~E(x8141,x8142)+E(f664(x8143,x8141,x8144,x8145,x8146),f664(x8143,x8142,x8144,x8145,x8146))
% 28.78/28.54 [815]~E(x8151,x8152)+E(f664(x8153,x8154,x8151,x8155,x8156),f664(x8153,x8154,x8152,x8155,x8156))
% 28.78/28.54 [816]~E(x8161,x8162)+E(f664(x8163,x8164,x8165,x8161,x8166),f664(x8163,x8164,x8165,x8162,x8166))
% 28.78/28.54 [817]~E(x8171,x8172)+E(f664(x8173,x8174,x8175,x8176,x8171),f664(x8173,x8174,x8175,x8176,x8172))
% 28.78/28.54 [818]~E(x8181,x8182)+E(f594(x8181,x8183,x8184),f594(x8182,x8183,x8184))
% 28.78/28.54 [819]~E(x8191,x8192)+E(f594(x8193,x8191,x8194),f594(x8193,x8192,x8194))
% 28.78/28.54 [820]~E(x8201,x8202)+E(f594(x8203,x8204,x8201),f594(x8203,x8204,x8202))
% 28.78/28.54 [821]~E(x8211,x8212)+E(f775(x8211,x8213,x8214),f775(x8212,x8213,x8214))
% 28.78/28.54 [822]~E(x8221,x8222)+E(f775(x8223,x8221,x8224),f775(x8223,x8222,x8224))
% 28.78/28.54 [823]~E(x8231,x8232)+E(f775(x8233,x8234,x8231),f775(x8233,x8234,x8232))
% 28.78/28.54 [824]~E(x8241,x8242)+E(f514(x8241,x8243,x8244,x8245,x8246),f514(x8242,x8243,x8244,x8245,x8246))
% 28.78/28.54 [825]~E(x8251,x8252)+E(f514(x8253,x8251,x8254,x8255,x8256),f514(x8253,x8252,x8254,x8255,x8256))
% 28.78/28.54 [826]~E(x8261,x8262)+E(f514(x8263,x8264,x8261,x8265,x8266),f514(x8263,x8264,x8262,x8265,x8266))
% 28.78/28.54 [827]~E(x8271,x8272)+E(f514(x8273,x8274,x8275,x8271,x8276),f514(x8273,x8274,x8275,x8272,x8276))
% 28.78/28.54 [828]~E(x8281,x8282)+E(f514(x8283,x8284,x8285,x8286,x8281),f514(x8283,x8284,x8285,x8286,x8282))
% 28.78/28.54 [829]~E(x8291,x8292)+E(f466(x8291,x8293,x8294,x8295),f466(x8292,x8293,x8294,x8295))
% 28.78/28.54 [830]~E(x8301,x8302)+E(f466(x8303,x8301,x8304,x8305),f466(x8303,x8302,x8304,x8305))
% 28.78/28.54 [831]~E(x8311,x8312)+E(f466(x8313,x8314,x8311,x8315),f466(x8313,x8314,x8312,x8315))
% 28.78/28.54 [832]~E(x8321,x8322)+E(f466(x8323,x8324,x8325,x8321),f466(x8323,x8324,x8325,x8322))
% 28.78/28.54 [833]~E(x8331,x8332)+E(f406(x8331,x8333,x8334,x8335),f406(x8332,x8333,x8334,x8335))
% 28.78/28.54 [834]~E(x8341,x8342)+E(f406(x8343,x8341,x8344,x8345),f406(x8343,x8342,x8344,x8345))
% 28.78/28.54 [835]~E(x8351,x8352)+E(f406(x8353,x8354,x8351,x8355),f406(x8353,x8354,x8352,x8355))
% 28.78/28.54 [836]~E(x8361,x8362)+E(f406(x8363,x8364,x8365,x8361),f406(x8363,x8364,x8365,x8362))
% 28.78/28.54 [837]~E(x8371,x8372)+E(f692(x8371,x8373,x8374,x8375),f692(x8372,x8373,x8374,x8375))
% 28.78/28.54 [838]~E(x8381,x8382)+E(f692(x8383,x8381,x8384,x8385),f692(x8383,x8382,x8384,x8385))
% 28.78/28.54 [839]~E(x8391,x8392)+E(f692(x8393,x8394,x8391,x8395),f692(x8393,x8394,x8392,x8395))
% 28.78/28.54 [840]~E(x8401,x8402)+E(f692(x8403,x8404,x8405,x8401),f692(x8403,x8404,x8405,x8402))
% 28.78/28.54 [841]~E(x8411,x8412)+E(f511(x8411,x8413,x8414),f511(x8412,x8413,x8414))
% 28.78/28.54 [842]~E(x8421,x8422)+E(f511(x8423,x8421,x8424),f511(x8423,x8422,x8424))
% 28.78/28.54 [843]~E(x8431,x8432)+E(f511(x8433,x8434,x8431),f511(x8433,x8434,x8432))
% 28.78/28.54 [844]~E(x8441,x8442)+E(f622(x8441,x8443,x8444,x8445,x8446,x8447,x8448,x8449),f622(x8442,x8443,x8444,x8445,x8446,x8447,x8448,x8449))
% 28.78/28.54 [845]~E(x8451,x8452)+E(f622(x8453,x8451,x8454,x8455,x8456,x8457,x8458,x8459),f622(x8453,x8452,x8454,x8455,x8456,x8457,x8458,x8459))
% 28.78/28.54 [846]~E(x8461,x8462)+E(f622(x8463,x8464,x8461,x8465,x8466,x8467,x8468,x8469),f622(x8463,x8464,x8462,x8465,x8466,x8467,x8468,x8469))
% 28.78/28.54 [847]~E(x8471,x8472)+E(f622(x8473,x8474,x8475,x8471,x8476,x8477,x8478,x8479),f622(x8473,x8474,x8475,x8472,x8476,x8477,x8478,x8479))
% 28.78/28.54 [848]~E(x8481,x8482)+E(f622(x8483,x8484,x8485,x8486,x8481,x8487,x8488,x8489),f622(x8483,x8484,x8485,x8486,x8482,x8487,x8488,x8489))
% 28.78/28.54 [849]~E(x8491,x8492)+E(f622(x8493,x8494,x8495,x8496,x8497,x8491,x8498,x8499),f622(x8493,x8494,x8495,x8496,x8497,x8492,x8498,x8499))
% 28.78/28.54 [850]~E(x8501,x8502)+E(f622(x8503,x8504,x8505,x8506,x8507,x8508,x8501,x8509),f622(x8503,x8504,x8505,x8506,x8507,x8508,x8502,x8509))
% 28.78/28.54 [851]~E(x8511,x8512)+E(f622(x8513,x8514,x8515,x8516,x8517,x8518,x8519,x8511),f622(x8513,x8514,x8515,x8516,x8517,x8518,x8519,x8512))
% 28.78/28.54 [852]~E(x8521,x8522)+E(f910(x8521,x8523,x8524,x8525,x8526),f910(x8522,x8523,x8524,x8525,x8526))
% 28.78/28.54 [853]~E(x8531,x8532)+E(f910(x8533,x8531,x8534,x8535,x8536),f910(x8533,x8532,x8534,x8535,x8536))
% 28.78/28.54 [854]~E(x8541,x8542)+E(f910(x8543,x8544,x8541,x8545,x8546),f910(x8543,x8544,x8542,x8545,x8546))
% 28.78/28.54 [855]~E(x8551,x8552)+E(f910(x8553,x8554,x8555,x8551,x8556),f910(x8553,x8554,x8555,x8552,x8556))
% 28.78/28.54 [856]~E(x8561,x8562)+E(f910(x8563,x8564,x8565,x8566,x8561),f910(x8563,x8564,x8565,x8566,x8562))
% 28.78/28.54 [857]~E(x8571,x8572)+E(f616(x8571,x8573,x8574,x8575),f616(x8572,x8573,x8574,x8575))
% 28.78/28.54 [858]~E(x8581,x8582)+E(f616(x8583,x8581,x8584,x8585),f616(x8583,x8582,x8584,x8585))
% 28.78/28.54 [859]~E(x8591,x8592)+E(f616(x8593,x8594,x8591,x8595),f616(x8593,x8594,x8592,x8595))
% 28.78/28.54 [860]~E(x8601,x8602)+E(f616(x8603,x8604,x8605,x8601),f616(x8603,x8604,x8605,x8602))
% 28.78/28.54 [861]~E(x8611,x8612)+E(f815(x8611,x8613,x8614,x8615),f815(x8612,x8613,x8614,x8615))
% 28.78/28.54 [862]~E(x8621,x8622)+E(f815(x8623,x8621,x8624,x8625),f815(x8623,x8622,x8624,x8625))
% 28.78/28.54 [863]~E(x8631,x8632)+E(f815(x8633,x8634,x8631,x8635),f815(x8633,x8634,x8632,x8635))
% 28.78/28.54 [864]~E(x8641,x8642)+E(f815(x8643,x8644,x8645,x8641),f815(x8643,x8644,x8645,x8642))
% 28.78/28.54 [865]~E(x8651,x8652)+E(f879(x8651,x8653,x8654),f879(x8652,x8653,x8654))
% 28.78/28.54 [866]~E(x8661,x8662)+E(f879(x8663,x8661,x8664),f879(x8663,x8662,x8664))
% 28.78/28.54 [867]~E(x8671,x8672)+E(f879(x8673,x8674,x8671),f879(x8673,x8674,x8672))
% 28.78/28.54 [868]~E(x8681,x8682)+E(f448(x8681,x8683,x8684),f448(x8682,x8683,x8684))
% 28.78/28.54 [869]~E(x8691,x8692)+E(f448(x8693,x8691,x8694),f448(x8693,x8692,x8694))
% 28.78/28.54 [870]~E(x8701,x8702)+E(f448(x8703,x8704,x8701),f448(x8703,x8704,x8702))
% 28.78/28.54 [871]~E(x8711,x8712)+E(f771(x8711,x8713,x8714),f771(x8712,x8713,x8714))
% 28.78/28.54 [872]~E(x8721,x8722)+E(f771(x8723,x8721,x8724),f771(x8723,x8722,x8724))
% 28.78/28.54 [873]~E(x8731,x8732)+E(f771(x8733,x8734,x8731),f771(x8733,x8734,x8732))
% 28.78/28.54 [874]~E(x8741,x8742)+E(f364(x8741,x8743,x8744,x8745,x8746),f364(x8742,x8743,x8744,x8745,x8746))
% 28.78/28.54 [875]~E(x8751,x8752)+E(f364(x8753,x8751,x8754,x8755,x8756),f364(x8753,x8752,x8754,x8755,x8756))
% 28.78/28.54 [876]~E(x8761,x8762)+E(f364(x8763,x8764,x8761,x8765,x8766),f364(x8763,x8764,x8762,x8765,x8766))
% 28.78/28.54 [877]~E(x8771,x8772)+E(f364(x8773,x8774,x8775,x8771,x8776),f364(x8773,x8774,x8775,x8772,x8776))
% 28.78/28.54 [878]~E(x8781,x8782)+E(f364(x8783,x8784,x8785,x8786,x8781),f364(x8783,x8784,x8785,x8786,x8782))
% 28.78/28.54 [879]~E(x8791,x8792)+E(f56(x8791,x8793,x8794),f56(x8792,x8793,x8794))
% 28.78/28.54 [880]~E(x8801,x8802)+E(f56(x8803,x8801,x8804),f56(x8803,x8802,x8804))
% 28.78/28.54 [881]~E(x8811,x8812)+E(f56(x8813,x8814,x8811),f56(x8813,x8814,x8812))
% 28.78/28.54 [882]~E(x8821,x8822)+E(f636(x8821,x8823,x8824,x8825,x8826),f636(x8822,x8823,x8824,x8825,x8826))
% 28.78/28.54 [883]~E(x8831,x8832)+E(f636(x8833,x8831,x8834,x8835,x8836),f636(x8833,x8832,x8834,x8835,x8836))
% 28.78/28.54 [884]~E(x8841,x8842)+E(f636(x8843,x8844,x8841,x8845,x8846),f636(x8843,x8844,x8842,x8845,x8846))
% 28.78/28.54 [885]~E(x8851,x8852)+E(f636(x8853,x8854,x8855,x8851,x8856),f636(x8853,x8854,x8855,x8852,x8856))
% 28.78/28.54 [886]~E(x8861,x8862)+E(f636(x8863,x8864,x8865,x8866,x8861),f636(x8863,x8864,x8865,x8866,x8862))
% 28.78/28.54 [887]~E(x8871,x8872)+E(f909(x8871,x8873,x8874,x8875,x8876),f909(x8872,x8873,x8874,x8875,x8876))
% 28.78/28.54 [888]~E(x8881,x8882)+E(f909(x8883,x8881,x8884,x8885,x8886),f909(x8883,x8882,x8884,x8885,x8886))
% 28.78/28.54 [889]~E(x8891,x8892)+E(f909(x8893,x8894,x8891,x8895,x8896),f909(x8893,x8894,x8892,x8895,x8896))
% 28.78/28.54 [890]~E(x8901,x8902)+E(f909(x8903,x8904,x8905,x8901,x8906),f909(x8903,x8904,x8905,x8902,x8906))
% 28.78/28.54 [891]~E(x8911,x8912)+E(f909(x8913,x8914,x8915,x8916,x8911),f909(x8913,x8914,x8915,x8916,x8912))
% 28.78/28.54 [892]~E(x8921,x8922)+E(f118(x8921,x8923,x8924),f118(x8922,x8923,x8924))
% 28.78/28.54 [893]~E(x8931,x8932)+E(f118(x8933,x8931,x8934),f118(x8933,x8932,x8934))
% 28.78/28.54 [894]~E(x8941,x8942)+E(f118(x8943,x8944,x8941),f118(x8943,x8944,x8942))
% 28.78/28.54 [895]~E(x8951,x8952)+E(f705(x8951,x8953,x8954,x8955),f705(x8952,x8953,x8954,x8955))
% 28.78/28.54 [896]~E(x8961,x8962)+E(f705(x8963,x8961,x8964,x8965),f705(x8963,x8962,x8964,x8965))
% 28.78/28.54 [897]~E(x8971,x8972)+E(f705(x8973,x8974,x8971,x8975),f705(x8973,x8974,x8972,x8975))
% 28.78/28.54 [898]~E(x8981,x8982)+E(f705(x8983,x8984,x8985,x8981),f705(x8983,x8984,x8985,x8982))
% 28.78/28.54 [899]~E(x8991,x8992)+E(f251(x8991,x8993,x8994,x8995),f251(x8992,x8993,x8994,x8995))
% 28.78/28.54 [900]~E(x9001,x9002)+E(f251(x9003,x9001,x9004,x9005),f251(x9003,x9002,x9004,x9005))
% 28.78/28.54 [901]~E(x9011,x9012)+E(f251(x9013,x9014,x9011,x9015),f251(x9013,x9014,x9012,x9015))
% 28.78/28.54 [902]~E(x9021,x9022)+E(f251(x9023,x9024,x9025,x9021),f251(x9023,x9024,x9025,x9022))
% 28.78/28.54 [903]~E(x9031,x9032)+E(f686(x9031,x9033,x9034,x9035),f686(x9032,x9033,x9034,x9035))
% 28.78/28.54 [904]~E(x9041,x9042)+E(f686(x9043,x9041,x9044,x9045),f686(x9043,x9042,x9044,x9045))
% 28.78/28.54 [905]~E(x9051,x9052)+E(f686(x9053,x9054,x9051,x9055),f686(x9053,x9054,x9052,x9055))
% 28.78/28.54 [906]~E(x9061,x9062)+E(f686(x9063,x9064,x9065,x9061),f686(x9063,x9064,x9065,x9062))
% 28.78/28.54 [907]~E(x9071,x9072)+E(f570(x9071,x9073,x9074,x9075),f570(x9072,x9073,x9074,x9075))
% 28.78/28.54 [908]~E(x9081,x9082)+E(f570(x9083,x9081,x9084,x9085),f570(x9083,x9082,x9084,x9085))
% 28.78/28.54 [909]~E(x9091,x9092)+E(f570(x9093,x9094,x9091,x9095),f570(x9093,x9094,x9092,x9095))
% 28.78/28.54 [910]~E(x9101,x9102)+E(f570(x9103,x9104,x9105,x9101),f570(x9103,x9104,x9105,x9102))
% 28.78/28.54 [911]~E(x9111,x9112)+E(f19(x9111,x9113,x9114,x9115),f19(x9112,x9113,x9114,x9115))
% 28.78/28.54 [912]~E(x9121,x9122)+E(f19(x9123,x9121,x9124,x9125),f19(x9123,x9122,x9124,x9125))
% 28.78/28.54 [913]~E(x9131,x9132)+E(f19(x9133,x9134,x9131,x9135),f19(x9133,x9134,x9132,x9135))
% 28.78/28.54 [914]~E(x9141,x9142)+E(f19(x9143,x9144,x9145,x9141),f19(x9143,x9144,x9145,x9142))
% 28.78/28.54 [915]~E(x9151,x9152)+E(f606(x9151,x9153,x9154,x9155,x9156,x9157),f606(x9152,x9153,x9154,x9155,x9156,x9157))
% 28.78/28.54 [916]~E(x9161,x9162)+E(f606(x9163,x9161,x9164,x9165,x9166,x9167),f606(x9163,x9162,x9164,x9165,x9166,x9167))
% 28.78/28.54 [917]~E(x9171,x9172)+E(f606(x9173,x9174,x9171,x9175,x9176,x9177),f606(x9173,x9174,x9172,x9175,x9176,x9177))
% 28.78/28.54 [918]~E(x9181,x9182)+E(f606(x9183,x9184,x9185,x9181,x9186,x9187),f606(x9183,x9184,x9185,x9182,x9186,x9187))
% 28.78/28.54 [919]~E(x9191,x9192)+E(f606(x9193,x9194,x9195,x9196,x9191,x9197),f606(x9193,x9194,x9195,x9196,x9192,x9197))
% 28.78/28.54 [920]~E(x9201,x9202)+E(f606(x9203,x9204,x9205,x9206,x9207,x9201),f606(x9203,x9204,x9205,x9206,x9207,x9202))
% 28.78/28.54 [921]~E(x9211,x9212)+E(f184(x9211,x9213),f184(x9212,x9213))
% 28.78/28.54 [922]~E(x9221,x9222)+E(f184(x9223,x9221),f184(x9223,x9222))
% 28.78/28.54 [923]~E(x9231,x9232)+E(f805(x9231,x9233,x9234,x9235),f805(x9232,x9233,x9234,x9235))
% 28.78/28.54 [924]~E(x9241,x9242)+E(f805(x9243,x9241,x9244,x9245),f805(x9243,x9242,x9244,x9245))
% 28.78/28.54 [925]~E(x9251,x9252)+E(f805(x9253,x9254,x9251,x9255),f805(x9253,x9254,x9252,x9255))
% 28.78/28.54 [926]~E(x9261,x9262)+E(f805(x9263,x9264,x9265,x9261),f805(x9263,x9264,x9265,x9262))
% 28.78/28.54 [927]~E(x9271,x9272)+E(f113(x9271,x9273),f113(x9272,x9273))
% 28.78/28.54 [928]~E(x9281,x9282)+E(f113(x9283,x9281),f113(x9283,x9282))
% 28.78/28.54 [929]~E(x9291,x9292)+E(f520(x9291,x9293,x9294),f520(x9292,x9293,x9294))
% 28.78/28.54 [930]~E(x9301,x9302)+E(f520(x9303,x9301,x9304),f520(x9303,x9302,x9304))
% 28.78/28.54 [931]~E(x9311,x9312)+E(f520(x9313,x9314,x9311),f520(x9313,x9314,x9312))
% 28.78/28.54 [932]~E(x9321,x9322)+E(f714(x9321,x9323,x9324),f714(x9322,x9323,x9324))
% 28.78/28.54 [933]~E(x9331,x9332)+E(f714(x9333,x9331,x9334),f714(x9333,x9332,x9334))
% 28.78/28.54 [934]~E(x9341,x9342)+E(f714(x9343,x9344,x9341),f714(x9343,x9344,x9342))
% 28.78/28.54 [935]~E(x9351,x9352)+E(f207(x9351,x9353),f207(x9352,x9353))
% 28.78/28.54 [936]~E(x9361,x9362)+E(f207(x9363,x9361),f207(x9363,x9362))
% 28.78/28.54 [937]~E(x9371,x9372)+E(f204(x9371),f204(x9372))
% 28.78/28.54 [938]~E(x9381,x9382)+E(f849(x9381,x9383,x9384,x9385,x9386,x9387,x9388,x9389),f849(x9382,x9383,x9384,x9385,x9386,x9387,x9388,x9389))
% 28.78/28.54 [939]~E(x9391,x9392)+E(f849(x9393,x9391,x9394,x9395,x9396,x9397,x9398,x9399),f849(x9393,x9392,x9394,x9395,x9396,x9397,x9398,x9399))
% 28.78/28.54 [940]~E(x9401,x9402)+E(f849(x9403,x9404,x9401,x9405,x9406,x9407,x9408,x9409),f849(x9403,x9404,x9402,x9405,x9406,x9407,x9408,x9409))
% 28.78/28.54 [941]~E(x9411,x9412)+E(f849(x9413,x9414,x9415,x9411,x9416,x9417,x9418,x9419),f849(x9413,x9414,x9415,x9412,x9416,x9417,x9418,x9419))
% 28.78/28.54 [942]~E(x9421,x9422)+E(f849(x9423,x9424,x9425,x9426,x9421,x9427,x9428,x9429),f849(x9423,x9424,x9425,x9426,x9422,x9427,x9428,x9429))
% 28.78/28.54 [943]~E(x9431,x9432)+E(f849(x9433,x9434,x9435,x9436,x9437,x9431,x9438,x9439),f849(x9433,x9434,x9435,x9436,x9437,x9432,x9438,x9439))
% 28.78/28.54 [944]~E(x9441,x9442)+E(f849(x9443,x9444,x9445,x9446,x9447,x9448,x9441,x9449),f849(x9443,x9444,x9445,x9446,x9447,x9448,x9442,x9449))
% 28.78/28.54 [945]~E(x9451,x9452)+E(f849(x9453,x9454,x9455,x9456,x9457,x9458,x9459,x9451),f849(x9453,x9454,x9455,x9456,x9457,x9458,x9459,x9452))
% 28.78/28.54 [946]~E(x9461,x9462)+E(f731(x9461,x9463),f731(x9462,x9463))
% 28.78/28.54 [947]~E(x9471,x9472)+E(f731(x9473,x9471),f731(x9473,x9472))
% 28.78/28.54 [948]~E(x9481,x9482)+E(f108(x9481,x9483,x9484),f108(x9482,x9483,x9484))
% 28.78/28.54 [949]~E(x9491,x9492)+E(f108(x9493,x9491,x9494),f108(x9493,x9492,x9494))
% 28.78/28.54 [950]~E(x9501,x9502)+E(f108(x9503,x9504,x9501),f108(x9503,x9504,x9502))
% 28.78/28.54 [951]~E(x9511,x9512)+E(f631(x9511,x9513,x9514),f631(x9512,x9513,x9514))
% 28.78/28.54 [952]~E(x9521,x9522)+E(f631(x9523,x9521,x9524),f631(x9523,x9522,x9524))
% 28.78/28.54 [953]~E(x9531,x9532)+E(f631(x9533,x9534,x9531),f631(x9533,x9534,x9532))
% 28.78/28.54 [954]~E(x9541,x9542)+E(f247(x9541,x9543,x9544,x9545),f247(x9542,x9543,x9544,x9545))
% 28.78/28.54 [955]~E(x9551,x9552)+E(f247(x9553,x9551,x9554,x9555),f247(x9553,x9552,x9554,x9555))
% 28.78/28.54 [956]~E(x9561,x9562)+E(f247(x9563,x9564,x9561,x9565),f247(x9563,x9564,x9562,x9565))
% 28.78/28.54 [957]~E(x9571,x9572)+E(f247(x9573,x9574,x9575,x9571),f247(x9573,x9574,x9575,x9572))
% 28.78/28.54 [958]~E(x9581,x9582)+E(f37(x9581),f37(x9582))
% 28.78/28.54 [959]~E(x9591,x9592)+E(f178(x9591),f178(x9592))
% 28.78/28.54 [960]~E(x9601,x9602)+E(f855(x9601,x9603,x9604,x9605,x9606,x9607,x9608,x9609),f855(x9602,x9603,x9604,x9605,x9606,x9607,x9608,x9609))
% 28.78/28.54 [961]~E(x9611,x9612)+E(f855(x9613,x9611,x9614,x9615,x9616,x9617,x9618,x9619),f855(x9613,x9612,x9614,x9615,x9616,x9617,x9618,x9619))
% 28.78/28.54 [962]~E(x9621,x9622)+E(f855(x9623,x9624,x9621,x9625,x9626,x9627,x9628,x9629),f855(x9623,x9624,x9622,x9625,x9626,x9627,x9628,x9629))
% 28.78/28.54 [963]~E(x9631,x9632)+E(f855(x9633,x9634,x9635,x9631,x9636,x9637,x9638,x9639),f855(x9633,x9634,x9635,x9632,x9636,x9637,x9638,x9639))
% 28.78/28.54 [964]~E(x9641,x9642)+E(f855(x9643,x9644,x9645,x9646,x9641,x9647,x9648,x9649),f855(x9643,x9644,x9645,x9646,x9642,x9647,x9648,x9649))
% 28.78/28.54 [965]~E(x9651,x9652)+E(f855(x9653,x9654,x9655,x9656,x9657,x9651,x9658,x9659),f855(x9653,x9654,x9655,x9656,x9657,x9652,x9658,x9659))
% 28.78/28.54 [966]~E(x9661,x9662)+E(f855(x9663,x9664,x9665,x9666,x9667,x9668,x9661,x9669),f855(x9663,x9664,x9665,x9666,x9667,x9668,x9662,x9669))
% 28.78/28.54 [967]~E(x9671,x9672)+E(f855(x9673,x9674,x9675,x9676,x9677,x9678,x9679,x9671),f855(x9673,x9674,x9675,x9676,x9677,x9678,x9679,x9672))
% 28.78/28.54 [968]~E(x9681,x9682)+E(f120(x9681,x9683),f120(x9682,x9683))
% 28.78/28.54 [969]~E(x9691,x9692)+E(f120(x9693,x9691),f120(x9693,x9692))
% 28.78/28.54 [970]~E(x9701,x9702)+E(f626(x9701,x9703,x9704),f626(x9702,x9703,x9704))
% 28.78/28.54 [971]~E(x9711,x9712)+E(f626(x9713,x9711,x9714),f626(x9713,x9712,x9714))
% 28.78/28.54 [972]~E(x9721,x9722)+E(f626(x9723,x9724,x9721),f626(x9723,x9724,x9722))
% 28.78/28.54 [973]~E(x9731,x9732)+E(f155(x9731,x9733,x9734,x9735),f155(x9732,x9733,x9734,x9735))
% 28.78/28.54 [974]~E(x9741,x9742)+E(f155(x9743,x9741,x9744,x9745),f155(x9743,x9742,x9744,x9745))
% 28.78/28.54 [975]~E(x9751,x9752)+E(f155(x9753,x9754,x9751,x9755),f155(x9753,x9754,x9752,x9755))
% 28.78/28.54 [976]~E(x9761,x9762)+E(f155(x9763,x9764,x9765,x9761),f155(x9763,x9764,x9765,x9762))
% 28.78/28.54 [977]~E(x9771,x9772)+E(f535(x9771,x9773,x9774),f535(x9772,x9773,x9774))
% 28.78/28.54 [978]~E(x9781,x9782)+E(f535(x9783,x9781,x9784),f535(x9783,x9782,x9784))
% 28.78/28.54 [979]~E(x9791,x9792)+E(f535(x9793,x9794,x9791),f535(x9793,x9794,x9792))
% 28.78/28.54 [980]~E(x9801,x9802)+E(f821(x9801,x9803),f821(x9802,x9803))
% 28.78/28.54 [981]~E(x9811,x9812)+E(f821(x9813,x9811),f821(x9813,x9812))
% 28.78/28.54 [982]~E(x9821,x9822)+E(f377(x9821,x9823,x9824),f377(x9822,x9823,x9824))
% 28.78/28.54 [983]~E(x9831,x9832)+E(f377(x9833,x9831,x9834),f377(x9833,x9832,x9834))
% 28.78/28.54 [984]~E(x9841,x9842)+E(f377(x9843,x9844,x9841),f377(x9843,x9844,x9842))
% 28.78/28.54 [985]~E(x9851,x9852)+E(f598(x9851,x9853,x9854),f598(x9852,x9853,x9854))
% 28.78/28.54 [986]~E(x9861,x9862)+E(f598(x9863,x9861,x9864),f598(x9863,x9862,x9864))
% 28.78/28.54 [987]~E(x9871,x9872)+E(f598(x9873,x9874,x9871),f598(x9873,x9874,x9872))
% 28.78/28.54 [988]~E(x9881,x9882)+E(f413(x9881,x9883,x9884,x9885,x9886,x9887),f413(x9882,x9883,x9884,x9885,x9886,x9887))
% 28.78/28.54 [989]~E(x9891,x9892)+E(f413(x9893,x9891,x9894,x9895,x9896,x9897),f413(x9893,x9892,x9894,x9895,x9896,x9897))
% 28.78/28.54 [990]~E(x9901,x9902)+E(f413(x9903,x9904,x9901,x9905,x9906,x9907),f413(x9903,x9904,x9902,x9905,x9906,x9907))
% 28.78/28.54 [991]~E(x9911,x9912)+E(f413(x9913,x9914,x9915,x9911,x9916,x9917),f413(x9913,x9914,x9915,x9912,x9916,x9917))
% 28.78/28.54 [992]~E(x9921,x9922)+E(f413(x9923,x9924,x9925,x9926,x9921,x9927),f413(x9923,x9924,x9925,x9926,x9922,x9927))
% 28.78/28.54 [993]~E(x9931,x9932)+E(f413(x9933,x9934,x9935,x9936,x9937,x9931),f413(x9933,x9934,x9935,x9936,x9937,x9932))
% 28.78/28.54 [994]~E(x9941,x9942)+E(f608(x9941,x9943),f608(x9942,x9943))
% 28.78/28.54 [995]~E(x9951,x9952)+E(f608(x9953,x9951),f608(x9953,x9952))
% 28.78/28.54 [996]~E(x9961,x9962)+E(f501(x9961,x9963,x9964),f501(x9962,x9963,x9964))
% 28.78/28.54 [997]~E(x9971,x9972)+E(f501(x9973,x9971,x9974),f501(x9973,x9972,x9974))
% 28.78/28.54 [998]~E(x9981,x9982)+E(f501(x9983,x9984,x9981),f501(x9983,x9984,x9982))
% 28.78/28.54 [999]~E(x9991,x9992)+E(f806(x9991,x9993,x9994,x9995,x9996),f806(x9992,x9993,x9994,x9995,x9996))
% 28.78/28.54 [1000]~E(x10001,x10002)+E(f806(x10003,x10001,x10004,x10005,x10006),f806(x10003,x10002,x10004,x10005,x10006))
% 28.78/28.54 [1001]~E(x10011,x10012)+E(f806(x10013,x10014,x10011,x10015,x10016),f806(x10013,x10014,x10012,x10015,x10016))
% 28.78/28.54 [1002]~E(x10021,x10022)+E(f806(x10023,x10024,x10025,x10021,x10026),f806(x10023,x10024,x10025,x10022,x10026))
% 28.78/28.54 [1003]~E(x10031,x10032)+E(f806(x10033,x10034,x10035,x10036,x10031),f806(x10033,x10034,x10035,x10036,x10032))
% 28.78/28.54 [1004]~E(x10041,x10042)+E(f613(x10041,x10043,x10044),f613(x10042,x10043,x10044))
% 28.78/28.54 [1005]~E(x10051,x10052)+E(f613(x10053,x10051,x10054),f613(x10053,x10052,x10054))
% 28.78/28.54 [1006]~E(x10061,x10062)+E(f613(x10063,x10064,x10061),f613(x10063,x10064,x10062))
% 28.78/28.54 [1007]~E(x10071,x10072)+E(f862(x10071,x10073,x10074,x10075,x10076,x10077,x10078,x10079),f862(x10072,x10073,x10074,x10075,x10076,x10077,x10078,x10079))
% 28.78/28.54 [1008]~E(x10081,x10082)+E(f862(x10083,x10081,x10084,x10085,x10086,x10087,x10088,x10089),f862(x10083,x10082,x10084,x10085,x10086,x10087,x10088,x10089))
% 28.78/28.54 [1009]~E(x10091,x10092)+E(f862(x10093,x10094,x10091,x10095,x10096,x10097,x10098,x10099),f862(x10093,x10094,x10092,x10095,x10096,x10097,x10098,x10099))
% 28.78/28.54 [1010]~E(x10101,x10102)+E(f862(x10103,x10104,x10105,x10101,x10106,x10107,x10108,x10109),f862(x10103,x10104,x10105,x10102,x10106,x10107,x10108,x10109))
% 28.78/28.54 [1011]~E(x10111,x10112)+E(f862(x10113,x10114,x10115,x10116,x10111,x10117,x10118,x10119),f862(x10113,x10114,x10115,x10116,x10112,x10117,x10118,x10119))
% 28.78/28.54 [1012]~E(x10121,x10122)+E(f862(x10123,x10124,x10125,x10126,x10127,x10121,x10128,x10129),f862(x10123,x10124,x10125,x10126,x10127,x10122,x10128,x10129))
% 28.78/28.54 [1013]~E(x10131,x10132)+E(f862(x10133,x10134,x10135,x10136,x10137,x10138,x10131,x10139),f862(x10133,x10134,x10135,x10136,x10137,x10138,x10132,x10139))
% 28.78/28.54 [1014]~E(x10141,x10142)+E(f862(x10143,x10144,x10145,x10146,x10147,x10148,x10149,x10141),f862(x10143,x10144,x10145,x10146,x10147,x10148,x10149,x10142))
% 28.78/28.54 [1015]~E(x10151,x10152)+E(f521(x10151,x10153,x10154,x10155),f521(x10152,x10153,x10154,x10155))
% 28.78/28.54 [1016]~E(x10161,x10162)+E(f521(x10163,x10161,x10164,x10165),f521(x10163,x10162,x10164,x10165))
% 28.78/28.54 [1017]~E(x10171,x10172)+E(f521(x10173,x10174,x10171,x10175),f521(x10173,x10174,x10172,x10175))
% 28.78/28.54 [1018]~E(x10181,x10182)+E(f521(x10183,x10184,x10185,x10181),f521(x10183,x10184,x10185,x10182))
% 28.78/28.54 [1019]~E(x10191,x10192)+E(f853(x10191,x10193,x10194,x10195,x10196,x10197,x10198,x10199),f853(x10192,x10193,x10194,x10195,x10196,x10197,x10198,x10199))
% 28.78/28.54 [1020]~E(x10201,x10202)+E(f853(x10203,x10201,x10204,x10205,x10206,x10207,x10208,x10209),f853(x10203,x10202,x10204,x10205,x10206,x10207,x10208,x10209))
% 28.78/28.54 [1021]~E(x10211,x10212)+E(f853(x10213,x10214,x10211,x10215,x10216,x10217,x10218,x10219),f853(x10213,x10214,x10212,x10215,x10216,x10217,x10218,x10219))
% 28.78/28.54 [1022]~E(x10221,x10222)+E(f853(x10223,x10224,x10225,x10221,x10226,x10227,x10228,x10229),f853(x10223,x10224,x10225,x10222,x10226,x10227,x10228,x10229))
% 28.78/28.54 [1023]~E(x10231,x10232)+E(f853(x10233,x10234,x10235,x10236,x10231,x10237,x10238,x10239),f853(x10233,x10234,x10235,x10236,x10232,x10237,x10238,x10239))
% 28.78/28.54 [1024]~E(x10241,x10242)+E(f853(x10243,x10244,x10245,x10246,x10247,x10241,x10248,x10249),f853(x10243,x10244,x10245,x10246,x10247,x10242,x10248,x10249))
% 28.78/28.54 [1025]~E(x10251,x10252)+E(f853(x10253,x10254,x10255,x10256,x10257,x10258,x10251,x10259),f853(x10253,x10254,x10255,x10256,x10257,x10258,x10252,x10259))
% 28.78/28.54 [1026]~E(x10261,x10262)+E(f853(x10263,x10264,x10265,x10266,x10267,x10268,x10269,x10261),f853(x10263,x10264,x10265,x10266,x10267,x10268,x10269,x10262))
% 28.78/28.54 [1027]~E(x10271,x10272)+E(f803(x10271,x10273,x10274,x10275),f803(x10272,x10273,x10274,x10275))
% 28.78/28.54 [1028]~E(x10281,x10282)+E(f803(x10283,x10281,x10284,x10285),f803(x10283,x10282,x10284,x10285))
% 28.78/28.54 [1029]~E(x10291,x10292)+E(f803(x10293,x10294,x10291,x10295),f803(x10293,x10294,x10292,x10295))
% 28.78/28.54 [1030]~E(x10301,x10302)+E(f803(x10303,x10304,x10305,x10301),f803(x10303,x10304,x10305,x10302))
% 28.78/28.54 [1031]~E(x10311,x10312)+E(f791(x10311,x10313,x10314,x10315),f791(x10312,x10313,x10314,x10315))
% 28.78/28.54 [1032]~E(x10321,x10322)+E(f791(x10323,x10321,x10324,x10325),f791(x10323,x10322,x10324,x10325))
% 28.78/28.54 [1033]~E(x10331,x10332)+E(f791(x10333,x10334,x10331,x10335),f791(x10333,x10334,x10332,x10335))
% 28.78/28.54 [1034]~E(x10341,x10342)+E(f791(x10343,x10344,x10345,x10341),f791(x10343,x10344,x10345,x10342))
% 28.78/28.54 [1035]~E(x10351,x10352)+E(f260(x10351,x10353),f260(x10352,x10353))
% 28.78/28.54 [1036]~E(x10361,x10362)+E(f260(x10363,x10361),f260(x10363,x10362))
% 28.78/28.54 [1037]~E(x10371,x10372)+E(f148(x10371,x10373,x10374,x10375),f148(x10372,x10373,x10374,x10375))
% 28.78/28.54 [1038]~E(x10381,x10382)+E(f148(x10383,x10381,x10384,x10385),f148(x10383,x10382,x10384,x10385))
% 28.78/28.54 [1039]~E(x10391,x10392)+E(f148(x10393,x10394,x10391,x10395),f148(x10393,x10394,x10392,x10395))
% 28.78/28.54 [1040]~E(x10401,x10402)+E(f148(x10403,x10404,x10405,x10401),f148(x10403,x10404,x10405,x10402))
% 28.78/28.54 [1041]~E(x10411,x10412)+E(f688(x10411,x10413),f688(x10412,x10413))
% 28.78/28.54 [1042]~E(x10421,x10422)+E(f688(x10423,x10421),f688(x10423,x10422))
% 28.78/28.54 [1043]~E(x10431,x10432)+E(f379(x10431,x10433),f379(x10432,x10433))
% 28.78/28.54 [1044]~E(x10441,x10442)+E(f379(x10443,x10441),f379(x10443,x10442))
% 28.78/28.54 [1045]~E(x10451,x10452)+E(f262(x10451,x10453),f262(x10452,x10453))
% 28.78/28.54 [1046]~E(x10461,x10462)+E(f262(x10463,x10461),f262(x10463,x10462))
% 28.78/28.54 [1047]~E(x10471,x10472)+E(f583(x10471,x10473,x10474),f583(x10472,x10473,x10474))
% 28.78/28.54 [1048]~E(x10481,x10482)+E(f583(x10483,x10481,x10484),f583(x10483,x10482,x10484))
% 28.78/28.54 [1049]~E(x10491,x10492)+E(f583(x10493,x10494,x10491),f583(x10493,x10494,x10492))
% 28.78/28.54 [1050]~E(x10501,x10502)+E(f222(x10501,x10503,x10504),f222(x10502,x10503,x10504))
% 28.78/28.54 [1051]~E(x10511,x10512)+E(f222(x10513,x10511,x10514),f222(x10513,x10512,x10514))
% 28.78/28.54 [1052]~E(x10521,x10522)+E(f222(x10523,x10524,x10521),f222(x10523,x10524,x10522))
% 28.78/28.54 [1053]~E(x10531,x10532)+E(f188(x10531,x10533,x10534,x10535),f188(x10532,x10533,x10534,x10535))
% 28.78/28.54 [1054]~E(x10541,x10542)+E(f188(x10543,x10541,x10544,x10545),f188(x10543,x10542,x10544,x10545))
% 28.78/28.54 [1055]~E(x10551,x10552)+E(f188(x10553,x10554,x10551,x10555),f188(x10553,x10554,x10552,x10555))
% 28.78/28.54 [1056]~E(x10561,x10562)+E(f188(x10563,x10564,x10565,x10561),f188(x10563,x10564,x10565,x10562))
% 28.78/28.54 [1057]~E(x10571,x10572)+E(f70(x10571,x10573,x10574,x10575,x10576),f70(x10572,x10573,x10574,x10575,x10576))
% 28.78/28.54 [1058]~E(x10581,x10582)+E(f70(x10583,x10581,x10584,x10585,x10586),f70(x10583,x10582,x10584,x10585,x10586))
% 28.78/28.54 [1059]~E(x10591,x10592)+E(f70(x10593,x10594,x10591,x10595,x10596),f70(x10593,x10594,x10592,x10595,x10596))
% 28.78/28.54 [1060]~E(x10601,x10602)+E(f70(x10603,x10604,x10605,x10601,x10606),f70(x10603,x10604,x10605,x10602,x10606))
% 28.78/28.54 [1061]~E(x10611,x10612)+E(f70(x10613,x10614,x10615,x10616,x10611),f70(x10613,x10614,x10615,x10616,x10612))
% 28.78/28.54 [1062]~E(x10621,x10622)+E(f463(x10621,x10623,x10624,x10625),f463(x10622,x10623,x10624,x10625))
% 28.78/28.54 [1063]~E(x10631,x10632)+E(f463(x10633,x10631,x10634,x10635),f463(x10633,x10632,x10634,x10635))
% 28.78/28.54 [1064]~E(x10641,x10642)+E(f463(x10643,x10644,x10641,x10645),f463(x10643,x10644,x10642,x10645))
% 28.78/28.54 [1065]~E(x10651,x10652)+E(f463(x10653,x10654,x10655,x10651),f463(x10653,x10654,x10655,x10652))
% 28.78/28.54 [1066]~E(x10661,x10662)+E(f873(x10661,x10663,x10664),f873(x10662,x10663,x10664))
% 28.78/28.54 [1067]~E(x10671,x10672)+E(f873(x10673,x10671,x10674),f873(x10673,x10672,x10674))
% 28.78/28.54 [1068]~E(x10681,x10682)+E(f873(x10683,x10684,x10681),f873(x10683,x10684,x10682))
% 28.78/28.54 [1069]~E(x10691,x10692)+E(f625(x10691,x10693,x10694),f625(x10692,x10693,x10694))
% 28.78/28.54 [1070]~E(x10701,x10702)+E(f625(x10703,x10701,x10704),f625(x10703,x10702,x10704))
% 28.78/28.54 [1071]~E(x10711,x10712)+E(f625(x10713,x10714,x10711),f625(x10713,x10714,x10712))
% 28.78/28.54 [1072]~E(x10721,x10722)+E(f567(x10721,x10723,x10724,x10725),f567(x10722,x10723,x10724,x10725))
% 28.78/28.54 [1073]~E(x10731,x10732)+E(f567(x10733,x10731,x10734,x10735),f567(x10733,x10732,x10734,x10735))
% 28.78/28.54 [1074]~E(x10741,x10742)+E(f567(x10743,x10744,x10741,x10745),f567(x10743,x10744,x10742,x10745))
% 28.78/28.54 [1075]~E(x10751,x10752)+E(f567(x10753,x10754,x10755,x10751),f567(x10753,x10754,x10755,x10752))
% 28.78/28.54 [1076]~E(x10761,x10762)+E(f630(x10761,x10763,x10764),f630(x10762,x10763,x10764))
% 28.78/28.54 [1077]~E(x10771,x10772)+E(f630(x10773,x10771,x10774),f630(x10773,x10772,x10774))
% 28.78/28.54 [1078]~E(x10781,x10782)+E(f630(x10783,x10784,x10781),f630(x10783,x10784,x10782))
% 28.78/28.54 [1079]~E(x10791,x10792)+E(f799(x10791,x10793,x10794,x10795),f799(x10792,x10793,x10794,x10795))
% 28.78/28.54 [1080]~E(x10801,x10802)+E(f799(x10803,x10801,x10804,x10805),f799(x10803,x10802,x10804,x10805))
% 28.78/28.54 [1081]~E(x10811,x10812)+E(f799(x10813,x10814,x10811,x10815),f799(x10813,x10814,x10812,x10815))
% 28.78/28.54 [1082]~E(x10821,x10822)+E(f799(x10823,x10824,x10825,x10821),f799(x10823,x10824,x10825,x10822))
% 28.78/28.54 [1083]~E(x10831,x10832)+E(f750(x10831,x10833),f750(x10832,x10833))
% 28.78/28.54 [1084]~E(x10841,x10842)+E(f750(x10843,x10841),f750(x10843,x10842))
% 28.78/28.54 [1085]~E(x10851,x10852)+E(f398(x10851,x10853,x10854,x10855),f398(x10852,x10853,x10854,x10855))
% 28.78/28.54 [1086]~E(x10861,x10862)+E(f398(x10863,x10861,x10864,x10865),f398(x10863,x10862,x10864,x10865))
% 28.78/28.54 [1087]~E(x10871,x10872)+E(f398(x10873,x10874,x10871,x10875),f398(x10873,x10874,x10872,x10875))
% 28.78/28.54 [1088]~E(x10881,x10882)+E(f398(x10883,x10884,x10885,x10881),f398(x10883,x10884,x10885,x10882))
% 28.78/28.54 [1089]~E(x10891,x10892)+E(f147(x10891,x10893,x10894),f147(x10892,x10893,x10894))
% 28.78/28.54 [1090]~E(x10901,x10902)+E(f147(x10903,x10901,x10904),f147(x10903,x10902,x10904))
% 28.78/28.54 [1091]~E(x10911,x10912)+E(f147(x10913,x10914,x10911),f147(x10913,x10914,x10912))
% 28.78/28.54 [1092]~E(x10921,x10922)+E(f292(x10921,x10923,x10924,x10925,x10926),f292(x10922,x10923,x10924,x10925,x10926))
% 28.78/28.54 [1093]~E(x10931,x10932)+E(f292(x10933,x10931,x10934,x10935,x10936),f292(x10933,x10932,x10934,x10935,x10936))
% 28.78/28.54 [1094]~E(x10941,x10942)+E(f292(x10943,x10944,x10941,x10945,x10946),f292(x10943,x10944,x10942,x10945,x10946))
% 28.78/28.54 [1095]~E(x10951,x10952)+E(f292(x10953,x10954,x10955,x10951,x10956),f292(x10953,x10954,x10955,x10952,x10956))
% 28.78/28.54 [1096]~E(x10961,x10962)+E(f292(x10963,x10964,x10965,x10966,x10961),f292(x10963,x10964,x10965,x10966,x10962))
% 28.78/28.54 [1097]~E(x10971,x10972)+E(f177(x10971,x10973,x10974,x10975),f177(x10972,x10973,x10974,x10975))
% 28.78/28.54 [1098]~E(x10981,x10982)+E(f177(x10983,x10981,x10984,x10985),f177(x10983,x10982,x10984,x10985))
% 28.78/28.54 [1099]~E(x10991,x10992)+E(f177(x10993,x10994,x10991,x10995),f177(x10993,x10994,x10992,x10995))
% 28.78/28.54 [1100]~E(x11001,x11002)+E(f177(x11003,x11004,x11005,x11001),f177(x11003,x11004,x11005,x11002))
% 28.78/28.54 [1101]~E(x11011,x11012)+E(f342(x11011,x11013,x11014,x11015,x11016),f342(x11012,x11013,x11014,x11015,x11016))
% 28.78/28.54 [1102]~E(x11021,x11022)+E(f342(x11023,x11021,x11024,x11025,x11026),f342(x11023,x11022,x11024,x11025,x11026))
% 28.78/28.54 [1103]~E(x11031,x11032)+E(f342(x11033,x11034,x11031,x11035,x11036),f342(x11033,x11034,x11032,x11035,x11036))
% 28.78/28.54 [1104]~E(x11041,x11042)+E(f342(x11043,x11044,x11045,x11041,x11046),f342(x11043,x11044,x11045,x11042,x11046))
% 28.78/28.54 [1105]~E(x11051,x11052)+E(f342(x11053,x11054,x11055,x11056,x11051),f342(x11053,x11054,x11055,x11056,x11052))
% 28.78/28.54 [1106]~E(x11061,x11062)+E(f843(x11061,x11063,x11064),f843(x11062,x11063,x11064))
% 28.78/28.54 [1107]~E(x11071,x11072)+E(f843(x11073,x11071,x11074),f843(x11073,x11072,x11074))
% 28.78/28.54 [1108]~E(x11081,x11082)+E(f843(x11083,x11084,x11081),f843(x11083,x11084,x11082))
% 28.78/28.54 [1109]~E(x11091,x11092)+E(f438(x11091),f438(x11092))
% 28.78/28.54 [1110]~E(x11101,x11102)+E(f512(x11101,x11103,x11104),f512(x11102,x11103,x11104))
% 28.78/28.54 [1111]~E(x11111,x11112)+E(f512(x11113,x11111,x11114),f512(x11113,x11112,x11114))
% 28.78/28.54 [1112]~E(x11121,x11122)+E(f512(x11123,x11124,x11121),f512(x11123,x11124,x11122))
% 28.78/28.54 [1113]~E(x11131,x11132)+E(f611(x11131,x11133,x11134),f611(x11132,x11133,x11134))
% 28.78/28.54 [1114]~E(x11141,x11142)+E(f611(x11143,x11141,x11144),f611(x11143,x11142,x11144))
% 28.78/28.54 [1115]~E(x11151,x11152)+E(f611(x11153,x11154,x11151),f611(x11153,x11154,x11152))
% 28.78/28.54 [1116]~E(x11161,x11162)+E(f498(x11161,x11163,x11164),f498(x11162,x11163,x11164))
% 28.78/28.54 [1117]~E(x11171,x11172)+E(f498(x11173,x11171,x11174),f498(x11173,x11172,x11174))
% 28.78/28.54 [1118]~E(x11181,x11182)+E(f498(x11183,x11184,x11181),f498(x11183,x11184,x11182))
% 28.78/28.54 [1119]~E(x11191,x11192)+E(f730(x11191,x11193),f730(x11192,x11193))
% 28.78/28.54 [1120]~E(x11201,x11202)+E(f730(x11203,x11201),f730(x11203,x11202))
% 28.78/28.54 [1121]~E(x11211,x11212)+E(f767(x11211,x11213,x11214,x11215,x11216),f767(x11212,x11213,x11214,x11215,x11216))
% 28.78/28.54 [1122]~E(x11221,x11222)+E(f767(x11223,x11221,x11224,x11225,x11226),f767(x11223,x11222,x11224,x11225,x11226))
% 28.78/28.54 [1123]~E(x11231,x11232)+E(f767(x11233,x11234,x11231,x11235,x11236),f767(x11233,x11234,x11232,x11235,x11236))
% 28.78/28.54 [1124]~E(x11241,x11242)+E(f767(x11243,x11244,x11245,x11241,x11246),f767(x11243,x11244,x11245,x11242,x11246))
% 28.78/28.54 [1125]~E(x11251,x11252)+E(f767(x11253,x11254,x11255,x11256,x11251),f767(x11253,x11254,x11255,x11256,x11252))
% 28.78/28.54 [1126]~E(x11261,x11262)+E(f304(x11261,x11263),f304(x11262,x11263))
% 28.78/28.54 [1127]~E(x11271,x11272)+E(f304(x11273,x11271),f304(x11273,x11272))
% 28.78/28.54 [1128]~E(x11281,x11282)+E(f844(x11281,x11283,x11284),f844(x11282,x11283,x11284))
% 28.78/28.54 [1129]~E(x11291,x11292)+E(f844(x11293,x11291,x11294),f844(x11293,x11292,x11294))
% 28.78/28.54 [1130]~E(x11301,x11302)+E(f844(x11303,x11304,x11301),f844(x11303,x11304,x11302))
% 28.78/28.54 [1131]~E(x11311,x11312)+E(f410(x11311,x11313,x11314,x11315,x11316),f410(x11312,x11313,x11314,x11315,x11316))
% 28.78/28.54 [1132]~E(x11321,x11322)+E(f410(x11323,x11321,x11324,x11325,x11326),f410(x11323,x11322,x11324,x11325,x11326))
% 28.78/28.54 [1133]~E(x11331,x11332)+E(f410(x11333,x11334,x11331,x11335,x11336),f410(x11333,x11334,x11332,x11335,x11336))
% 28.78/28.54 [1134]~E(x11341,x11342)+E(f410(x11343,x11344,x11345,x11341,x11346),f410(x11343,x11344,x11345,x11342,x11346))
% 28.78/28.54 [1135]~E(x11351,x11352)+E(f410(x11353,x11354,x11355,x11356,x11351),f410(x11353,x11354,x11355,x11356,x11352))
% 28.78/28.54 [1136]~E(x11361,x11362)+E(f114(x11361,x11363,x11364,x11365),f114(x11362,x11363,x11364,x11365))
% 28.78/28.54 [1137]~E(x11371,x11372)+E(f114(x11373,x11371,x11374,x11375),f114(x11373,x11372,x11374,x11375))
% 28.78/28.54 [1138]~E(x11381,x11382)+E(f114(x11383,x11384,x11381,x11385),f114(x11383,x11384,x11382,x11385))
% 28.78/28.54 [1139]~E(x11391,x11392)+E(f114(x11393,x11394,x11395,x11391),f114(x11393,x11394,x11395,x11392))
% 28.78/28.54 [1140]~E(x11401,x11402)+E(f264(x11401,x11403),f264(x11402,x11403))
% 28.78/28.54 [1141]~E(x11411,x11412)+E(f264(x11413,x11411),f264(x11413,x11412))
% 28.78/28.54 [1142]~E(x11421,x11422)+E(f601(x11421,x11423,x11424,x11425),f601(x11422,x11423,x11424,x11425))
% 28.78/28.54 [1143]~E(x11431,x11432)+E(f601(x11433,x11431,x11434,x11435),f601(x11433,x11432,x11434,x11435))
% 28.78/28.54 [1144]~E(x11441,x11442)+E(f601(x11443,x11444,x11441,x11445),f601(x11443,x11444,x11442,x11445))
% 28.78/28.54 [1145]~E(x11451,x11452)+E(f601(x11453,x11454,x11455,x11451),f601(x11453,x11454,x11455,x11452))
% 28.78/28.54 [1146]~E(x11461,x11462)+E(f809(x11461,x11463,x11464,x11465,x11466,x11467,x11468),f809(x11462,x11463,x11464,x11465,x11466,x11467,x11468))
% 28.78/28.54 [1147]~E(x11471,x11472)+E(f809(x11473,x11471,x11474,x11475,x11476,x11477,x11478),f809(x11473,x11472,x11474,x11475,x11476,x11477,x11478))
% 28.78/28.54 [1148]~E(x11481,x11482)+E(f809(x11483,x11484,x11481,x11485,x11486,x11487,x11488),f809(x11483,x11484,x11482,x11485,x11486,x11487,x11488))
% 28.78/28.54 [1149]~E(x11491,x11492)+E(f809(x11493,x11494,x11495,x11491,x11496,x11497,x11498),f809(x11493,x11494,x11495,x11492,x11496,x11497,x11498))
% 28.78/28.54 [1150]~E(x11501,x11502)+E(f809(x11503,x11504,x11505,x11506,x11501,x11507,x11508),f809(x11503,x11504,x11505,x11506,x11502,x11507,x11508))
% 28.78/28.54 [1151]~E(x11511,x11512)+E(f809(x11513,x11514,x11515,x11516,x11517,x11511,x11518),f809(x11513,x11514,x11515,x11516,x11517,x11512,x11518))
% 28.78/28.54 [1152]~E(x11521,x11522)+E(f809(x11523,x11524,x11525,x11526,x11527,x11528,x11521),f809(x11523,x11524,x11525,x11526,x11527,x11528,x11522))
% 28.78/28.54 [1153]~E(x11531,x11532)+E(f603(x11531,x11533,x11534),f603(x11532,x11533,x11534))
% 28.78/28.54 [1154]~E(x11541,x11542)+E(f603(x11543,x11541,x11544),f603(x11543,x11542,x11544))
% 28.78/28.54 [1155]~E(x11551,x11552)+E(f603(x11553,x11554,x11551),f603(x11553,x11554,x11552))
% 28.78/28.54 [1156]~E(x11561,x11562)+E(f904(x11561,x11563,x11564),f904(x11562,x11563,x11564))
% 28.78/28.54 [1157]~E(x11571,x11572)+E(f904(x11573,x11571,x11574),f904(x11573,x11572,x11574))
% 28.78/28.54 [1158]~E(x11581,x11582)+E(f904(x11583,x11584,x11581),f904(x11583,x11584,x11582))
% 28.78/28.54 [1159]~E(x11591,x11592)+E(f358(x11591,x11593,x11594),f358(x11592,x11593,x11594))
% 28.78/28.54 [1160]~E(x11601,x11602)+E(f358(x11603,x11601,x11604),f358(x11603,x11602,x11604))
% 28.78/28.54 [1161]~E(x11611,x11612)+E(f358(x11613,x11614,x11611),f358(x11613,x11614,x11612))
% 28.78/28.54 [1162]~E(x11621,x11622)+E(f198(x11621,x11623,x11624,x11625),f198(x11622,x11623,x11624,x11625))
% 28.78/28.54 [1163]~E(x11631,x11632)+E(f198(x11633,x11631,x11634,x11635),f198(x11633,x11632,x11634,x11635))
% 28.78/28.54 [1164]~E(x11641,x11642)+E(f198(x11643,x11644,x11641,x11645),f198(x11643,x11644,x11642,x11645))
% 28.78/28.54 [1165]~E(x11651,x11652)+E(f198(x11653,x11654,x11655,x11651),f198(x11653,x11654,x11655,x11652))
% 28.78/28.54 [1166]~E(x11661,x11662)+E(f523(x11661,x11663,x11664),f523(x11662,x11663,x11664))
% 28.78/28.54 [1167]~E(x11671,x11672)+E(f523(x11673,x11671,x11674),f523(x11673,x11672,x11674))
% 28.78/28.54 [1168]~E(x11681,x11682)+E(f523(x11683,x11684,x11681),f523(x11683,x11684,x11682))
% 28.78/28.54 [1169]~E(x11691,x11692)+E(f265(x11691,x11693,x11694,x11695),f265(x11692,x11693,x11694,x11695))
% 28.78/28.54 [1170]~E(x11701,x11702)+E(f265(x11703,x11701,x11704,x11705),f265(x11703,x11702,x11704,x11705))
% 28.78/28.54 [1171]~E(x11711,x11712)+E(f265(x11713,x11714,x11711,x11715),f265(x11713,x11714,x11712,x11715))
% 28.78/28.54 [1172]~E(x11721,x11722)+E(f265(x11723,x11724,x11725,x11721),f265(x11723,x11724,x11725,x11722))
% 28.78/28.54 [1173]~E(x11731,x11732)+E(f858(x11731,x11733,x11734,x11735),f858(x11732,x11733,x11734,x11735))
% 28.78/28.54 [1174]~E(x11741,x11742)+E(f858(x11743,x11741,x11744,x11745),f858(x11743,x11742,x11744,x11745))
% 28.78/28.54 [1175]~E(x11751,x11752)+E(f858(x11753,x11754,x11751,x11755),f858(x11753,x11754,x11752,x11755))
% 28.78/28.54 [1176]~E(x11761,x11762)+E(f858(x11763,x11764,x11765,x11761),f858(x11763,x11764,x11765,x11762))
% 28.78/28.54 [1177]~E(x11771,x11772)+E(f135(x11771,x11773),f135(x11772,x11773))
% 28.78/28.54 [1178]~E(x11781,x11782)+E(f135(x11783,x11781),f135(x11783,x11782))
% 28.78/28.54 [1179]~E(x11791,x11792)+E(f780(x11791,x11793,x11794),f780(x11792,x11793,x11794))
% 28.78/28.54 [1180]~E(x11801,x11802)+E(f780(x11803,x11801,x11804),f780(x11803,x11802,x11804))
% 28.78/28.54 [1181]~E(x11811,x11812)+E(f780(x11813,x11814,x11811),f780(x11813,x11814,x11812))
% 28.78/28.54 [1182]~E(x11821,x11822)+E(f469(x11821,x11823,x11824),f469(x11822,x11823,x11824))
% 28.78/28.54 [1183]~E(x11831,x11832)+E(f469(x11833,x11831,x11834),f469(x11833,x11832,x11834))
% 28.78/28.54 [1184]~E(x11841,x11842)+E(f469(x11843,x11844,x11841),f469(x11843,x11844,x11842))
% 28.78/28.54 [1185]~E(x11851,x11852)+E(f919(x11851,x11853,x11854),f919(x11852,x11853,x11854))
% 28.78/28.54 [1186]~E(x11861,x11862)+E(f919(x11863,x11861,x11864),f919(x11863,x11862,x11864))
% 28.78/28.54 [1187]~E(x11871,x11872)+E(f919(x11873,x11874,x11871),f919(x11873,x11874,x11872))
% 28.78/28.54 [1188]~E(x11881,x11882)+E(f219(x11881,x11883),f219(x11882,x11883))
% 28.78/28.54 [1189]~E(x11891,x11892)+E(f219(x11893,x11891),f219(x11893,x11892))
% 28.78/28.54 [1190]~E(x11901,x11902)+E(f401(x11901,x11903,x11904,x11905),f401(x11902,x11903,x11904,x11905))
% 28.78/28.54 [1191]~E(x11911,x11912)+E(f401(x11913,x11911,x11914,x11915),f401(x11913,x11912,x11914,x11915))
% 28.78/28.54 [1192]~E(x11921,x11922)+E(f401(x11923,x11924,x11921,x11925),f401(x11923,x11924,x11922,x11925))
% 28.78/28.54 [1193]~E(x11931,x11932)+E(f401(x11933,x11934,x11935,x11931),f401(x11933,x11934,x11935,x11932))
% 28.78/28.54 [1194]~E(x11941,x11942)+E(f191(x11941,x11943),f191(x11942,x11943))
% 28.78/28.54 [1195]~E(x11951,x11952)+E(f191(x11953,x11951),f191(x11953,x11952))
% 28.78/28.54 [1196]~E(x11961,x11962)+E(f732(x11961,x11963,x11964),f732(x11962,x11963,x11964))
% 28.78/28.54 [1197]~E(x11971,x11972)+E(f732(x11973,x11971,x11974),f732(x11973,x11972,x11974))
% 28.78/28.54 [1198]~E(x11981,x11982)+E(f732(x11983,x11984,x11981),f732(x11983,x11984,x11982))
% 28.78/28.54 [1199]~E(x11991,x11992)+E(f617(x11991,x11993,x11994,x11995),f617(x11992,x11993,x11994,x11995))
% 28.78/28.54 [1200]~E(x12001,x12002)+E(f617(x12003,x12001,x12004,x12005),f617(x12003,x12002,x12004,x12005))
% 28.78/28.54 [1201]~E(x12011,x12012)+E(f617(x12013,x12014,x12011,x12015),f617(x12013,x12014,x12012,x12015))
% 28.78/28.54 [1202]~E(x12021,x12022)+E(f617(x12023,x12024,x12025,x12021),f617(x12023,x12024,x12025,x12022))
% 28.78/28.54 [1203]~E(x12031,x12032)+E(f727(x12031,x12033),f727(x12032,x12033))
% 28.78/28.54 [1204]~E(x12041,x12042)+E(f727(x12043,x12041),f727(x12043,x12042))
% 28.78/28.54 [1205]~E(x12051,x12052)+E(f132(x12051,x12053,x12054),f132(x12052,x12053,x12054))
% 28.78/28.54 [1206]~E(x12061,x12062)+E(f132(x12063,x12061,x12064),f132(x12063,x12062,x12064))
% 28.78/28.54 [1207]~E(x12071,x12072)+E(f132(x12073,x12074,x12071),f132(x12073,x12074,x12072))
% 28.78/28.54 [1208]~E(x12081,x12082)+E(f334(x12081,x12083,x12084),f334(x12082,x12083,x12084))
% 28.78/28.54 [1209]~E(x12091,x12092)+E(f334(x12093,x12091,x12094),f334(x12093,x12092,x12094))
% 28.78/28.54 [1210]~E(x12101,x12102)+E(f334(x12103,x12104,x12101),f334(x12103,x12104,x12102))
% 28.78/28.54 [1211]~E(x12111,x12112)+E(f223(x12111,x12113,x12114,x12115),f223(x12112,x12113,x12114,x12115))
% 28.78/28.54 [1212]~E(x12121,x12122)+E(f223(x12123,x12121,x12124,x12125),f223(x12123,x12122,x12124,x12125))
% 28.78/28.54 [1213]~E(x12131,x12132)+E(f223(x12133,x12134,x12131,x12135),f223(x12133,x12134,x12132,x12135))
% 28.78/28.54 [1214]~E(x12141,x12142)+E(f223(x12143,x12144,x12145,x12141),f223(x12143,x12144,x12145,x12142))
% 28.78/28.54 [1215]~E(x12151,x12152)+E(f119(x12151,x12153,x12154,x12155,x12156),f119(x12152,x12153,x12154,x12155,x12156))
% 28.78/28.54 [1216]~E(x12161,x12162)+E(f119(x12163,x12161,x12164,x12165,x12166),f119(x12163,x12162,x12164,x12165,x12166))
% 28.78/28.54 [1217]~E(x12171,x12172)+E(f119(x12173,x12174,x12171,x12175,x12176),f119(x12173,x12174,x12172,x12175,x12176))
% 28.78/28.54 [1218]~E(x12181,x12182)+E(f119(x12183,x12184,x12185,x12181,x12186),f119(x12183,x12184,x12185,x12182,x12186))
% 28.78/28.54 [1219]~E(x12191,x12192)+E(f119(x12193,x12194,x12195,x12196,x12191),f119(x12193,x12194,x12195,x12196,x12192))
% 28.78/28.54 [1220]~E(x12201,x12202)+E(f906(x12201,x12203,x12204,x12205,x12206),f906(x12202,x12203,x12204,x12205,x12206))
% 28.78/28.54 [1221]~E(x12211,x12212)+E(f906(x12213,x12211,x12214,x12215,x12216),f906(x12213,x12212,x12214,x12215,x12216))
% 28.78/28.54 [1222]~E(x12221,x12222)+E(f906(x12223,x12224,x12221,x12225,x12226),f906(x12223,x12224,x12222,x12225,x12226))
% 28.78/28.54 [1223]~E(x12231,x12232)+E(f906(x12233,x12234,x12235,x12231,x12236),f906(x12233,x12234,x12235,x12232,x12236))
% 28.78/28.54 [1224]~E(x12241,x12242)+E(f906(x12243,x12244,x12245,x12246,x12241),f906(x12243,x12244,x12245,x12246,x12242))
% 28.78/28.54 [1225]~E(x12251,x12252)+E(f557(x12251,x12253,x12254,x12255,x12256),f557(x12252,x12253,x12254,x12255,x12256))
% 28.78/28.54 [1226]~E(x12261,x12262)+E(f557(x12263,x12261,x12264,x12265,x12266),f557(x12263,x12262,x12264,x12265,x12266))
% 28.78/28.54 [1227]~E(x12271,x12272)+E(f557(x12273,x12274,x12271,x12275,x12276),f557(x12273,x12274,x12272,x12275,x12276))
% 28.78/28.54 [1228]~E(x12281,x12282)+E(f557(x12283,x12284,x12285,x12281,x12286),f557(x12283,x12284,x12285,x12282,x12286))
% 28.78/28.54 [1229]~E(x12291,x12292)+E(f557(x12293,x12294,x12295,x12296,x12291),f557(x12293,x12294,x12295,x12296,x12292))
% 28.78/28.54 [1230]~E(x12301,x12302)+E(f349(x12301,x12303,x12304,x12305,x12306),f349(x12302,x12303,x12304,x12305,x12306))
% 28.78/28.54 [1231]~E(x12311,x12312)+E(f349(x12313,x12311,x12314,x12315,x12316),f349(x12313,x12312,x12314,x12315,x12316))
% 28.78/28.54 [1232]~E(x12321,x12322)+E(f349(x12323,x12324,x12321,x12325,x12326),f349(x12323,x12324,x12322,x12325,x12326))
% 28.78/28.54 [1233]~E(x12331,x12332)+E(f349(x12333,x12334,x12335,x12331,x12336),f349(x12333,x12334,x12335,x12332,x12336))
% 28.78/28.54 [1234]~E(x12341,x12342)+E(f349(x12343,x12344,x12345,x12346,x12341),f349(x12343,x12344,x12345,x12346,x12342))
% 28.78/28.54 [1235]~E(x12351,x12352)+E(f669(x12351,x12353,x12354,x12355),f669(x12352,x12353,x12354,x12355))
% 28.78/28.54 [1236]~E(x12361,x12362)+E(f669(x12363,x12361,x12364,x12365),f669(x12363,x12362,x12364,x12365))
% 28.78/28.54 [1237]~E(x12371,x12372)+E(f669(x12373,x12374,x12371,x12375),f669(x12373,x12374,x12372,x12375))
% 28.78/28.54 [1238]~E(x12381,x12382)+E(f669(x12383,x12384,x12385,x12381),f669(x12383,x12384,x12385,x12382))
% 28.78/28.54 [1239]~E(x12391,x12392)+E(f245(x12391,x12393,x12394,x12395,x12396),f245(x12392,x12393,x12394,x12395,x12396))
% 28.78/28.54 [1240]~E(x12401,x12402)+E(f245(x12403,x12401,x12404,x12405,x12406),f245(x12403,x12402,x12404,x12405,x12406))
% 28.78/28.54 [1241]~E(x12411,x12412)+E(f245(x12413,x12414,x12411,x12415,x12416),f245(x12413,x12414,x12412,x12415,x12416))
% 28.78/28.54 [1242]~E(x12421,x12422)+E(f245(x12423,x12424,x12425,x12421,x12426),f245(x12423,x12424,x12425,x12422,x12426))
% 28.78/28.54 [1243]~E(x12431,x12432)+E(f245(x12433,x12434,x12435,x12436,x12431),f245(x12433,x12434,x12435,x12436,x12432))
% 28.78/28.54 [1244]~E(x12441,x12442)+E(f189(x12441,x12443,x12444,x12445),f189(x12442,x12443,x12444,x12445))
% 28.78/28.54 [1245]~E(x12451,x12452)+E(f189(x12453,x12451,x12454,x12455),f189(x12453,x12452,x12454,x12455))
% 28.78/28.54 [1246]~E(x12461,x12462)+E(f189(x12463,x12464,x12461,x12465),f189(x12463,x12464,x12462,x12465))
% 28.78/28.54 [1247]~E(x12471,x12472)+E(f189(x12473,x12474,x12475,x12471),f189(x12473,x12474,x12475,x12472))
% 28.78/28.54 [1248]~E(x12481,x12482)+E(f817(x12481,x12483,x12484,x12485),f817(x12482,x12483,x12484,x12485))
% 28.78/28.54 [1249]~E(x12491,x12492)+E(f817(x12493,x12491,x12494,x12495),f817(x12493,x12492,x12494,x12495))
% 28.78/28.54 [1250]~E(x12501,x12502)+E(f817(x12503,x12504,x12501,x12505),f817(x12503,x12504,x12502,x12505))
% 28.78/28.54 [1251]~E(x12511,x12512)+E(f817(x12513,x12514,x12515,x12511),f817(x12513,x12514,x12515,x12512))
% 28.78/28.54 [1252]~E(x12521,x12522)+E(f850(x12521,x12523,x12524,x12525,x12526,x12527,x12528),f850(x12522,x12523,x12524,x12525,x12526,x12527,x12528))
% 28.78/28.54 [1253]~E(x12531,x12532)+E(f850(x12533,x12531,x12534,x12535,x12536,x12537,x12538),f850(x12533,x12532,x12534,x12535,x12536,x12537,x12538))
% 28.78/28.54 [1254]~E(x12541,x12542)+E(f850(x12543,x12544,x12541,x12545,x12546,x12547,x12548),f850(x12543,x12544,x12542,x12545,x12546,x12547,x12548))
% 28.78/28.54 [1255]~E(x12551,x12552)+E(f850(x12553,x12554,x12555,x12551,x12556,x12557,x12558),f850(x12553,x12554,x12555,x12552,x12556,x12557,x12558))
% 28.78/28.54 [1256]~E(x12561,x12562)+E(f850(x12563,x12564,x12565,x12566,x12561,x12567,x12568),f850(x12563,x12564,x12565,x12566,x12562,x12567,x12568))
% 28.78/28.54 [1257]~E(x12571,x12572)+E(f850(x12573,x12574,x12575,x12576,x12577,x12571,x12578),f850(x12573,x12574,x12575,x12576,x12577,x12572,x12578))
% 28.78/28.54 [1258]~E(x12581,x12582)+E(f850(x12583,x12584,x12585,x12586,x12587,x12588,x12581),f850(x12583,x12584,x12585,x12586,x12587,x12588,x12582))
% 28.78/28.54 [1259]~E(x12591,x12592)+E(f829(x12591,x12593,x12594,x12595,x12596,x12597),f829(x12592,x12593,x12594,x12595,x12596,x12597))
% 28.78/28.54 [1260]~E(x12601,x12602)+E(f829(x12603,x12601,x12604,x12605,x12606,x12607),f829(x12603,x12602,x12604,x12605,x12606,x12607))
% 28.78/28.54 [1261]~E(x12611,x12612)+E(f829(x12613,x12614,x12611,x12615,x12616,x12617),f829(x12613,x12614,x12612,x12615,x12616,x12617))
% 28.78/28.54 [1262]~E(x12621,x12622)+E(f829(x12623,x12624,x12625,x12621,x12626,x12627),f829(x12623,x12624,x12625,x12622,x12626,x12627))
% 28.78/28.54 [1263]~E(x12631,x12632)+E(f829(x12633,x12634,x12635,x12636,x12631,x12637),f829(x12633,x12634,x12635,x12636,x12632,x12637))
% 28.78/28.54 [1264]~E(x12641,x12642)+E(f829(x12643,x12644,x12645,x12646,x12647,x12641),f829(x12643,x12644,x12645,x12646,x12647,x12642))
% 28.78/28.54 [1265]~E(x12651,x12652)+E(f340(x12651,x12653,x12654,x12655),f340(x12652,x12653,x12654,x12655))
% 28.78/28.54 [1266]~E(x12661,x12662)+E(f340(x12663,x12661,x12664,x12665),f340(x12663,x12662,x12664,x12665))
% 28.78/28.54 [1267]~E(x12671,x12672)+E(f340(x12673,x12674,x12671,x12675),f340(x12673,x12674,x12672,x12675))
% 28.78/28.54 [1268]~E(x12681,x12682)+E(f340(x12683,x12684,x12685,x12681),f340(x12683,x12684,x12685,x12682))
% 28.78/28.54 [1269]~E(x12691,x12692)+E(f272(x12691,x12693,x12694,x12695),f272(x12692,x12693,x12694,x12695))
% 28.78/28.54 [1270]~E(x12701,x12702)+E(f272(x12703,x12701,x12704,x12705),f272(x12703,x12702,x12704,x12705))
% 28.78/28.54 [1271]~E(x12711,x12712)+E(f272(x12713,x12714,x12711,x12715),f272(x12713,x12714,x12712,x12715))
% 28.78/28.54 [1272]~E(x12721,x12722)+E(f272(x12723,x12724,x12725,x12721),f272(x12723,x12724,x12725,x12722))
% 28.78/28.54 [1273]~E(x12731,x12732)+E(f122(x12731,x12733,x12734,x12735),f122(x12732,x12733,x12734,x12735))
% 28.78/28.54 [1274]~E(x12741,x12742)+E(f122(x12743,x12741,x12744,x12745),f122(x12743,x12742,x12744,x12745))
% 28.78/28.54 [1275]~E(x12751,x12752)+E(f122(x12753,x12754,x12751,x12755),f122(x12753,x12754,x12752,x12755))
% 28.78/28.54 [1276]~E(x12761,x12762)+E(f122(x12763,x12764,x12765,x12761),f122(x12763,x12764,x12765,x12762))
% 28.78/28.54 [1277]~E(x12771,x12772)+E(f353(x12771,x12773,x12774,x12775,x12776),f353(x12772,x12773,x12774,x12775,x12776))
% 28.78/28.54 [1278]~E(x12781,x12782)+E(f353(x12783,x12781,x12784,x12785,x12786),f353(x12783,x12782,x12784,x12785,x12786))
% 28.78/28.54 [1279]~E(x12791,x12792)+E(f353(x12793,x12794,x12791,x12795,x12796),f353(x12793,x12794,x12792,x12795,x12796))
% 28.78/28.54 [1280]~E(x12801,x12802)+E(f353(x12803,x12804,x12805,x12801,x12806),f353(x12803,x12804,x12805,x12802,x12806))
% 28.78/28.54 [1281]~E(x12811,x12812)+E(f353(x12813,x12814,x12815,x12816,x12811),f353(x12813,x12814,x12815,x12816,x12812))
% 28.78/28.54 [1282]~E(x12821,x12822)+E(f210(x12821,x12823),f210(x12822,x12823))
% 28.78/28.54 [1283]~E(x12831,x12832)+E(f210(x12833,x12831),f210(x12833,x12832))
% 28.78/28.54 [1284]~E(x12841,x12842)+E(f101(x12841),f101(x12842))
% 28.78/28.54 [1285]~E(x12851,x12852)+E(f883(x12851,x12853,x12854),f883(x12852,x12853,x12854))
% 28.78/28.54 [1286]~E(x12861,x12862)+E(f883(x12863,x12861,x12864),f883(x12863,x12862,x12864))
% 28.78/28.54 [1287]~E(x12871,x12872)+E(f883(x12873,x12874,x12871),f883(x12873,x12874,x12872))
% 28.78/28.54 [1288]~E(x12881,x12882)+E(f741(x12881,x12883,x12884,x12885,x12886),f741(x12882,x12883,x12884,x12885,x12886))
% 28.78/28.54 [1289]~E(x12891,x12892)+E(f741(x12893,x12891,x12894,x12895,x12896),f741(x12893,x12892,x12894,x12895,x12896))
% 28.78/28.54 [1290]~E(x12901,x12902)+E(f741(x12903,x12904,x12901,x12905,x12906),f741(x12903,x12904,x12902,x12905,x12906))
% 28.78/28.54 [1291]~E(x12911,x12912)+E(f741(x12913,x12914,x12915,x12911,x12916),f741(x12913,x12914,x12915,x12912,x12916))
% 28.78/28.54 [1292]~E(x12921,x12922)+E(f741(x12923,x12924,x12925,x12926,x12921),f741(x12923,x12924,x12925,x12926,x12922))
% 28.78/28.54 [1293]~E(x12931,x12932)+E(f519(x12931,x12933,x12934),f519(x12932,x12933,x12934))
% 28.78/28.54 [1294]~E(x12941,x12942)+E(f519(x12943,x12941,x12944),f519(x12943,x12942,x12944))
% 28.78/28.54 [1295]~E(x12951,x12952)+E(f519(x12953,x12954,x12951),f519(x12953,x12954,x12952))
% 28.78/28.54 [1296]~E(x12961,x12962)+E(f338(x12961,x12963,x12964),f338(x12962,x12963,x12964))
% 28.78/28.54 [1297]~E(x12971,x12972)+E(f338(x12973,x12971,x12974),f338(x12973,x12972,x12974))
% 28.78/28.54 [1298]~E(x12981,x12982)+E(f338(x12983,x12984,x12981),f338(x12983,x12984,x12982))
% 28.78/28.54 [1299]~E(x12991,x12992)+E(f273(x12991),f273(x12992))
% 28.78/28.54 [1300]~E(x13001,x13002)+E(f258(x13001,x13003),f258(x13002,x13003))
% 28.78/28.54 [1301]~E(x13011,x13012)+E(f258(x13013,x13011),f258(x13013,x13012))
% 28.78/28.54 [1302]~E(x13021,x13022)+E(f691(x13021,x13023,x13024,x13025,x13026),f691(x13022,x13023,x13024,x13025,x13026))
% 28.78/28.54 [1303]~E(x13031,x13032)+E(f691(x13033,x13031,x13034,x13035,x13036),f691(x13033,x13032,x13034,x13035,x13036))
% 28.78/28.54 [1304]~E(x13041,x13042)+E(f691(x13043,x13044,x13041,x13045,x13046),f691(x13043,x13044,x13042,x13045,x13046))
% 28.78/28.54 [1305]~E(x13051,x13052)+E(f691(x13053,x13054,x13055,x13051,x13056),f691(x13053,x13054,x13055,x13052,x13056))
% 28.78/28.54 [1306]~E(x13061,x13062)+E(f691(x13063,x13064,x13065,x13066,x13061),f691(x13063,x13064,x13065,x13066,x13062))
% 28.78/28.54 [1307]~E(x13071,x13072)+E(f680(x13071,x13073,x13074,x13075),f680(x13072,x13073,x13074,x13075))
% 28.78/28.54 [1308]~E(x13081,x13082)+E(f680(x13083,x13081,x13084,x13085),f680(x13083,x13082,x13084,x13085))
% 28.78/28.54 [1309]~E(x13091,x13092)+E(f680(x13093,x13094,x13091,x13095),f680(x13093,x13094,x13092,x13095))
% 28.78/28.54 [1310]~E(x13101,x13102)+E(f680(x13103,x13104,x13105,x13101),f680(x13103,x13104,x13105,x13102))
% 28.78/28.54 [1311]~E(x13111,x13112)+E(f402(x13111,x13113,x13114,x13115,x13116),f402(x13112,x13113,x13114,x13115,x13116))
% 28.78/28.54 [1312]~E(x13121,x13122)+E(f402(x13123,x13121,x13124,x13125,x13126),f402(x13123,x13122,x13124,x13125,x13126))
% 28.78/28.54 [1313]~E(x13131,x13132)+E(f402(x13133,x13134,x13131,x13135,x13136),f402(x13133,x13134,x13132,x13135,x13136))
% 28.78/28.54 [1314]~E(x13141,x13142)+E(f402(x13143,x13144,x13145,x13141,x13146),f402(x13143,x13144,x13145,x13142,x13146))
% 28.78/28.54 [1315]~E(x13151,x13152)+E(f402(x13153,x13154,x13155,x13156,x13151),f402(x13153,x13154,x13155,x13156,x13152))
% 28.78/28.54 [1316]~E(x13161,x13162)+E(f847(x13161,x13163,x13164,x13165),f847(x13162,x13163,x13164,x13165))
% 28.78/28.54 [1317]~E(x13171,x13172)+E(f847(x13173,x13171,x13174,x13175),f847(x13173,x13172,x13174,x13175))
% 28.78/28.54 [1318]~E(x13181,x13182)+E(f847(x13183,x13184,x13181,x13185),f847(x13183,x13184,x13182,x13185))
% 28.78/28.54 [1319]~E(x13191,x13192)+E(f847(x13193,x13194,x13195,x13191),f847(x13193,x13194,x13195,x13192))
% 28.78/28.54 [1320]~E(x13201,x13202)+E(f796(x13201,x13203,x13204),f796(x13202,x13203,x13204))
% 28.78/28.54 [1321]~E(x13211,x13212)+E(f796(x13213,x13211,x13214),f796(x13213,x13212,x13214))
% 28.78/28.54 [1322]~E(x13221,x13222)+E(f796(x13223,x13224,x13221),f796(x13223,x13224,x13222))
% 28.78/28.54 [1323]~E(x13231,x13232)+E(f633(x13231,x13233),f633(x13232,x13233))
% 28.78/28.54 [1324]~E(x13241,x13242)+E(f633(x13243,x13241),f633(x13243,x13242))
% 28.78/28.54 [1325]~E(x13251,x13252)+E(f610(x13251,x13253,x13254),f610(x13252,x13253,x13254))
% 28.78/28.54 [1326]~E(x13261,x13262)+E(f610(x13263,x13261,x13264),f610(x13263,x13262,x13264))
% 28.78/28.54 [1327]~E(x13271,x13272)+E(f610(x13273,x13274,x13271),f610(x13273,x13274,x13272))
% 28.78/28.54 [1328]~E(x13281,x13282)+E(f717(x13281,x13283),f717(x13282,x13283))
% 28.78/28.54 [1329]~E(x13291,x13292)+E(f717(x13293,x13291),f717(x13293,x13292))
% 28.78/28.54 [1330]~E(x13301,x13302)+E(f681(x13301,x13303,x13304,x13305),f681(x13302,x13303,x13304,x13305))
% 28.78/28.54 [1331]~E(x13311,x13312)+E(f681(x13313,x13311,x13314,x13315),f681(x13313,x13312,x13314,x13315))
% 28.78/28.54 [1332]~E(x13321,x13322)+E(f681(x13323,x13324,x13321,x13325),f681(x13323,x13324,x13322,x13325))
% 28.78/28.54 [1333]~E(x13331,x13332)+E(f681(x13333,x13334,x13335,x13331),f681(x13333,x13334,x13335,x13332))
% 28.78/28.54 [1334]~E(x13341,x13342)+E(f515(x13341,x13343),f515(x13342,x13343))
% 28.78/28.54 [1335]~E(x13351,x13352)+E(f515(x13353,x13351),f515(x13353,x13352))
% 28.78/28.54 [1336]~E(x13361,x13362)+E(f698(x13361,x13363,x13364),f698(x13362,x13363,x13364))
% 28.78/28.54 [1337]~E(x13371,x13372)+E(f698(x13373,x13371,x13374),f698(x13373,x13372,x13374))
% 28.78/28.54 [1338]~E(x13381,x13382)+E(f698(x13383,x13384,x13381),f698(x13383,x13384,x13382))
% 28.78/28.54 [1339]~E(x13391,x13392)+E(f516(x13391),f516(x13392))
% 28.78/28.54 [1340]~E(x13401,x13402)+E(f645(x13401,x13403,x13404,x13405,x13406),f645(x13402,x13403,x13404,x13405,x13406))
% 28.78/28.54 [1341]~E(x13411,x13412)+E(f645(x13413,x13411,x13414,x13415,x13416),f645(x13413,x13412,x13414,x13415,x13416))
% 28.78/28.54 [1342]~E(x13421,x13422)+E(f645(x13423,x13424,x13421,x13425,x13426),f645(x13423,x13424,x13422,x13425,x13426))
% 28.78/28.54 [1343]~E(x13431,x13432)+E(f645(x13433,x13434,x13435,x13431,x13436),f645(x13433,x13434,x13435,x13432,x13436))
% 28.78/28.54 [1344]~E(x13441,x13442)+E(f645(x13443,x13444,x13445,x13446,x13441),f645(x13443,x13444,x13445,x13446,x13442))
% 28.78/28.54 [1345]~E(x13451,x13452)+E(f890(x13451,x13453,x13454,x13455),f890(x13452,x13453,x13454,x13455))
% 28.78/28.54 [1346]~E(x13461,x13462)+E(f890(x13463,x13461,x13464,x13465),f890(x13463,x13462,x13464,x13465))
% 28.78/28.54 [1347]~E(x13471,x13472)+E(f890(x13473,x13474,x13471,x13475),f890(x13473,x13474,x13472,x13475))
% 28.78/28.54 [1348]~E(x13481,x13482)+E(f890(x13483,x13484,x13485,x13481),f890(x13483,x13484,x13485,x13482))
% 28.78/28.54 [1349]~E(x13491,x13492)+E(f470(x13491,x13493,x13494),f470(x13492,x13493,x13494))
% 28.78/28.54 [1350]~E(x13501,x13502)+E(f470(x13503,x13501,x13504),f470(x13503,x13502,x13504))
% 28.78/28.54 [1351]~E(x13511,x13512)+E(f470(x13513,x13514,x13511),f470(x13513,x13514,x13512))
% 28.78/28.54 [1352]~E(x13521,x13522)+E(f460(x13521,x13523,x13524,x13525),f460(x13522,x13523,x13524,x13525))
% 28.78/28.54 [1353]~E(x13531,x13532)+E(f460(x13533,x13531,x13534,x13535),f460(x13533,x13532,x13534,x13535))
% 28.78/28.54 [1354]~E(x13541,x13542)+E(f460(x13543,x13544,x13541,x13545),f460(x13543,x13544,x13542,x13545))
% 28.78/28.54 [1355]~E(x13551,x13552)+E(f460(x13553,x13554,x13555,x13551),f460(x13553,x13554,x13555,x13552))
% 28.78/28.54 [1356]~E(x13561,x13562)+E(f241(x13561,x13563,x13564),f241(x13562,x13563,x13564))
% 28.78/28.54 [1357]~E(x13571,x13572)+E(f241(x13573,x13571,x13574),f241(x13573,x13572,x13574))
% 28.78/28.54 [1358]~E(x13581,x13582)+E(f241(x13583,x13584,x13581),f241(x13583,x13584,x13582))
% 28.78/28.54 [1359]~E(x13591,x13592)+E(f115(x13591),f115(x13592))
% 28.78/28.54 [1360]~E(x13601,x13602)+E(f884(x13601,x13603,x13604),f884(x13602,x13603,x13604))
% 28.78/28.54 [1361]~E(x13611,x13612)+E(f884(x13613,x13611,x13614),f884(x13613,x13612,x13614))
% 28.78/28.54 [1362]~E(x13621,x13622)+E(f884(x13623,x13624,x13621),f884(x13623,x13624,x13622))
% 28.78/28.54 [1363]~E(x13631,x13632)+E(f699(x13631,x13633,x13634),f699(x13632,x13633,x13634))
% 28.78/28.54 [1364]~E(x13641,x13642)+E(f699(x13643,x13641,x13644),f699(x13643,x13642,x13644))
% 28.78/28.54 [1365]~E(x13651,x13652)+E(f699(x13653,x13654,x13651),f699(x13653,x13654,x13652))
% 28.78/28.54 [1366]~E(x13661,x13662)+E(f461(x13661,x13663,x13664,x13665,x13666),f461(x13662,x13663,x13664,x13665,x13666))
% 28.78/28.54 [1367]~E(x13671,x13672)+E(f461(x13673,x13671,x13674,x13675,x13676),f461(x13673,x13672,x13674,x13675,x13676))
% 28.78/28.54 [1368]~E(x13681,x13682)+E(f461(x13683,x13684,x13681,x13685,x13686),f461(x13683,x13684,x13682,x13685,x13686))
% 28.78/28.54 [1369]~E(x13691,x13692)+E(f461(x13693,x13694,x13695,x13691,x13696),f461(x13693,x13694,x13695,x13692,x13696))
% 28.78/28.54 [1370]~E(x13701,x13702)+E(f461(x13703,x13704,x13705,x13706,x13701),f461(x13703,x13704,x13705,x13706,x13702))
% 28.78/28.54 [1371]~E(x13711,x13712)+E(f389(x13711,x13713,x13714,x13715,x13716),f389(x13712,x13713,x13714,x13715,x13716))
% 28.78/28.54 [1372]~E(x13721,x13722)+E(f389(x13723,x13721,x13724,x13725,x13726),f389(x13723,x13722,x13724,x13725,x13726))
% 28.78/28.54 [1373]~E(x13731,x13732)+E(f389(x13733,x13734,x13731,x13735,x13736),f389(x13733,x13734,x13732,x13735,x13736))
% 28.78/28.54 [1374]~E(x13741,x13742)+E(f389(x13743,x13744,x13745,x13741,x13746),f389(x13743,x13744,x13745,x13742,x13746))
% 28.78/28.54 [1375]~E(x13751,x13752)+E(f389(x13753,x13754,x13755,x13756,x13751),f389(x13753,x13754,x13755,x13756,x13752))
% 28.78/28.54 [1376]~E(x13761,x13762)+E(f495(x13761,x13763,x13764,x13765,x13766),f495(x13762,x13763,x13764,x13765,x13766))
% 28.78/28.54 [1377]~E(x13771,x13772)+E(f495(x13773,x13771,x13774,x13775,x13776),f495(x13773,x13772,x13774,x13775,x13776))
% 28.78/28.54 [1378]~E(x13781,x13782)+E(f495(x13783,x13784,x13781,x13785,x13786),f495(x13783,x13784,x13782,x13785,x13786))
% 28.78/28.54 [1379]~E(x13791,x13792)+E(f495(x13793,x13794,x13795,x13791,x13796),f495(x13793,x13794,x13795,x13792,x13796))
% 28.78/28.54 [1380]~E(x13801,x13802)+E(f495(x13803,x13804,x13805,x13806,x13801),f495(x13803,x13804,x13805,x13806,x13802))
% 28.78/28.54 [1381]~E(x13811,x13812)+E(f142(x13811,x13813,x13814,x13815),f142(x13812,x13813,x13814,x13815))
% 28.78/28.54 [1382]~E(x13821,x13822)+E(f142(x13823,x13821,x13824,x13825),f142(x13823,x13822,x13824,x13825))
% 28.78/28.54 [1383]~E(x13831,x13832)+E(f142(x13833,x13834,x13831,x13835),f142(x13833,x13834,x13832,x13835))
% 28.78/28.54 [1384]~E(x13841,x13842)+E(f142(x13843,x13844,x13845,x13841),f142(x13843,x13844,x13845,x13842))
% 28.78/28.54 [1385]~E(x13851,x13852)+E(f794(x13851,x13853,x13854,x13855),f794(x13852,x13853,x13854,x13855))
% 28.78/28.54 [1386]~E(x13861,x13862)+E(f794(x13863,x13861,x13864,x13865),f794(x13863,x13862,x13864,x13865))
% 28.78/28.54 [1387]~E(x13871,x13872)+E(f794(x13873,x13874,x13871,x13875),f794(x13873,x13874,x13872,x13875))
% 28.78/28.54 [1388]~E(x13881,x13882)+E(f794(x13883,x13884,x13885,x13881),f794(x13883,x13884,x13885,x13882))
% 28.78/28.54 [1389]~E(x13891,x13892)+E(f804(x13891,x13893,x13894,x13895),f804(x13892,x13893,x13894,x13895))
% 28.78/28.54 [1390]~E(x13901,x13902)+E(f804(x13903,x13901,x13904,x13905),f804(x13903,x13902,x13904,x13905))
% 28.78/28.54 [1391]~E(x13911,x13912)+E(f804(x13913,x13914,x13911,x13915),f804(x13913,x13914,x13912,x13915))
% 28.78/28.54 [1392]~E(x13921,x13922)+E(f804(x13923,x13924,x13925,x13921),f804(x13923,x13924,x13925,x13922))
% 28.78/28.54 [1393]~E(x13931,x13932)+E(f768(x13931,x13933,x13934,x13935,x13936,x13937,x13938),f768(x13932,x13933,x13934,x13935,x13936,x13937,x13938))
% 28.78/28.54 [1394]~E(x13941,x13942)+E(f768(x13943,x13941,x13944,x13945,x13946,x13947,x13948),f768(x13943,x13942,x13944,x13945,x13946,x13947,x13948))
% 28.78/28.54 [1395]~E(x13951,x13952)+E(f768(x13953,x13954,x13951,x13955,x13956,x13957,x13958),f768(x13953,x13954,x13952,x13955,x13956,x13957,x13958))
% 28.78/28.54 [1396]~E(x13961,x13962)+E(f768(x13963,x13964,x13965,x13961,x13966,x13967,x13968),f768(x13963,x13964,x13965,x13962,x13966,x13967,x13968))
% 28.78/28.54 [1397]~E(x13971,x13972)+E(f768(x13973,x13974,x13975,x13976,x13971,x13977,x13978),f768(x13973,x13974,x13975,x13976,x13972,x13977,x13978))
% 28.78/28.54 [1398]~E(x13981,x13982)+E(f768(x13983,x13984,x13985,x13986,x13987,x13981,x13988),f768(x13983,x13984,x13985,x13986,x13987,x13982,x13988))
% 28.78/28.54 [1399]~E(x13991,x13992)+E(f768(x13993,x13994,x13995,x13996,x13997,x13998,x13991),f768(x13993,x13994,x13995,x13996,x13997,x13998,x13992))
% 28.78/28.54 [1400]~E(x14001,x14002)+E(f915(x14001,x14003),f915(x14002,x14003))
% 28.78/28.54 [1401]~E(x14011,x14012)+E(f915(x14013,x14011),f915(x14013,x14012))
% 28.78/28.54 [1402]~E(x14021,x14022)+E(f826(x14021,x14023),f826(x14022,x14023))
% 28.78/28.54 [1403]~E(x14031,x14032)+E(f826(x14033,x14031),f826(x14033,x14032))
% 28.78/28.54 [1404]~E(x14041,x14042)+E(f833(x14041),f833(x14042))
% 28.78/28.54 [1405]~E(x14051,x14052)+E(f457(x14051,x14053),f457(x14052,x14053))
% 28.78/28.54 [1406]~E(x14061,x14062)+E(f457(x14063,x14061),f457(x14063,x14062))
% 28.78/28.54 [1407]~E(x14071,x14072)+E(f720(x14071,x14073,x14074,x14075,x14076),f720(x14072,x14073,x14074,x14075,x14076))
% 28.78/28.54 [1408]~E(x14081,x14082)+E(f720(x14083,x14081,x14084,x14085,x14086),f720(x14083,x14082,x14084,x14085,x14086))
% 28.78/28.54 [1409]~E(x14091,x14092)+E(f720(x14093,x14094,x14091,x14095,x14096),f720(x14093,x14094,x14092,x14095,x14096))
% 28.78/28.54 [1410]~E(x14101,x14102)+E(f720(x14103,x14104,x14105,x14101,x14106),f720(x14103,x14104,x14105,x14102,x14106))
% 28.78/28.54 [1411]~E(x14111,x14112)+E(f720(x14113,x14114,x14115,x14116,x14111),f720(x14113,x14114,x14115,x14116,x14112))
% 28.78/28.54 [1412]~E(x14121,x14122)+E(f474(x14121,x14123,x14124),f474(x14122,x14123,x14124))
% 28.78/28.54 [1413]~E(x14131,x14132)+E(f474(x14133,x14131,x14134),f474(x14133,x14132,x14134))
% 28.78/28.54 [1414]~E(x14141,x14142)+E(f474(x14143,x14144,x14141),f474(x14143,x14144,x14142))
% 28.78/28.54 [1415]~E(x14151,x14152)+E(f446(x14151,x14153,x14154,x14155,x14156),f446(x14152,x14153,x14154,x14155,x14156))
% 28.78/28.54 [1416]~E(x14161,x14162)+E(f446(x14163,x14161,x14164,x14165,x14166),f446(x14163,x14162,x14164,x14165,x14166))
% 28.78/28.54 [1417]~E(x14171,x14172)+E(f446(x14173,x14174,x14171,x14175,x14176),f446(x14173,x14174,x14172,x14175,x14176))
% 28.78/28.54 [1418]~E(x14181,x14182)+E(f446(x14183,x14184,x14185,x14181,x14186),f446(x14183,x14184,x14185,x14182,x14186))
% 28.78/28.54 [1419]~E(x14191,x14192)+E(f446(x14193,x14194,x14195,x14196,x14191),f446(x14193,x14194,x14195,x14196,x14192))
% 28.78/28.54 [1420]~E(x14201,x14202)+E(f808(x14201,x14203),f808(x14202,x14203))
% 28.78/28.54 [1421]~E(x14211,x14212)+E(f808(x14213,x14211),f808(x14213,x14212))
% 28.78/28.54 [1422]~E(x14221,x14222)+E(f218(x14221,x14223,x14224,x14225,x14226),f218(x14222,x14223,x14224,x14225,x14226))
% 28.78/28.54 [1423]~E(x14231,x14232)+E(f218(x14233,x14231,x14234,x14235,x14236),f218(x14233,x14232,x14234,x14235,x14236))
% 28.78/28.54 [1424]~E(x14241,x14242)+E(f218(x14243,x14244,x14241,x14245,x14246),f218(x14243,x14244,x14242,x14245,x14246))
% 28.78/28.54 [1425]~E(x14251,x14252)+E(f218(x14253,x14254,x14255,x14251,x14256),f218(x14253,x14254,x14255,x14252,x14256))
% 28.78/28.54 [1426]~E(x14261,x14262)+E(f218(x14263,x14264,x14265,x14266,x14261),f218(x14263,x14264,x14265,x14266,x14262))
% 28.78/28.54 [1427]~E(x14271,x14272)+E(f506(x14271,x14273,x14274,x14275,x14276),f506(x14272,x14273,x14274,x14275,x14276))
% 28.78/28.54 [1428]~E(x14281,x14282)+E(f506(x14283,x14281,x14284,x14285,x14286),f506(x14283,x14282,x14284,x14285,x14286))
% 28.78/28.54 [1429]~E(x14291,x14292)+E(f506(x14293,x14294,x14291,x14295,x14296),f506(x14293,x14294,x14292,x14295,x14296))
% 28.78/28.54 [1430]~E(x14301,x14302)+E(f506(x14303,x14304,x14305,x14301,x14306),f506(x14303,x14304,x14305,x14302,x14306))
% 28.78/28.54 [1431]~E(x14311,x14312)+E(f506(x14313,x14314,x14315,x14316,x14311),f506(x14313,x14314,x14315,x14316,x14312))
% 28.78/28.54 [1432]~E(x14321,x14322)+E(f913(x14321,x14323),f913(x14322,x14323))
% 28.78/28.54 [1433]~E(x14331,x14332)+E(f913(x14333,x14331),f913(x14333,x14332))
% 28.78/28.54 [1434]~E(x14341,x14342)+E(f718(x14341,x14343),f718(x14342,x14343))
% 28.78/28.54 [1435]~E(x14351,x14352)+E(f718(x14353,x14351),f718(x14353,x14352))
% 28.78/28.54 [1436]~E(x14361,x14362)+E(f782(x14361,x14363,x14364),f782(x14362,x14363,x14364))
% 28.78/28.54 [1437]~E(x14371,x14372)+E(f782(x14373,x14371,x14374),f782(x14373,x14372,x14374))
% 28.78/28.54 [1438]~E(x14381,x14382)+E(f782(x14383,x14384,x14381),f782(x14383,x14384,x14382))
% 28.78/28.54 [1439]~E(x14391,x14392)+E(f202(x14391,x14393,x14394,x14395),f202(x14392,x14393,x14394,x14395))
% 28.78/28.54 [1440]~E(x14401,x14402)+E(f202(x14403,x14401,x14404,x14405),f202(x14403,x14402,x14404,x14405))
% 28.78/28.54 [1441]~E(x14411,x14412)+E(f202(x14413,x14414,x14411,x14415),f202(x14413,x14414,x14412,x14415))
% 28.78/28.54 [1442]~E(x14421,x14422)+E(f202(x14423,x14424,x14425,x14421),f202(x14423,x14424,x14425,x14422))
% 28.78/28.54 [1443]~E(x14431,x14432)+E(f388(x14431,x14433,x14434,x14435),f388(x14432,x14433,x14434,x14435))
% 28.78/28.54 [1444]~E(x14441,x14442)+E(f388(x14443,x14441,x14444,x14445),f388(x14443,x14442,x14444,x14445))
% 28.78/28.54 [1445]~E(x14451,x14452)+E(f388(x14453,x14454,x14451,x14455),f388(x14453,x14454,x14452,x14455))
% 28.78/28.54 [1446]~E(x14461,x14462)+E(f388(x14463,x14464,x14465,x14461),f388(x14463,x14464,x14465,x14462))
% 28.78/28.54 [1447]~E(x14471,x14472)+E(f597(x14471,x14473),f597(x14472,x14473))
% 28.78/28.54 [1448]~E(x14481,x14482)+E(f597(x14483,x14481),f597(x14483,x14482))
% 28.78/28.54 [1449]~E(x14491,x14492)+E(f532(x14491,x14493),f532(x14492,x14493))
% 28.78/28.54 [1450]~E(x14501,x14502)+E(f532(x14503,x14501),f532(x14503,x14502))
% 28.78/28.54 [1451]~E(x14511,x14512)+E(f642(x14511,x14513,x14514,x14515,x14516),f642(x14512,x14513,x14514,x14515,x14516))
% 28.78/28.54 [1452]~E(x14521,x14522)+E(f642(x14523,x14521,x14524,x14525,x14526),f642(x14523,x14522,x14524,x14525,x14526))
% 28.78/28.54 [1453]~E(x14531,x14532)+E(f642(x14533,x14534,x14531,x14535,x14536),f642(x14533,x14534,x14532,x14535,x14536))
% 28.78/28.54 [1454]~E(x14541,x14542)+E(f642(x14543,x14544,x14545,x14541,x14546),f642(x14543,x14544,x14545,x14542,x14546))
% 28.78/28.54 [1455]~E(x14551,x14552)+E(f642(x14553,x14554,x14555,x14556,x14551),f642(x14553,x14554,x14555,x14556,x14552))
% 28.78/28.54 [1456]~E(x14561,x14562)+E(f562(x14561,x14563,x14564,x14565,x14566),f562(x14562,x14563,x14564,x14565,x14566))
% 28.78/28.54 [1457]~E(x14571,x14572)+E(f562(x14573,x14571,x14574,x14575,x14576),f562(x14573,x14572,x14574,x14575,x14576))
% 28.78/28.54 [1458]~E(x14581,x14582)+E(f562(x14583,x14584,x14581,x14585,x14586),f562(x14583,x14584,x14582,x14585,x14586))
% 28.78/28.54 [1459]~E(x14591,x14592)+E(f562(x14593,x14594,x14595,x14591,x14596),f562(x14593,x14594,x14595,x14592,x14596))
% 28.78/28.54 [1460]~E(x14601,x14602)+E(f562(x14603,x14604,x14605,x14606,x14601),f562(x14603,x14604,x14605,x14606,x14602))
% 28.78/28.54 [1461]~E(x14611,x14612)+E(f607(x14611,x14613,x14614,x14615,x14616,x14617),f607(x14612,x14613,x14614,x14615,x14616,x14617))
% 28.78/28.54 [1462]~E(x14621,x14622)+E(f607(x14623,x14621,x14624,x14625,x14626,x14627),f607(x14623,x14622,x14624,x14625,x14626,x14627))
% 28.78/28.54 [1463]~E(x14631,x14632)+E(f607(x14633,x14634,x14631,x14635,x14636,x14637),f607(x14633,x14634,x14632,x14635,x14636,x14637))
% 28.78/28.54 [1464]~E(x14641,x14642)+E(f607(x14643,x14644,x14645,x14641,x14646,x14647),f607(x14643,x14644,x14645,x14642,x14646,x14647))
% 28.78/28.54 [1465]~E(x14651,x14652)+E(f607(x14653,x14654,x14655,x14656,x14651,x14657),f607(x14653,x14654,x14655,x14656,x14652,x14657))
% 28.78/28.54 [1466]~E(x14661,x14662)+E(f607(x14663,x14664,x14665,x14666,x14667,x14661),f607(x14663,x14664,x14665,x14666,x14667,x14662))
% 28.78/28.54 [1467]~E(x14671,x14672)+E(f797(x14671,x14673,x14674,x14675,x14676),f797(x14672,x14673,x14674,x14675,x14676))
% 28.78/28.54 [1468]~E(x14681,x14682)+E(f797(x14683,x14681,x14684,x14685,x14686),f797(x14683,x14682,x14684,x14685,x14686))
% 28.78/28.54 [1469]~E(x14691,x14692)+E(f797(x14693,x14694,x14691,x14695,x14696),f797(x14693,x14694,x14692,x14695,x14696))
% 28.78/28.54 [1470]~E(x14701,x14702)+E(f797(x14703,x14704,x14705,x14701,x14706),f797(x14703,x14704,x14705,x14702,x14706))
% 28.78/28.54 [1471]~E(x14711,x14712)+E(f797(x14713,x14714,x14715,x14716,x14711),f797(x14713,x14714,x14715,x14716,x14712))
% 28.78/28.54 [1472]~E(x14721,x14722)+E(f422(x14721,x14723,x14724,x14725),f422(x14722,x14723,x14724,x14725))
% 28.78/28.54 [1473]~E(x14731,x14732)+E(f422(x14733,x14731,x14734,x14735),f422(x14733,x14732,x14734,x14735))
% 28.78/28.54 [1474]~E(x14741,x14742)+E(f422(x14743,x14744,x14741,x14745),f422(x14743,x14744,x14742,x14745))
% 28.78/28.54 [1475]~E(x14751,x14752)+E(f422(x14753,x14754,x14755,x14751),f422(x14753,x14754,x14755,x14752))
% 28.78/28.54 [1476]~E(x14761,x14762)+E(f674(x14761,x14763,x14764,x14765,x14766),f674(x14762,x14763,x14764,x14765,x14766))
% 28.78/28.54 [1477]~E(x14771,x14772)+E(f674(x14773,x14771,x14774,x14775,x14776),f674(x14773,x14772,x14774,x14775,x14776))
% 28.78/28.54 [1478]~E(x14781,x14782)+E(f674(x14783,x14784,x14781,x14785,x14786),f674(x14783,x14784,x14782,x14785,x14786))
% 28.78/28.54 [1479]~E(x14791,x14792)+E(f674(x14793,x14794,x14795,x14791,x14796),f674(x14793,x14794,x14795,x14792,x14796))
% 28.78/28.54 [1480]~E(x14801,x14802)+E(f674(x14803,x14804,x14805,x14806,x14801),f674(x14803,x14804,x14805,x14806,x14802))
% 28.78/28.54 [1481]~E(x14811,x14812)+E(f433(x14811,x14813),f433(x14812,x14813))
% 28.78/28.54 [1482]~E(x14821,x14822)+E(f433(x14823,x14821),f433(x14823,x14822))
% 28.78/28.54 [1483]~E(x14831,x14832)+E(f599(x14831,x14833,x14834),f599(x14832,x14833,x14834))
% 28.78/28.54 [1484]~E(x14841,x14842)+E(f599(x14843,x14841,x14844),f599(x14843,x14842,x14844))
% 28.78/28.54 [1485]~E(x14851,x14852)+E(f599(x14853,x14854,x14851),f599(x14853,x14854,x14852))
% 28.78/28.54 [1486]~E(x14861,x14862)+E(f891(x14861,x14863,x14864,x14865,x14866),f891(x14862,x14863,x14864,x14865,x14866))
% 28.78/28.54 [1487]~E(x14871,x14872)+E(f891(x14873,x14871,x14874,x14875,x14876),f891(x14873,x14872,x14874,x14875,x14876))
% 28.78/28.54 [1488]~E(x14881,x14882)+E(f891(x14883,x14884,x14881,x14885,x14886),f891(x14883,x14884,x14882,x14885,x14886))
% 28.78/28.54 [1489]~E(x14891,x14892)+E(f891(x14893,x14894,x14895,x14891,x14896),f891(x14893,x14894,x14895,x14892,x14896))
% 28.78/28.54 [1490]~E(x14901,x14902)+E(f891(x14903,x14904,x14905,x14906,x14901),f891(x14903,x14904,x14905,x14906,x14902))
% 28.78/28.54 [1491]~E(x14911,x14912)+E(f712(x14911,x14913,x14914),f712(x14912,x14913,x14914))
% 28.78/28.54 [1492]~E(x14921,x14922)+E(f712(x14923,x14921,x14924),f712(x14923,x14922,x14924))
% 28.78/28.54 [1493]~E(x14931,x14932)+E(f712(x14933,x14934,x14931),f712(x14933,x14934,x14932))
% 28.78/28.54 [1494]~E(x14941,x14942)+E(f704(x14941,x14943,x14944,x14945,x14946),f704(x14942,x14943,x14944,x14945,x14946))
% 28.78/28.54 [1495]~E(x14951,x14952)+E(f704(x14953,x14951,x14954,x14955,x14956),f704(x14953,x14952,x14954,x14955,x14956))
% 28.78/28.54 [1496]~E(x14961,x14962)+E(f704(x14963,x14964,x14961,x14965,x14966),f704(x14963,x14964,x14962,x14965,x14966))
% 28.78/28.54 [1497]~E(x14971,x14972)+E(f704(x14973,x14974,x14975,x14971,x14976),f704(x14973,x14974,x14975,x14972,x14976))
% 28.78/28.54 [1498]~E(x14981,x14982)+E(f704(x14983,x14984,x14985,x14986,x14981),f704(x14983,x14984,x14985,x14986,x14982))
% 28.78/28.54 [1499]~E(x14991,x14992)+E(f336(x14991,x14993,x14994),f336(x14992,x14993,x14994))
% 28.78/28.54 [1500]~E(x15001,x15002)+E(f336(x15003,x15001,x15004),f336(x15003,x15002,x15004))
% 28.78/28.54 [1501]~E(x15011,x15012)+E(f336(x15013,x15014,x15011),f336(x15013,x15014,x15012))
% 28.78/28.54 [1502]~E(x15021,x15022)+E(f652(x15021,x15023,x15024,x15025),f652(x15022,x15023,x15024,x15025))
% 28.78/28.54 [1503]~E(x15031,x15032)+E(f652(x15033,x15031,x15034,x15035),f652(x15033,x15032,x15034,x15035))
% 28.78/28.54 [1504]~E(x15041,x15042)+E(f652(x15043,x15044,x15041,x15045),f652(x15043,x15044,x15042,x15045))
% 28.78/28.54 [1505]~E(x15051,x15052)+E(f652(x15053,x15054,x15055,x15051),f652(x15053,x15054,x15055,x15052))
% 28.78/28.54 [1506]~E(x15061,x15062)+E(f835(x15061,x15063),f835(x15062,x15063))
% 28.78/28.54 [1507]~E(x15071,x15072)+E(f835(x15073,x15071),f835(x15073,x15072))
% 28.78/28.54 [1508]~E(x15081,x15082)+E(f335(x15081,x15083,x15084),f335(x15082,x15083,x15084))
% 28.78/28.54 [1509]~E(x15091,x15092)+E(f335(x15093,x15091,x15094),f335(x15093,x15092,x15094))
% 28.78/28.54 [1510]~E(x15101,x15102)+E(f335(x15103,x15104,x15101),f335(x15103,x15104,x15102))
% 28.78/28.54 [1511]~E(x15111,x15112)+E(f109(x15111,x15113,x15114),f109(x15112,x15113,x15114))
% 28.78/28.54 [1512]~E(x15121,x15122)+E(f109(x15123,x15121,x15124),f109(x15123,x15122,x15124))
% 28.78/28.54 [1513]~E(x15131,x15132)+E(f109(x15133,x15134,x15131),f109(x15133,x15134,x15132))
% 28.78/28.54 [1514]~E(x15141,x15142)+E(f242(x15141,x15143,x15144),f242(x15142,x15143,x15144))
% 28.78/28.54 [1515]~E(x15151,x15152)+E(f242(x15153,x15151,x15154),f242(x15153,x15152,x15154))
% 28.78/28.54 [1516]~E(x15161,x15162)+E(f242(x15163,x15164,x15161),f242(x15163,x15164,x15162))
% 28.78/28.54 [1517]~E(x15171,x15172)+E(f527(x15171,x15173,x15174,x15175,x15176,x15177),f527(x15172,x15173,x15174,x15175,x15176,x15177))
% 28.78/28.54 [1518]~E(x15181,x15182)+E(f527(x15183,x15181,x15184,x15185,x15186,x15187),f527(x15183,x15182,x15184,x15185,x15186,x15187))
% 28.78/28.54 [1519]~E(x15191,x15192)+E(f527(x15193,x15194,x15191,x15195,x15196,x15197),f527(x15193,x15194,x15192,x15195,x15196,x15197))
% 28.78/28.54 [1520]~E(x15201,x15202)+E(f527(x15203,x15204,x15205,x15201,x15206,x15207),f527(x15203,x15204,x15205,x15202,x15206,x15207))
% 28.78/28.54 [1521]~E(x15211,x15212)+E(f527(x15213,x15214,x15215,x15216,x15211,x15217),f527(x15213,x15214,x15215,x15216,x15212,x15217))
% 28.78/28.54 [1522]~E(x15221,x15222)+E(f527(x15223,x15224,x15225,x15226,x15227,x15221),f527(x15223,x15224,x15225,x15226,x15227,x15222))
% 28.78/28.54 [1523]~E(x15231,x15232)+E(f807(x15231,x15233,x15234,x15235),f807(x15232,x15233,x15234,x15235))
% 28.78/28.54 [1524]~E(x15241,x15242)+E(f807(x15243,x15241,x15244,x15245),f807(x15243,x15242,x15244,x15245))
% 28.78/28.54 [1525]~E(x15251,x15252)+E(f807(x15253,x15254,x15251,x15255),f807(x15253,x15254,x15252,x15255))
% 28.78/28.54 [1526]~E(x15261,x15262)+E(f807(x15263,x15264,x15265,x15261),f807(x15263,x15264,x15265,x15262))
% 28.78/28.54 [1527]~E(x15271,x15272)+E(f437(x15271,x15273,x15274,x15275,x15276,x15277),f437(x15272,x15273,x15274,x15275,x15276,x15277))
% 28.78/28.54 [1528]~E(x15281,x15282)+E(f437(x15283,x15281,x15284,x15285,x15286,x15287),f437(x15283,x15282,x15284,x15285,x15286,x15287))
% 28.78/28.54 [1529]~E(x15291,x15292)+E(f437(x15293,x15294,x15291,x15295,x15296,x15297),f437(x15293,x15294,x15292,x15295,x15296,x15297))
% 28.78/28.54 [1530]~E(x15301,x15302)+E(f437(x15303,x15304,x15305,x15301,x15306,x15307),f437(x15303,x15304,x15305,x15302,x15306,x15307))
% 28.78/28.54 [1531]~E(x15311,x15312)+E(f437(x15313,x15314,x15315,x15316,x15311,x15317),f437(x15313,x15314,x15315,x15316,x15312,x15317))
% 28.78/28.54 [1532]~E(x15321,x15322)+E(f437(x15323,x15324,x15325,x15326,x15327,x15321),f437(x15323,x15324,x15325,x15326,x15327,x15322))
% 28.78/28.54 [1533]~E(x15331,x15332)+E(f518(x15331,x15333,x15334),f518(x15332,x15333,x15334))
% 28.78/28.54 [1534]~E(x15341,x15342)+E(f518(x15343,x15341,x15344),f518(x15343,x15342,x15344))
% 28.78/28.54 [1535]~E(x15351,x15352)+E(f518(x15353,x15354,x15351),f518(x15353,x15354,x15352))
% 28.78/28.54 [1536]~E(x15361,x15362)+E(f703(x15361,x15363,x15364,x15365,x15366),f703(x15362,x15363,x15364,x15365,x15366))
% 28.78/28.54 [1537]~E(x15371,x15372)+E(f703(x15373,x15371,x15374,x15375,x15376),f703(x15373,x15372,x15374,x15375,x15376))
% 28.78/28.54 [1538]~E(x15381,x15382)+E(f703(x15383,x15384,x15381,x15385,x15386),f703(x15383,x15384,x15382,x15385,x15386))
% 28.78/28.54 [1539]~E(x15391,x15392)+E(f703(x15393,x15394,x15395,x15391,x15396),f703(x15393,x15394,x15395,x15392,x15396))
% 28.78/28.54 [1540]~E(x15401,x15402)+E(f703(x15403,x15404,x15405,x15406,x15401),f703(x15403,x15404,x15405,x15406,x15402))
% 28.78/28.54 [1541]~E(x15411,x15412)+E(f291(x15411,x15413,x15414,x15415),f291(x15412,x15413,x15414,x15415))
% 28.78/28.54 [1542]~E(x15421,x15422)+E(f291(x15423,x15421,x15424,x15425),f291(x15423,x15422,x15424,x15425))
% 28.78/28.54 [1543]~E(x15431,x15432)+E(f291(x15433,x15434,x15431,x15435),f291(x15433,x15434,x15432,x15435))
% 28.78/28.54 [1544]~E(x15441,x15442)+E(f291(x15443,x15444,x15445,x15441),f291(x15443,x15444,x15445,x15442))
% 28.78/28.54 [1545]~E(x15451,x15452)+E(f82(x15451),f82(x15452))
% 28.78/28.54 [1546]~E(x15461,x15462)+E(f166(x15461,x15463,x15464),f166(x15462,x15463,x15464))
% 28.78/28.54 [1547]~E(x15471,x15472)+E(f166(x15473,x15471,x15474),f166(x15473,x15472,x15474))
% 28.78/28.54 [1548]~E(x15481,x15482)+E(f166(x15483,x15484,x15481),f166(x15483,x15484,x15482))
% 28.78/28.54 [1549]~E(x15491,x15492)+E(f621(x15491,x15493,x15494,x15495,x15496,x15497,x15498,x15499),f621(x15492,x15493,x15494,x15495,x15496,x15497,x15498,x15499))
% 28.78/28.54 [1550]~E(x15501,x15502)+E(f621(x15503,x15501,x15504,x15505,x15506,x15507,x15508,x15509),f621(x15503,x15502,x15504,x15505,x15506,x15507,x15508,x15509))
% 28.78/28.54 [1551]~E(x15511,x15512)+E(f621(x15513,x15514,x15511,x15515,x15516,x15517,x15518,x15519),f621(x15513,x15514,x15512,x15515,x15516,x15517,x15518,x15519))
% 28.78/28.54 [1552]~E(x15521,x15522)+E(f621(x15523,x15524,x15525,x15521,x15526,x15527,x15528,x15529),f621(x15523,x15524,x15525,x15522,x15526,x15527,x15528,x15529))
% 28.78/28.54 [1553]~E(x15531,x15532)+E(f621(x15533,x15534,x15535,x15536,x15531,x15537,x15538,x15539),f621(x15533,x15534,x15535,x15536,x15532,x15537,x15538,x15539))
% 28.78/28.54 [1554]~E(x15541,x15542)+E(f621(x15543,x15544,x15545,x15546,x15547,x15541,x15548,x15549),f621(x15543,x15544,x15545,x15546,x15547,x15542,x15548,x15549))
% 28.78/28.54 [1555]~E(x15551,x15552)+E(f621(x15553,x15554,x15555,x15556,x15557,x15558,x15551,x15559),f621(x15553,x15554,x15555,x15556,x15557,x15558,x15552,x15559))
% 28.78/28.54 [1556]~E(x15561,x15562)+E(f621(x15563,x15564,x15565,x15566,x15567,x15568,x15569,x15561),f621(x15563,x15564,x15565,x15566,x15567,x15568,x15569,x15562))
% 28.78/28.54 [1557]~E(x15571,x15572)+E(f587(x15571,x15573,x15574,x15575,x15576,x15577,x15578,x15579),f587(x15572,x15573,x15574,x15575,x15576,x15577,x15578,x15579))
% 28.78/28.54 [1558]~E(x15581,x15582)+E(f587(x15583,x15581,x15584,x15585,x15586,x15587,x15588,x15589),f587(x15583,x15582,x15584,x15585,x15586,x15587,x15588,x15589))
% 28.78/28.54 [1559]~E(x15591,x15592)+E(f587(x15593,x15594,x15591,x15595,x15596,x15597,x15598,x15599),f587(x15593,x15594,x15592,x15595,x15596,x15597,x15598,x15599))
% 28.78/28.54 [1560]~E(x15601,x15602)+E(f587(x15603,x15604,x15605,x15601,x15606,x15607,x15608,x15609),f587(x15603,x15604,x15605,x15602,x15606,x15607,x15608,x15609))
% 28.78/28.54 [1561]~E(x15611,x15612)+E(f587(x15613,x15614,x15615,x15616,x15611,x15617,x15618,x15619),f587(x15613,x15614,x15615,x15616,x15612,x15617,x15618,x15619))
% 28.78/28.54 [1562]~E(x15621,x15622)+E(f587(x15623,x15624,x15625,x15626,x15627,x15621,x15628,x15629),f587(x15623,x15624,x15625,x15626,x15627,x15622,x15628,x15629))
% 28.78/28.54 [1563]~E(x15631,x15632)+E(f587(x15633,x15634,x15635,x15636,x15637,x15638,x15631,x15639),f587(x15633,x15634,x15635,x15636,x15637,x15638,x15632,x15639))
% 28.78/28.54 [1564]~E(x15641,x15642)+E(f587(x15643,x15644,x15645,x15646,x15647,x15648,x15649,x15641),f587(x15643,x15644,x15645,x15646,x15647,x15648,x15649,x15642))
% 28.78/28.54 [1565]~E(x15651,x15652)+E(f341(x15651,x15653,x15654,x15655),f341(x15652,x15653,x15654,x15655))
% 28.78/28.54 [1566]~E(x15661,x15662)+E(f341(x15663,x15661,x15664,x15665),f341(x15663,x15662,x15664,x15665))
% 28.78/28.54 [1567]~E(x15671,x15672)+E(f341(x15673,x15674,x15671,x15675),f341(x15673,x15674,x15672,x15675))
% 28.78/28.54 [1568]~E(x15681,x15682)+E(f341(x15683,x15684,x15685,x15681),f341(x15683,x15684,x15685,x15682))
% 28.78/28.54 [1569]~E(x15691,x15692)+E(f836(x15691,x15693),f836(x15692,x15693))
% 28.78/28.54 [1570]~E(x15701,x15702)+E(f836(x15703,x15701),f836(x15703,x15702))
% 28.78/28.54 [1571]~E(x15711,x15712)+E(f885(x15711,x15713,x15714),f885(x15712,x15713,x15714))
% 28.78/28.54 [1572]~E(x15721,x15722)+E(f885(x15723,x15721,x15724),f885(x15723,x15722,x15724))
% 28.78/28.54 [1573]~E(x15731,x15732)+E(f885(x15733,x15734,x15731),f885(x15733,x15734,x15732))
% 28.78/28.54 [1574]~E(x15741,x15742)+E(f623(x15741,x15743),f623(x15742,x15743))
% 28.78/28.54 [1575]~E(x15751,x15752)+E(f623(x15753,x15751),f623(x15753,x15752))
% 28.78/28.54 [1576]~E(x15761,x15762)+E(f742(x15761,x15763),f742(x15762,x15763))
% 28.78/28.54 [1577]~E(x15771,x15772)+E(f742(x15773,x15771),f742(x15773,x15772))
% 28.78/28.54 [1578]~E(x15781,x15782)+E(f200(x15781),f200(x15782))
% 28.78/28.54 [1579]~E(x15791,x15792)+E(f62(x15791,x15793,x15794),f62(x15792,x15793,x15794))
% 28.78/28.54 [1580]~E(x15801,x15802)+E(f62(x15803,x15801,x15804),f62(x15803,x15802,x15804))
% 28.78/28.54 [1581]~E(x15811,x15812)+E(f62(x15813,x15814,x15811),f62(x15813,x15814,x15812))
% 28.78/28.54 [1582]~E(x15821,x15822)+E(f331(x15821,x15823),f331(x15822,x15823))
% 28.78/28.54 [1583]~E(x15831,x15832)+E(f331(x15833,x15831),f331(x15833,x15832))
% 28.78/28.54 [1584]~E(x15841,x15842)+E(f671(x15841,x15843,x15844,x15845),f671(x15842,x15843,x15844,x15845))
% 28.78/28.54 [1585]~E(x15851,x15852)+E(f671(x15853,x15851,x15854,x15855),f671(x15853,x15852,x15854,x15855))
% 28.78/28.54 [1586]~E(x15861,x15862)+E(f671(x15863,x15864,x15861,x15865),f671(x15863,x15864,x15862,x15865))
% 28.78/28.54 [1587]~E(x15871,x15872)+E(f671(x15873,x15874,x15875,x15871),f671(x15873,x15874,x15875,x15872))
% 28.78/28.54 [1588]~E(x15881,x15882)+E(f646(x15881,x15883,x15884,x15885,x15886),f646(x15882,x15883,x15884,x15885,x15886))
% 28.78/28.54 [1589]~E(x15891,x15892)+E(f646(x15893,x15891,x15894,x15895,x15896),f646(x15893,x15892,x15894,x15895,x15896))
% 28.78/28.54 [1590]~E(x15901,x15902)+E(f646(x15903,x15904,x15901,x15905,x15906),f646(x15903,x15904,x15902,x15905,x15906))
% 28.78/28.54 [1591]~E(x15911,x15912)+E(f646(x15913,x15914,x15915,x15911,x15916),f646(x15913,x15914,x15915,x15912,x15916))
% 28.78/28.54 [1592]~E(x15921,x15922)+E(f646(x15923,x15924,x15925,x15926,x15921),f646(x15923,x15924,x15925,x15926,x15922))
% 28.78/28.54 [1593]~E(x15931,x15932)+E(f592(x15931,x15933,x15934,x15935),f592(x15932,x15933,x15934,x15935))
% 28.78/28.54 [1594]~E(x15941,x15942)+E(f592(x15943,x15941,x15944,x15945),f592(x15943,x15942,x15944,x15945))
% 28.78/28.54 [1595]~E(x15951,x15952)+E(f592(x15953,x15954,x15951,x15955),f592(x15953,x15954,x15952,x15955))
% 28.78/28.54 [1596]~E(x15961,x15962)+E(f592(x15963,x15964,x15965,x15961),f592(x15963,x15964,x15965,x15962))
% 28.78/28.54 [1597]~E(x15971,x15972)+E(f841(x15971,x15973,x15974,x15975),f841(x15972,x15973,x15974,x15975))
% 28.78/28.54 [1598]~E(x15981,x15982)+E(f841(x15983,x15981,x15984,x15985),f841(x15983,x15982,x15984,x15985))
% 28.78/28.54 [1599]~E(x15991,x15992)+E(f841(x15993,x15994,x15991,x15995),f841(x15993,x15994,x15992,x15995))
% 28.78/28.54 [1600]~E(x16001,x16002)+E(f841(x16003,x16004,x16005,x16001),f841(x16003,x16004,x16005,x16002))
% 28.78/28.54 [1601]~E(x16011,x16012)+E(f441(x16011,x16013,x16014),f441(x16012,x16013,x16014))
% 28.78/28.54 [1602]~E(x16021,x16022)+E(f441(x16023,x16021,x16024),f441(x16023,x16022,x16024))
% 28.78/28.54 [1603]~E(x16031,x16032)+E(f441(x16033,x16034,x16031),f441(x16033,x16034,x16032))
% 28.78/28.54 [1604]~E(x16041,x16042)+E(f837(x16041,x16043),f837(x16042,x16043))
% 28.78/28.54 [1605]~E(x16051,x16052)+E(f837(x16053,x16051),f837(x16053,x16052))
% 28.78/28.54 [1606]~E(x16061,x16062)+E(f138(x16061,x16063),f138(x16062,x16063))
% 28.78/28.54 [1607]~E(x16071,x16072)+E(f138(x16073,x16071),f138(x16073,x16072))
% 28.78/28.54 [1608]~E(x16081,x16082)+E(f593(x16081,x16083,x16084),f593(x16082,x16083,x16084))
% 28.78/28.54 [1609]~E(x16091,x16092)+E(f593(x16093,x16091,x16094),f593(x16093,x16092,x16094))
% 28.78/28.54 [1610]~E(x16101,x16102)+E(f593(x16103,x16104,x16101),f593(x16103,x16104,x16102))
% 28.78/28.54 [1611]~E(x16111,x16112)+E(f880(x16111,x16113,x16114),f880(x16112,x16113,x16114))
% 28.78/28.54 [1612]~E(x16121,x16122)+E(f880(x16123,x16121,x16124),f880(x16123,x16122,x16124))
% 28.78/28.54 [1613]~E(x16131,x16132)+E(f880(x16133,x16134,x16131),f880(x16133,x16134,x16132))
% 28.78/28.54 [1614]~E(x16141,x16142)+E(f533(x16141,x16143,x16144),f533(x16142,x16143,x16144))
% 28.78/28.54 [1615]~E(x16151,x16152)+E(f533(x16153,x16151,x16154),f533(x16153,x16152,x16154))
% 28.78/28.54 [1616]~E(x16161,x16162)+E(f533(x16163,x16164,x16161),f533(x16163,x16164,x16162))
% 28.78/28.54 [1617]~E(x16171,x16172)+E(f478(x16171,x16173,x16174),f478(x16172,x16173,x16174))
% 28.78/28.54 [1618]~E(x16181,x16182)+E(f478(x16183,x16181,x16184),f478(x16183,x16182,x16184))
% 28.78/28.54 [1619]~E(x16191,x16192)+E(f478(x16193,x16194,x16191),f478(x16193,x16194,x16192))
% 28.78/28.54 [1620]~E(x16201,x16202)+E(f351(x16201,x16203),f351(x16202,x16203))
% 28.78/28.54 [1621]~E(x16211,x16212)+E(f351(x16213,x16211),f351(x16213,x16212))
% 28.78/28.54 [1622]~E(x16221,x16222)+E(f399(x16221,x16223,x16224,x16225),f399(x16222,x16223,x16224,x16225))
% 28.78/28.54 [1623]~E(x16231,x16232)+E(f399(x16233,x16231,x16234,x16235),f399(x16233,x16232,x16234,x16235))
% 28.78/28.54 [1624]~E(x16241,x16242)+E(f399(x16243,x16244,x16241,x16245),f399(x16243,x16244,x16242,x16245))
% 28.78/28.54 [1625]~E(x16251,x16252)+E(f399(x16253,x16254,x16255,x16251),f399(x16253,x16254,x16255,x16252))
% 28.78/28.54 [1626]~E(x16261,x16262)+E(f182(x16261,x16263,x16264,x16265),f182(x16262,x16263,x16264,x16265))
% 28.78/28.54 [1627]~E(x16271,x16272)+E(f182(x16273,x16271,x16274,x16275),f182(x16273,x16272,x16274,x16275))
% 28.78/28.54 [1628]~E(x16281,x16282)+E(f182(x16283,x16284,x16281,x16285),f182(x16283,x16284,x16282,x16285))
% 28.78/28.54 [1629]~E(x16291,x16292)+E(f182(x16293,x16294,x16295,x16291),f182(x16293,x16294,x16295,x16292))
% 28.78/28.54 [1630]~E(x16301,x16302)+E(f350(x16301,x16303,x16304,x16305,x16306),f350(x16302,x16303,x16304,x16305,x16306))
% 28.78/28.54 [1631]~E(x16311,x16312)+E(f350(x16313,x16311,x16314,x16315,x16316),f350(x16313,x16312,x16314,x16315,x16316))
% 28.78/28.54 [1632]~E(x16321,x16322)+E(f350(x16323,x16324,x16321,x16325,x16326),f350(x16323,x16324,x16322,x16325,x16326))
% 28.78/28.54 [1633]~E(x16331,x16332)+E(f350(x16333,x16334,x16335,x16331,x16336),f350(x16333,x16334,x16335,x16332,x16336))
% 28.78/28.54 [1634]~E(x16341,x16342)+E(f350(x16343,x16344,x16345,x16346,x16341),f350(x16343,x16344,x16345,x16346,x16342))
% 28.78/28.54 [1635]~E(x16351,x16352)+E(f644(x16351,x16353,x16354,x16355,x16356),f644(x16352,x16353,x16354,x16355,x16356))
% 28.78/28.54 [1636]~E(x16361,x16362)+E(f644(x16363,x16361,x16364,x16365,x16366),f644(x16363,x16362,x16364,x16365,x16366))
% 28.78/28.54 [1637]~E(x16371,x16372)+E(f644(x16373,x16374,x16371,x16375,x16376),f644(x16373,x16374,x16372,x16375,x16376))
% 28.78/28.54 [1638]~E(x16381,x16382)+E(f644(x16383,x16384,x16385,x16381,x16386),f644(x16383,x16384,x16385,x16382,x16386))
% 28.78/28.54 [1639]~E(x16391,x16392)+E(f644(x16393,x16394,x16395,x16396,x16391),f644(x16393,x16394,x16395,x16396,x16392))
% 28.78/28.54 [1640]~E(x16401,x16402)+E(f757(x16401,x16403,x16404),f757(x16402,x16403,x16404))
% 28.78/28.54 [1641]~E(x16411,x16412)+E(f757(x16413,x16411,x16414),f757(x16413,x16412,x16414))
% 28.78/28.54 [1642]~E(x16421,x16422)+E(f757(x16423,x16424,x16421),f757(x16423,x16424,x16422))
% 28.78/28.54 [1643]~E(x16431,x16432)+E(f344(x16431,x16433,x16434,x16435,x16436,x16437,x16438),f344(x16432,x16433,x16434,x16435,x16436,x16437,x16438))
% 28.78/28.54 [1644]~E(x16441,x16442)+E(f344(x16443,x16441,x16444,x16445,x16446,x16447,x16448),f344(x16443,x16442,x16444,x16445,x16446,x16447,x16448))
% 28.78/28.54 [1645]~E(x16451,x16452)+E(f344(x16453,x16454,x16451,x16455,x16456,x16457,x16458),f344(x16453,x16454,x16452,x16455,x16456,x16457,x16458))
% 28.78/28.54 [1646]~E(x16461,x16462)+E(f344(x16463,x16464,x16465,x16461,x16466,x16467,x16468),f344(x16463,x16464,x16465,x16462,x16466,x16467,x16468))
% 28.78/28.54 [1647]~E(x16471,x16472)+E(f344(x16473,x16474,x16475,x16476,x16471,x16477,x16478),f344(x16473,x16474,x16475,x16476,x16472,x16477,x16478))
% 28.78/28.54 [1648]~E(x16481,x16482)+E(f344(x16483,x16484,x16485,x16486,x16487,x16481,x16488),f344(x16483,x16484,x16485,x16486,x16487,x16482,x16488))
% 28.78/28.54 [1649]~E(x16491,x16492)+E(f344(x16493,x16494,x16495,x16496,x16497,x16498,x16491),f344(x16493,x16494,x16495,x16496,x16497,x16498,x16492))
% 28.78/28.54 [1650]~E(x16501,x16502)+E(f747(x16501,x16503),f747(x16502,x16503))
% 28.78/28.54 [1651]~E(x16511,x16512)+E(f747(x16513,x16511),f747(x16513,x16512))
% 28.78/28.54 [1652]~E(x16521,x16522)+E(f269(x16521,x16523,x16524,x16525),f269(x16522,x16523,x16524,x16525))
% 28.78/28.54 [1653]~E(x16531,x16532)+E(f269(x16533,x16531,x16534,x16535),f269(x16533,x16532,x16534,x16535))
% 28.78/28.54 [1654]~E(x16541,x16542)+E(f269(x16543,x16544,x16541,x16545),f269(x16543,x16544,x16542,x16545))
% 28.78/28.54 [1655]~E(x16551,x16552)+E(f269(x16553,x16554,x16555,x16551),f269(x16553,x16554,x16555,x16552))
% 28.78/28.54 [1656]~E(x16561,x16562)+E(f793(x16561,x16563,x16564,x16565,x16566),f793(x16562,x16563,x16564,x16565,x16566))
% 28.78/28.54 [1657]~E(x16571,x16572)+E(f793(x16573,x16571,x16574,x16575,x16576),f793(x16573,x16572,x16574,x16575,x16576))
% 28.78/28.54 [1658]~E(x16581,x16582)+E(f793(x16583,x16584,x16581,x16585,x16586),f793(x16583,x16584,x16582,x16585,x16586))
% 28.78/28.54 [1659]~E(x16591,x16592)+E(f793(x16593,x16594,x16595,x16591,x16596),f793(x16593,x16594,x16595,x16592,x16596))
% 28.78/28.54 [1660]~E(x16601,x16602)+E(f793(x16603,x16604,x16605,x16606,x16601),f793(x16603,x16604,x16605,x16606,x16602))
% 28.78/28.54 [1661]~E(x16611,x16612)+E(f569(x16611,x16613,x16614),f569(x16612,x16613,x16614))
% 28.78/28.54 [1662]~E(x16621,x16622)+E(f569(x16623,x16621,x16624),f569(x16623,x16622,x16624))
% 28.78/28.54 [1663]~E(x16631,x16632)+E(f569(x16633,x16634,x16631),f569(x16633,x16634,x16632))
% 28.78/28.54 [1664]~E(x16641,x16642)+E(f751(x16641,x16643),f751(x16642,x16643))
% 28.78/28.54 [1665]~E(x16651,x16652)+E(f751(x16653,x16651),f751(x16653,x16652))
% 28.78/28.54 [1666]~E(x16661,x16662)+E(f417(x16661,x16663,x16664,x16665,x16666),f417(x16662,x16663,x16664,x16665,x16666))
% 28.78/28.54 [1667]~E(x16671,x16672)+E(f417(x16673,x16671,x16674,x16675,x16676),f417(x16673,x16672,x16674,x16675,x16676))
% 28.78/28.54 [1668]~E(x16681,x16682)+E(f417(x16683,x16684,x16681,x16685,x16686),f417(x16683,x16684,x16682,x16685,x16686))
% 28.78/28.54 [1669]~E(x16691,x16692)+E(f417(x16693,x16694,x16695,x16691,x16696),f417(x16693,x16694,x16695,x16692,x16696))
% 28.78/28.54 [1670]~E(x16701,x16702)+E(f417(x16703,x16704,x16705,x16706,x16701),f417(x16703,x16704,x16705,x16706,x16702))
% 28.78/28.54 [1671]~E(x16711,x16712)+E(f619(x16711,x16713,x16714,x16715,x16716),f619(x16712,x16713,x16714,x16715,x16716))
% 28.78/28.54 [1672]~E(x16721,x16722)+E(f619(x16723,x16721,x16724,x16725,x16726),f619(x16723,x16722,x16724,x16725,x16726))
% 28.78/28.54 [1673]~E(x16731,x16732)+E(f619(x16733,x16734,x16731,x16735,x16736),f619(x16733,x16734,x16732,x16735,x16736))
% 28.78/28.54 [1674]~E(x16741,x16742)+E(f619(x16743,x16744,x16745,x16741,x16746),f619(x16743,x16744,x16745,x16742,x16746))
% 28.78/28.54 [1675]~E(x16751,x16752)+E(f619(x16753,x16754,x16755,x16756,x16751),f619(x16753,x16754,x16755,x16756,x16752))
% 28.78/28.54 [1676]~E(x16761,x16762)+E(f479(x16761,x16763,x16764),f479(x16762,x16763,x16764))
% 28.78/28.54 [1677]~E(x16771,x16772)+E(f479(x16773,x16771,x16774),f479(x16773,x16772,x16774))
% 28.78/28.54 [1678]~E(x16781,x16782)+E(f479(x16783,x16784,x16781),f479(x16783,x16784,x16782))
% 28.78/28.54 [1679]~E(x16791,x16792)+E(f627(x16791,x16793,x16794),f627(x16792,x16793,x16794))
% 28.78/28.54 [1680]~E(x16801,x16802)+E(f627(x16803,x16801,x16804),f627(x16803,x16802,x16804))
% 28.78/28.54 [1681]~E(x16811,x16812)+E(f627(x16813,x16814,x16811),f627(x16813,x16814,x16812))
% 28.78/28.54 [1682]~E(x16821,x16822)+E(f444(x16821,x16823,x16824),f444(x16822,x16823,x16824))
% 28.78/28.54 [1683]~E(x16831,x16832)+E(f444(x16833,x16831,x16834),f444(x16833,x16832,x16834))
% 28.78/28.54 [1684]~E(x16841,x16842)+E(f444(x16843,x16844,x16841),f444(x16843,x16844,x16842))
% 28.78/28.54 [1685]~E(x16851,x16852)+E(f445(x16851,x16853,x16854,x16855,x16856),f445(x16852,x16853,x16854,x16855,x16856))
% 28.78/28.54 [1686]~E(x16861,x16862)+E(f445(x16863,x16861,x16864,x16865,x16866),f445(x16863,x16862,x16864,x16865,x16866))
% 28.78/28.54 [1687]~E(x16871,x16872)+E(f445(x16873,x16874,x16871,x16875,x16876),f445(x16873,x16874,x16872,x16875,x16876))
% 28.78/28.54 [1688]~E(x16881,x16882)+E(f445(x16883,x16884,x16885,x16881,x16886),f445(x16883,x16884,x16885,x16882,x16886))
% 28.78/28.54 [1689]~E(x16891,x16892)+E(f445(x16893,x16894,x16895,x16896,x16891),f445(x16893,x16894,x16895,x16896,x16892))
% 28.78/28.54 [1690]~E(x16901,x16902)+E(f456(x16901,x16903),f456(x16902,x16903))
% 28.78/28.54 [1691]~E(x16911,x16912)+E(f456(x16913,x16911),f456(x16913,x16912))
% 28.78/28.54 [1692]~E(x16921,x16922)+E(f414(x16921,x16923,x16924,x16925,x16926,x16927),f414(x16922,x16923,x16924,x16925,x16926,x16927))
% 28.78/28.54 [1693]~E(x16931,x16932)+E(f414(x16933,x16931,x16934,x16935,x16936,x16937),f414(x16933,x16932,x16934,x16935,x16936,x16937))
% 28.78/28.54 [1694]~E(x16941,x16942)+E(f414(x16943,x16944,x16941,x16945,x16946,x16947),f414(x16943,x16944,x16942,x16945,x16946,x16947))
% 28.78/28.54 [1695]~E(x16951,x16952)+E(f414(x16953,x16954,x16955,x16951,x16956,x16957),f414(x16953,x16954,x16955,x16952,x16956,x16957))
% 28.78/28.54 [1696]~E(x16961,x16962)+E(f414(x16963,x16964,x16965,x16966,x16961,x16967),f414(x16963,x16964,x16965,x16966,x16962,x16967))
% 28.78/28.54 [1697]~E(x16971,x16972)+E(f414(x16973,x16974,x16975,x16976,x16977,x16971),f414(x16973,x16974,x16975,x16976,x16977,x16972))
% 28.78/28.54 [1698]~E(x16981,x16982)+E(f38(x16981),f38(x16982))
% 28.78/28.54 [1699]~E(x16991,x16992)+E(f196(x16991),f196(x16992))
% 28.78/28.54 [1700]~E(x17001,x17002)+E(f176(x17001,x17003,x17004),f176(x17002,x17003,x17004))
% 28.78/28.54 [1701]~E(x17011,x17012)+E(f176(x17013,x17011,x17014),f176(x17013,x17012,x17014))
% 28.78/28.54 [1702]~E(x17021,x17022)+E(f176(x17023,x17024,x17021),f176(x17023,x17024,x17022))
% 28.78/28.54 [1703]~E(x17031,x17032)+E(f694(x17031,x17033),f694(x17032,x17033))
% 28.78/28.54 [1704]~E(x17041,x17042)+E(f694(x17043,x17041),f694(x17043,x17042))
% 28.78/28.54 [1705]~E(x17051,x17052)+E(f71(x17051,x17053,x17054,x17055),f71(x17052,x17053,x17054,x17055))
% 28.78/28.54 [1706]~E(x17061,x17062)+E(f71(x17063,x17061,x17064,x17065),f71(x17063,x17062,x17064,x17065))
% 28.78/28.54 [1707]~E(x17071,x17072)+E(f71(x17073,x17074,x17071,x17075),f71(x17073,x17074,x17072,x17075))
% 28.78/28.54 [1708]~E(x17081,x17082)+E(f71(x17083,x17084,x17085,x17081),f71(x17083,x17084,x17085,x17082))
% 28.78/28.54 [1709]~E(x17091,x17092)+E(f596(x17091),f596(x17092))
% 28.78/28.54 [1710]~E(x17101,x17102)+E(f186(x17101,x17103),f186(x17102,x17103))
% 28.78/28.54 [1711]~E(x17111,x17112)+E(f186(x17113,x17111),f186(x17113,x17112))
% 28.78/28.54 [1712]~E(x17121,x17122)+E(f602(x17121,x17123,x17124,x17125),f602(x17122,x17123,x17124,x17125))
% 28.78/28.54 [1713]~E(x17131,x17132)+E(f602(x17133,x17131,x17134,x17135),f602(x17133,x17132,x17134,x17135))
% 28.78/28.54 [1714]~E(x17141,x17142)+E(f602(x17143,x17144,x17141,x17145),f602(x17143,x17144,x17142,x17145))
% 28.78/28.54 [1715]~E(x17151,x17152)+E(f602(x17153,x17154,x17155,x17151),f602(x17153,x17154,x17155,x17152))
% 28.78/28.54 [1716]~E(x17161,x17162)+E(f738(x17161,x17163),f738(x17162,x17163))
% 28.78/28.54 [1717]~E(x17171,x17172)+E(f738(x17173,x17171),f738(x17173,x17172))
% 28.78/28.54 [1718]~E(x17181,x17182)+E(f676(x17181,x17183,x17184,x17185,x17186),f676(x17182,x17183,x17184,x17185,x17186))
% 28.78/28.54 [1719]~E(x17191,x17192)+E(f676(x17193,x17191,x17194,x17195,x17196),f676(x17193,x17192,x17194,x17195,x17196))
% 28.78/28.54 [1720]~E(x17201,x17202)+E(f676(x17203,x17204,x17201,x17205,x17206),f676(x17203,x17204,x17202,x17205,x17206))
% 28.78/28.54 [1721]~E(x17211,x17212)+E(f676(x17213,x17214,x17215,x17211,x17216),f676(x17213,x17214,x17215,x17212,x17216))
% 28.78/28.54 [1722]~E(x17221,x17222)+E(f676(x17223,x17224,x17225,x17226,x17221),f676(x17223,x17224,x17225,x17226,x17222))
% 28.78/28.54 [1723]~E(x17231,x17232)+E(f423(x17231,x17233,x17234),f423(x17232,x17233,x17234))
% 28.78/28.54 [1724]~E(x17241,x17242)+E(f423(x17243,x17241,x17244),f423(x17243,x17242,x17244))
% 28.78/28.54 [1725]~E(x17251,x17252)+E(f423(x17253,x17254,x17251),f423(x17253,x17254,x17252))
% 28.78/28.54 [1726]~E(x17261,x17262)+E(f637(x17261,x17263,x17264,x17265,x17266),f637(x17262,x17263,x17264,x17265,x17266))
% 28.78/28.54 [1727]~E(x17271,x17272)+E(f637(x17273,x17271,x17274,x17275,x17276),f637(x17273,x17272,x17274,x17275,x17276))
% 28.78/28.54 [1728]~E(x17281,x17282)+E(f637(x17283,x17284,x17281,x17285,x17286),f637(x17283,x17284,x17282,x17285,x17286))
% 28.78/28.54 [1729]~E(x17291,x17292)+E(f637(x17293,x17294,x17295,x17291,x17296),f637(x17293,x17294,x17295,x17292,x17296))
% 28.78/28.54 [1730]~E(x17301,x17302)+E(f637(x17303,x17304,x17305,x17306,x17301),f637(x17303,x17304,x17305,x17306,x17302))
% 28.78/28.54 [1731]~E(x17311,x17312)+E(f663(x17311,x17313),f663(x17312,x17313))
% 28.78/28.54 [1732]~E(x17321,x17322)+E(f663(x17323,x17321),f663(x17323,x17322))
% 28.78/28.54 [1733]~E(x17331,x17332)+E(f852(x17331,x17333,x17334,x17335,x17336,x17337,x17338,x17339),f852(x17332,x17333,x17334,x17335,x17336,x17337,x17338,x17339))
% 28.78/28.54 [1734]~E(x17341,x17342)+E(f852(x17343,x17341,x17344,x17345,x17346,x17347,x17348,x17349),f852(x17343,x17342,x17344,x17345,x17346,x17347,x17348,x17349))
% 28.78/28.54 [1735]~E(x17351,x17352)+E(f852(x17353,x17354,x17351,x17355,x17356,x17357,x17358,x17359),f852(x17353,x17354,x17352,x17355,x17356,x17357,x17358,x17359))
% 28.78/28.54 [1736]~E(x17361,x17362)+E(f852(x17363,x17364,x17365,x17361,x17366,x17367,x17368,x17369),f852(x17363,x17364,x17365,x17362,x17366,x17367,x17368,x17369))
% 28.78/28.54 [1737]~E(x17371,x17372)+E(f852(x17373,x17374,x17375,x17376,x17371,x17377,x17378,x17379),f852(x17373,x17374,x17375,x17376,x17372,x17377,x17378,x17379))
% 28.78/28.54 [1738]~E(x17381,x17382)+E(f852(x17383,x17384,x17385,x17386,x17387,x17381,x17388,x17389),f852(x17383,x17384,x17385,x17386,x17387,x17382,x17388,x17389))
% 28.78/28.54 [1739]~E(x17391,x17392)+E(f852(x17393,x17394,x17395,x17396,x17397,x17398,x17391,x17399),f852(x17393,x17394,x17395,x17396,x17397,x17398,x17392,x17399))
% 28.78/28.54 [1740]~E(x17401,x17402)+E(f852(x17403,x17404,x17405,x17406,x17407,x17408,x17409,x17401),f852(x17403,x17404,x17405,x17406,x17407,x17408,x17409,x17402))
% 28.78/28.54 [1741]~E(x17411,x17412)+E(f531(x17411,x17413,x17414),f531(x17412,x17413,x17414))
% 28.78/28.54 [1742]~E(x17421,x17422)+E(f531(x17423,x17421,x17424),f531(x17423,x17422,x17424))
% 28.78/28.54 [1743]~E(x17431,x17432)+E(f531(x17433,x17434,x17431),f531(x17433,x17434,x17432))
% 28.78/28.54 [1744]~E(x17441,x17442)+E(f194(x17441,x17443),f194(x17442,x17443))
% 28.78/28.54 [1745]~E(x17451,x17452)+E(f194(x17453,x17451),f194(x17453,x17452))
% 28.78/28.54 [1746]~E(x17461,x17462)+E(f288(x17461,x17463,x17464),f288(x17462,x17463,x17464))
% 28.78/28.54 [1747]~E(x17471,x17472)+E(f288(x17473,x17471,x17474),f288(x17473,x17472,x17474))
% 28.78/28.54 [1748]~E(x17481,x17482)+E(f288(x17483,x17484,x17481),f288(x17483,x17484,x17482))
% 28.78/28.54 [1749]~E(x17491,x17492)+E(f650(x17491,x17493,x17494,x17495),f650(x17492,x17493,x17494,x17495))
% 28.78/28.54 [1750]~E(x17501,x17502)+E(f650(x17503,x17501,x17504,x17505),f650(x17503,x17502,x17504,x17505))
% 28.78/28.54 [1751]~E(x17511,x17512)+E(f650(x17513,x17514,x17511,x17515),f650(x17513,x17514,x17512,x17515))
% 28.78/28.54 [1752]~E(x17521,x17522)+E(f650(x17523,x17524,x17525,x17521),f650(x17523,x17524,x17525,x17522))
% 28.78/28.54 [1753]~E(x17531,x17532)+E(f432(x17531,x17533,x17534),f432(x17532,x17533,x17534))
% 28.78/28.54 [1754]~E(x17541,x17542)+E(f432(x17543,x17541,x17544),f432(x17543,x17542,x17544))
% 28.78/28.54 [1755]~E(x17551,x17552)+E(f432(x17553,x17554,x17551),f432(x17553,x17554,x17552))
% 28.78/28.54 [1756]~E(x17561,x17562)+E(f822(x17561,x17563),f822(x17562,x17563))
% 28.78/28.54 [1757]~E(x17571,x17572)+E(f822(x17573,x17571),f822(x17573,x17572))
% 28.78/28.54 [1758]~E(x17581,x17582)+E(f660(x17581,x17583,x17584),f660(x17582,x17583,x17584))
% 28.78/28.54 [1759]~E(x17591,x17592)+E(f660(x17593,x17591,x17594),f660(x17593,x17592,x17594))
% 28.78/28.54 [1760]~E(x17601,x17602)+E(f660(x17603,x17604,x17601),f660(x17603,x17604,x17602))
% 28.78/28.54 [1761]~E(x17611,x17612)+E(f689(x17611,x17613,x17614,x17615),f689(x17612,x17613,x17614,x17615))
% 28.78/28.54 [1762]~E(x17621,x17622)+E(f689(x17623,x17621,x17624,x17625),f689(x17623,x17622,x17624,x17625))
% 28.78/28.54 [1763]~E(x17631,x17632)+E(f689(x17633,x17634,x17631,x17635),f689(x17633,x17634,x17632,x17635))
% 28.78/28.54 [1764]~E(x17641,x17642)+E(f689(x17643,x17644,x17645,x17641),f689(x17643,x17644,x17645,x17642))
% 28.78/28.54 [1765]~E(x17651,x17652)+E(f326(x17651),f326(x17652))
% 28.78/28.54 [1766]~E(x17661,x17662)+E(f450(x17661,x17663,x17664,x17665,x17666,x17667,x17668),f450(x17662,x17663,x17664,x17665,x17666,x17667,x17668))
% 28.78/28.54 [1767]~E(x17671,x17672)+E(f450(x17673,x17671,x17674,x17675,x17676,x17677,x17678),f450(x17673,x17672,x17674,x17675,x17676,x17677,x17678))
% 28.78/28.54 [1768]~E(x17681,x17682)+E(f450(x17683,x17684,x17681,x17685,x17686,x17687,x17688),f450(x17683,x17684,x17682,x17685,x17686,x17687,x17688))
% 28.78/28.54 [1769]~E(x17691,x17692)+E(f450(x17693,x17694,x17695,x17691,x17696,x17697,x17698),f450(x17693,x17694,x17695,x17692,x17696,x17697,x17698))
% 28.78/28.54 [1770]~E(x17701,x17702)+E(f450(x17703,x17704,x17705,x17706,x17701,x17707,x17708),f450(x17703,x17704,x17705,x17706,x17702,x17707,x17708))
% 28.78/28.54 [1771]~E(x17711,x17712)+E(f450(x17713,x17714,x17715,x17716,x17717,x17711,x17718),f450(x17713,x17714,x17715,x17716,x17717,x17712,x17718))
% 28.78/28.54 [1772]~E(x17721,x17722)+E(f450(x17723,x17724,x17725,x17726,x17727,x17728,x17721),f450(x17723,x17724,x17725,x17726,x17727,x17728,x17722))
% 28.78/28.54 [1773]~E(x17731,x17732)+E(f677(x17731,x17733,x17734),f677(x17732,x17733,x17734))
% 28.78/28.54 [1774]~E(x17741,x17742)+E(f677(x17743,x17741,x17744),f677(x17743,x17742,x17744))
% 28.78/28.54 [1775]~E(x17751,x17752)+E(f677(x17753,x17754,x17751),f677(x17753,x17754,x17752))
% 28.78/28.54 [1776]~E(x17761,x17762)+E(f190(x17761,x17763,x17764,x17765),f190(x17762,x17763,x17764,x17765))
% 28.78/28.54 [1777]~E(x17771,x17772)+E(f190(x17773,x17771,x17774,x17775),f190(x17773,x17772,x17774,x17775))
% 28.78/28.54 [1778]~E(x17781,x17782)+E(f190(x17783,x17784,x17781,x17785),f190(x17783,x17784,x17782,x17785))
% 28.78/28.54 [1779]~E(x17791,x17792)+E(f190(x17793,x17794,x17795,x17791),f190(x17793,x17794,x17795,x17792))
% 28.78/28.54 [1780]~E(x17801,x17802)+E(f517(x17801,x17803),f517(x17802,x17803))
% 28.78/28.54 [1781]~E(x17811,x17812)+E(f517(x17813,x17811),f517(x17813,x17812))
% 28.78/28.54 [1782]~E(x17821,x17822)+E(f746(x17821,x17823,x17824,x17825,x17826,x17827),f746(x17822,x17823,x17824,x17825,x17826,x17827))
% 28.78/28.54 [1783]~E(x17831,x17832)+E(f746(x17833,x17831,x17834,x17835,x17836,x17837),f746(x17833,x17832,x17834,x17835,x17836,x17837))
% 28.78/28.54 [1784]~E(x17841,x17842)+E(f746(x17843,x17844,x17841,x17845,x17846,x17847),f746(x17843,x17844,x17842,x17845,x17846,x17847))
% 28.78/28.54 [1785]~E(x17851,x17852)+E(f746(x17853,x17854,x17855,x17851,x17856,x17857),f746(x17853,x17854,x17855,x17852,x17856,x17857))
% 28.78/28.54 [1786]~E(x17861,x17862)+E(f746(x17863,x17864,x17865,x17866,x17861,x17867),f746(x17863,x17864,x17865,x17866,x17862,x17867))
% 28.78/28.54 [1787]~E(x17871,x17872)+E(f746(x17873,x17874,x17875,x17876,x17877,x17871),f746(x17873,x17874,x17875,x17876,x17877,x17872))
% 28.78/28.54 [1788]~E(x17881,x17882)+E(f436(x17881,x17883,x17884),f436(x17882,x17883,x17884))
% 28.78/28.54 [1789]~E(x17891,x17892)+E(f436(x17893,x17891,x17894),f436(x17893,x17892,x17894))
% 28.78/28.54 [1790]~E(x17901,x17902)+E(f436(x17903,x17904,x17901),f436(x17903,x17904,x17902))
% 28.78/28.54 [1791]~E(x17911,x17912)+E(f911(x17911,x17913),f911(x17912,x17913))
% 28.78/28.54 [1792]~E(x17921,x17922)+E(f911(x17923,x17921),f911(x17923,x17922))
% 28.78/28.54 [1793]~E(x17931,x17932)+E(f499(x17931,x17933,x17934),f499(x17932,x17933,x17934))
% 28.78/28.54 [1794]~E(x17941,x17942)+E(f499(x17943,x17941,x17944),f499(x17943,x17942,x17944))
% 28.78/28.54 [1795]~E(x17951,x17952)+E(f499(x17953,x17954,x17951),f499(x17953,x17954,x17952))
% 28.78/28.54 [1796]~E(x17961,x17962)+E(f802(x17961,x17963),f802(x17962,x17963))
% 28.78/28.54 [1797]~E(x17971,x17972)+E(f802(x17973,x17971),f802(x17973,x17972))
% 28.78/28.54 [1798]~E(x17981,x17982)+E(f507(x17981,x17983,x17984,x17985,x17986,x17987,x17988),f507(x17982,x17983,x17984,x17985,x17986,x17987,x17988))
% 28.78/28.54 [1799]~E(x17991,x17992)+E(f507(x17993,x17991,x17994,x17995,x17996,x17997,x17998),f507(x17993,x17992,x17994,x17995,x17996,x17997,x17998))
% 28.78/28.54 [1800]~E(x18001,x18002)+E(f507(x18003,x18004,x18001,x18005,x18006,x18007,x18008),f507(x18003,x18004,x18002,x18005,x18006,x18007,x18008))
% 28.78/28.54 [1801]~E(x18011,x18012)+E(f507(x18013,x18014,x18015,x18011,x18016,x18017,x18018),f507(x18013,x18014,x18015,x18012,x18016,x18017,x18018))
% 28.78/28.54 [1802]~E(x18021,x18022)+E(f507(x18023,x18024,x18025,x18026,x18021,x18027,x18028),f507(x18023,x18024,x18025,x18026,x18022,x18027,x18028))
% 28.78/28.54 [1803]~E(x18031,x18032)+E(f507(x18033,x18034,x18035,x18036,x18037,x18031,x18038),f507(x18033,x18034,x18035,x18036,x18037,x18032,x18038))
% 28.78/28.54 [1804]~E(x18041,x18042)+E(f507(x18043,x18044,x18045,x18046,x18047,x18048,x18041),f507(x18043,x18044,x18045,x18046,x18047,x18048,x18042))
% 28.78/28.54 [1805]~E(x18051,x18052)+E(f682(x18051,x18053,x18054,x18055,x18056),f682(x18052,x18053,x18054,x18055,x18056))
% 28.78/28.54 [1806]~E(x18061,x18062)+E(f682(x18063,x18061,x18064,x18065,x18066),f682(x18063,x18062,x18064,x18065,x18066))
% 28.78/28.54 [1807]~E(x18071,x18072)+E(f682(x18073,x18074,x18071,x18075,x18076),f682(x18073,x18074,x18072,x18075,x18076))
% 28.78/28.54 [1808]~E(x18081,x18082)+E(f682(x18083,x18084,x18085,x18081,x18086),f682(x18083,x18084,x18085,x18082,x18086))
% 28.78/28.54 [1809]~E(x18091,x18092)+E(f682(x18093,x18094,x18095,x18096,x18091),f682(x18093,x18094,x18095,x18096,x18092))
% 28.78/28.54 [1810]~E(x18101,x18102)+E(f772(x18101,x18103,x18104),f772(x18102,x18103,x18104))
% 28.78/28.54 [1811]~E(x18111,x18112)+E(f772(x18113,x18111,x18114),f772(x18113,x18112,x18114))
% 28.78/28.54 [1812]~E(x18121,x18122)+E(f772(x18123,x18124,x18121),f772(x18123,x18124,x18122))
% 28.78/28.54 [1813]~E(x18131,x18132)+E(f831(x18131,x18133,x18134,x18135,x18136,x18137),f831(x18132,x18133,x18134,x18135,x18136,x18137))
% 28.78/28.54 [1814]~E(x18141,x18142)+E(f831(x18143,x18141,x18144,x18145,x18146,x18147),f831(x18143,x18142,x18144,x18145,x18146,x18147))
% 28.78/28.54 [1815]~E(x18151,x18152)+E(f831(x18153,x18154,x18151,x18155,x18156,x18157),f831(x18153,x18154,x18152,x18155,x18156,x18157))
% 28.78/28.54 [1816]~E(x18161,x18162)+E(f831(x18163,x18164,x18165,x18161,x18166,x18167),f831(x18163,x18164,x18165,x18162,x18166,x18167))
% 28.78/28.54 [1817]~E(x18171,x18172)+E(f831(x18173,x18174,x18175,x18176,x18171,x18177),f831(x18173,x18174,x18175,x18176,x18172,x18177))
% 28.78/28.54 [1818]~E(x18181,x18182)+E(f831(x18183,x18184,x18185,x18186,x18187,x18181),f831(x18183,x18184,x18185,x18186,x18187,x18182))
% 28.78/28.54 [1819]~E(x18191,x18192)+E(f347(x18191,x18193),f347(x18192,x18193))
% 28.78/28.54 [1820]~E(x18201,x18202)+E(f347(x18203,x18201),f347(x18203,x18202))
% 28.78/28.54 [1821]~E(x18211,x18212)+E(f384(x18211,x18213,x18214,x18215),f384(x18212,x18213,x18214,x18215))
% 28.78/28.54 [1822]~E(x18221,x18222)+E(f384(x18223,x18221,x18224,x18225),f384(x18223,x18222,x18224,x18225))
% 28.78/28.54 [1823]~E(x18231,x18232)+E(f384(x18233,x18234,x18231,x18235),f384(x18233,x18234,x18232,x18235))
% 28.78/28.54 [1824]~E(x18241,x18242)+E(f384(x18243,x18244,x18245,x18241),f384(x18243,x18244,x18245,x18242))
% 28.78/28.54 [1825]~E(x18251,x18252)+E(f898(x18251,x18253,x18254,x18255,x18256,x18257,x18258),f898(x18252,x18253,x18254,x18255,x18256,x18257,x18258))
% 28.78/28.54 [1826]~E(x18261,x18262)+E(f898(x18263,x18261,x18264,x18265,x18266,x18267,x18268),f898(x18263,x18262,x18264,x18265,x18266,x18267,x18268))
% 28.78/28.54 [1827]~E(x18271,x18272)+E(f898(x18273,x18274,x18271,x18275,x18276,x18277,x18278),f898(x18273,x18274,x18272,x18275,x18276,x18277,x18278))
% 28.78/28.54 [1828]~E(x18281,x18282)+E(f898(x18283,x18284,x18285,x18281,x18286,x18287,x18288),f898(x18283,x18284,x18285,x18282,x18286,x18287,x18288))
% 28.78/28.54 [1829]~E(x18291,x18292)+E(f898(x18293,x18294,x18295,x18296,x18291,x18297,x18298),f898(x18293,x18294,x18295,x18296,x18292,x18297,x18298))
% 28.78/28.54 [1830]~E(x18301,x18302)+E(f898(x18303,x18304,x18305,x18306,x18307,x18301,x18308),f898(x18303,x18304,x18305,x18306,x18307,x18302,x18308))
% 28.78/28.54 [1831]~E(x18311,x18312)+E(f898(x18313,x18314,x18315,x18316,x18317,x18318,x18311),f898(x18313,x18314,x18315,x18316,x18317,x18318,x18312))
% 28.78/28.54 [1832]~E(x18321,x18322)+E(f493(x18321,x18323,x18324,x18325,x18326),f493(x18322,x18323,x18324,x18325,x18326))
% 28.78/28.54 [1833]~E(x18331,x18332)+E(f493(x18333,x18331,x18334,x18335,x18336),f493(x18333,x18332,x18334,x18335,x18336))
% 28.78/28.54 [1834]~E(x18341,x18342)+E(f493(x18343,x18344,x18341,x18345,x18346),f493(x18343,x18344,x18342,x18345,x18346))
% 28.78/28.54 [1835]~E(x18351,x18352)+E(f493(x18353,x18354,x18355,x18351,x18356),f493(x18353,x18354,x18355,x18352,x18356))
% 28.78/28.54 [1836]~E(x18361,x18362)+E(f493(x18363,x18364,x18365,x18366,x18361),f493(x18363,x18364,x18365,x18366,x18362))
% 28.78/28.54 [1837]~E(x18371,x18372)+E(f508(x18371,x18373,x18374),f508(x18372,x18373,x18374))
% 28.78/28.54 [1838]~E(x18381,x18382)+E(f508(x18383,x18381,x18384),f508(x18383,x18382,x18384))
% 28.78/28.54 [1839]~E(x18391,x18392)+E(f508(x18393,x18394,x18391),f508(x18393,x18394,x18392))
% 28.78/28.54 [1840]~E(x18401,x18402)+E(f454(x18401,x18403,x18404),f454(x18402,x18403,x18404))
% 28.78/28.54 [1841]~E(x18411,x18412)+E(f454(x18413,x18411,x18414),f454(x18413,x18412,x18414))
% 28.78/28.54 [1842]~E(x18421,x18422)+E(f454(x18423,x18424,x18421),f454(x18423,x18424,x18422))
% 28.78/28.54 [1843]~E(x18431,x18432)+E(f465(x18431,x18433,x18434,x18435,x18436,x18437,x18438),f465(x18432,x18433,x18434,x18435,x18436,x18437,x18438))
% 28.78/28.54 [1844]~E(x18441,x18442)+E(f465(x18443,x18441,x18444,x18445,x18446,x18447,x18448),f465(x18443,x18442,x18444,x18445,x18446,x18447,x18448))
% 28.78/28.54 [1845]~E(x18451,x18452)+E(f465(x18453,x18454,x18451,x18455,x18456,x18457,x18458),f465(x18453,x18454,x18452,x18455,x18456,x18457,x18458))
% 28.78/28.54 [1846]~E(x18461,x18462)+E(f465(x18463,x18464,x18465,x18461,x18466,x18467,x18468),f465(x18463,x18464,x18465,x18462,x18466,x18467,x18468))
% 28.78/28.54 [1847]~E(x18471,x18472)+E(f465(x18473,x18474,x18475,x18476,x18471,x18477,x18478),f465(x18473,x18474,x18475,x18476,x18472,x18477,x18478))
% 28.78/28.54 [1848]~E(x18481,x18482)+E(f465(x18483,x18484,x18485,x18486,x18487,x18481,x18488),f465(x18483,x18484,x18485,x18486,x18487,x18482,x18488))
% 28.78/28.54 [1849]~E(x18491,x18492)+E(f465(x18493,x18494,x18495,x18496,x18497,x18498,x18491),f465(x18493,x18494,x18495,x18496,x18497,x18498,x18492))
% 28.78/28.54 [1850]~E(x18501,x18502)+E(f154(x18501,x18503),f154(x18502,x18503))
% 28.78/28.54 [1851]~E(x18511,x18512)+E(f154(x18513,x18511),f154(x18513,x18512))
% 28.78/28.54 [1852]~E(x18521,x18522)+E(f325(x18521),f325(x18522))
% 28.78/28.54 [1853]~E(x18531,x18532)+E(f394(x18531,x18533,x18534,x18535),f394(x18532,x18533,x18534,x18535))
% 28.78/28.54 [1854]~E(x18541,x18542)+E(f394(x18543,x18541,x18544,x18545),f394(x18543,x18542,x18544,x18545))
% 28.78/28.54 [1855]~E(x18551,x18552)+E(f394(x18553,x18554,x18551,x18555),f394(x18553,x18554,x18552,x18555))
% 28.78/28.54 [1856]~E(x18561,x18562)+E(f394(x18563,x18564,x18565,x18561),f394(x18563,x18564,x18565,x18562))
% 28.78/28.54 [1857]~E(x18571,x18572)+E(f810(x18571,x18573,x18574,x18575,x18576,x18577,x18578),f810(x18572,x18573,x18574,x18575,x18576,x18577,x18578))
% 28.78/28.54 [1858]~E(x18581,x18582)+E(f810(x18583,x18581,x18584,x18585,x18586,x18587,x18588),f810(x18583,x18582,x18584,x18585,x18586,x18587,x18588))
% 28.78/28.54 [1859]~E(x18591,x18592)+E(f810(x18593,x18594,x18591,x18595,x18596,x18597,x18598),f810(x18593,x18594,x18592,x18595,x18596,x18597,x18598))
% 28.78/28.54 [1860]~E(x18601,x18602)+E(f810(x18603,x18604,x18605,x18601,x18606,x18607,x18608),f810(x18603,x18604,x18605,x18602,x18606,x18607,x18608))
% 28.78/28.54 [1861]~E(x18611,x18612)+E(f810(x18613,x18614,x18615,x18616,x18611,x18617,x18618),f810(x18613,x18614,x18615,x18616,x18612,x18617,x18618))
% 28.78/28.54 [1862]~E(x18621,x18622)+E(f810(x18623,x18624,x18625,x18626,x18627,x18621,x18628),f810(x18623,x18624,x18625,x18626,x18627,x18622,x18628))
% 28.78/28.54 [1863]~E(x18631,x18632)+E(f810(x18633,x18634,x18635,x18636,x18637,x18638,x18631),f810(x18633,x18634,x18635,x18636,x18637,x18638,x18632))
% 28.78/28.54 [1864]~E(x18641,x18642)+E(f360(x18641,x18643),f360(x18642,x18643))
% 28.78/28.54 [1865]~E(x18651,x18652)+E(f360(x18653,x18651),f360(x18653,x18652))
% 28.78/28.54 [1866]~E(x18661,x18662)+E(f327(x18661),f327(x18662))
% 28.78/28.54 [1867]~E(x18671,x18672)+E(f418(x18671,x18673,x18674),f418(x18672,x18673,x18674))
% 28.78/28.54 [1868]~E(x18681,x18682)+E(f418(x18683,x18681,x18684),f418(x18683,x18682,x18684))
% 28.78/28.54 [1869]~E(x18691,x18692)+E(f418(x18693,x18694,x18691),f418(x18693,x18694,x18692))
% 28.78/28.54 [1870]~E(x18701,x18702)+E(f561(x18701,x18703,x18704,x18705),f561(x18702,x18703,x18704,x18705))
% 28.78/28.54 [1871]~E(x18711,x18712)+E(f561(x18713,x18711,x18714,x18715),f561(x18713,x18712,x18714,x18715))
% 28.78/28.54 [1872]~E(x18721,x18722)+E(f561(x18723,x18724,x18721,x18725),f561(x18723,x18724,x18722,x18725))
% 28.78/28.54 [1873]~E(x18731,x18732)+E(f561(x18733,x18734,x18735,x18731),f561(x18733,x18734,x18735,x18732))
% 28.78/28.54 [1874]~E(x18741,x18742)+E(f259(x18741),f259(x18742))
% 28.78/28.54 [1875]~E(x18751,x18752)+E(f412(x18751,x18753,x18754,x18755),f412(x18752,x18753,x18754,x18755))
% 28.78/28.54 [1876]~E(x18761,x18762)+E(f412(x18763,x18761,x18764,x18765),f412(x18763,x18762,x18764,x18765))
% 28.78/28.54 [1877]~E(x18771,x18772)+E(f412(x18773,x18774,x18771,x18775),f412(x18773,x18774,x18772,x18775))
% 28.78/28.54 [1878]~E(x18781,x18782)+E(f412(x18783,x18784,x18785,x18781),f412(x18783,x18784,x18785,x18782))
% 28.78/28.54 [1879]~E(x18791,x18792)+E(f877(x18791,x18793,x18794,x18795),f877(x18792,x18793,x18794,x18795))
% 28.78/28.54 [1880]~E(x18801,x18802)+E(f877(x18803,x18801,x18804,x18805),f877(x18803,x18802,x18804,x18805))
% 28.78/28.54 [1881]~E(x18811,x18812)+E(f877(x18813,x18814,x18811,x18815),f877(x18813,x18814,x18812,x18815))
% 28.78/28.54 [1882]~E(x18821,x18822)+E(f877(x18823,x18824,x18825,x18821),f877(x18823,x18824,x18825,x18822))
% 28.78/28.54 [1883]~E(x18831,x18832)+E(f522(x18831,x18833,x18834,x18835),f522(x18832,x18833,x18834,x18835))
% 28.78/28.54 [1884]~E(x18841,x18842)+E(f522(x18843,x18841,x18844,x18845),f522(x18843,x18842,x18844,x18845))
% 28.78/28.54 [1885]~E(x18851,x18852)+E(f522(x18853,x18854,x18851,x18855),f522(x18853,x18854,x18852,x18855))
% 28.78/28.54 [1886]~E(x18861,x18862)+E(f522(x18863,x18864,x18865,x18861),f522(x18863,x18864,x18865,x18862))
% 28.78/28.54 [1887]~E(x18871,x18872)+E(f539(x18871,x18873,x18874),f539(x18872,x18873,x18874))
% 28.78/28.54 [1888]~E(x18881,x18882)+E(f539(x18883,x18881,x18884),f539(x18883,x18882,x18884))
% 28.78/28.54 [1889]~E(x18891,x18892)+E(f539(x18893,x18894,x18891),f539(x18893,x18894,x18892))
% 28.78/28.54 [1890]~E(x18901,x18902)+E(f270(x18901),f270(x18902))
% 28.78/28.54 [1891]~E(x18911,x18912)+E(f110(x18911,x18913,x18914),f110(x18912,x18913,x18914))
% 28.78/28.54 [1892]~E(x18921,x18922)+E(f110(x18923,x18921,x18924),f110(x18923,x18922,x18924))
% 28.78/28.54 [1893]~E(x18931,x18932)+E(f110(x18933,x18934,x18931),f110(x18933,x18934,x18932))
% 28.78/28.54 [1894]~E(x18941,x18942)+E(f678(x18941,x18943,x18944),f678(x18942,x18943,x18944))
% 28.78/28.54 [1895]~E(x18951,x18952)+E(f678(x18953,x18951,x18954),f678(x18953,x18952,x18954))
% 28.78/28.54 [1896]~E(x18961,x18962)+E(f678(x18963,x18964,x18961),f678(x18963,x18964,x18962))
% 28.78/28.54 [1897]~E(x18971,x18972)+E(f268(x18971,x18973,x18974,x18975),f268(x18972,x18973,x18974,x18975))
% 28.78/28.54 [1898]~E(x18981,x18982)+E(f268(x18983,x18981,x18984,x18985),f268(x18983,x18982,x18984,x18985))
% 28.78/28.54 [1899]~E(x18991,x18992)+E(f268(x18993,x18994,x18991,x18995),f268(x18993,x18994,x18992,x18995))
% 28.78/28.54 [1900]~E(x19001,x19002)+E(f268(x19003,x19004,x19005,x19001),f268(x19003,x19004,x19005,x19002))
% 28.78/28.54 [1901]~E(x19011,x19012)+E(f396(x19011,x19013,x19014,x19015),f396(x19012,x19013,x19014,x19015))
% 28.78/28.54 [1902]~E(x19021,x19022)+E(f396(x19023,x19021,x19024,x19025),f396(x19023,x19022,x19024,x19025))
% 28.78/28.54 [1903]~E(x19031,x19032)+E(f396(x19033,x19034,x19031,x19035),f396(x19033,x19034,x19032,x19035))
% 28.78/28.54 [1904]~E(x19041,x19042)+E(f396(x19043,x19044,x19045,x19041),f396(x19043,x19044,x19045,x19042))
% 28.78/28.54 [1905]~E(x19051,x19052)+E(f783(x19051,x19053,x19054,x19055),f783(x19052,x19053,x19054,x19055))
% 28.78/28.54 [1906]~E(x19061,x19062)+E(f783(x19063,x19061,x19064,x19065),f783(x19063,x19062,x19064,x19065))
% 28.78/28.54 [1907]~E(x19071,x19072)+E(f783(x19073,x19074,x19071,x19075),f783(x19073,x19074,x19072,x19075))
% 28.78/28.54 [1908]~E(x19081,x19082)+E(f783(x19083,x19084,x19085,x19081),f783(x19083,x19084,x19085,x19082))
% 28.78/28.54 [1909]~E(x19091,x19092)+E(f386(x19091,x19093,x19094,x19095),f386(x19092,x19093,x19094,x19095))
% 28.78/28.54 [1910]~E(x19101,x19102)+E(f386(x19103,x19101,x19104,x19105),f386(x19103,x19102,x19104,x19105))
% 28.78/28.54 [1911]~E(x19111,x19112)+E(f386(x19113,x19114,x19111,x19115),f386(x19113,x19114,x19112,x19115))
% 28.78/28.54 [1912]~E(x19121,x19122)+E(f386(x19123,x19124,x19125,x19121),f386(x19123,x19124,x19125,x19122))
% 28.78/28.54 [1913]~E(x19131,x19132)+E(f337(x19131,x19133,x19134),f337(x19132,x19133,x19134))
% 28.78/28.54 [1914]~E(x19141,x19142)+E(f337(x19143,x19141,x19144),f337(x19143,x19142,x19144))
% 28.78/28.54 [1915]~E(x19151,x19152)+E(f337(x19153,x19154,x19151),f337(x19153,x19154,x19152))
% 28.78/28.54 [1916]~E(x19161,x19162)+E(f193(x19161),f193(x19162))
% 28.78/28.54 [1917]~E(x19171,x19172)+E(f481(x19171,x19173),f481(x19172,x19173))
% 28.78/28.54 [1918]~E(x19181,x19182)+E(f481(x19183,x19181),f481(x19183,x19182))
% 28.78/28.54 [1919]~E(x19191,x19192)+E(f786(x19191,x19193,x19194),f786(x19192,x19193,x19194))
% 28.78/28.54 [1920]~E(x19201,x19202)+E(f786(x19203,x19201,x19204),f786(x19203,x19202,x19204))
% 28.78/28.54 [1921]~E(x19211,x19212)+E(f786(x19213,x19214,x19211),f786(x19213,x19214,x19212))
% 28.78/28.54 [1922]~E(x19221,x19222)+E(f355(x19221,x19223,x19224),f355(x19222,x19223,x19224))
% 28.78/28.54 [1923]~E(x19231,x19232)+E(f355(x19233,x19231,x19234),f355(x19233,x19232,x19234))
% 28.78/28.54 [1924]~E(x19241,x19242)+E(f355(x19243,x19244,x19241),f355(x19243,x19244,x19242))
% 28.78/28.54 [1925]~E(x19251,x19252)+E(f920(x19251,x19253,x19254),f920(x19252,x19253,x19254))
% 28.78/28.54 [1926]~E(x19261,x19262)+E(f920(x19263,x19261,x19264),f920(x19263,x19262,x19264))
% 28.78/28.54 [1927]~E(x19271,x19272)+E(f920(x19273,x19274,x19271),f920(x19273,x19274,x19272))
% 28.78/28.54 [1928]~E(x19281,x19282)+E(f756(x19281,x19283),f756(x19282,x19283))
% 28.78/28.54 [1929]~E(x19291,x19292)+E(f756(x19293,x19291),f756(x19293,x19292))
% 28.78/28.54 [1930]~E(x19301,x19302)+E(f760(x19301,x19303,x19304,x19305),f760(x19302,x19303,x19304,x19305))
% 28.78/28.54 [1931]~E(x19311,x19312)+E(f760(x19313,x19311,x19314,x19315),f760(x19313,x19312,x19314,x19315))
% 28.78/28.54 [1932]~E(x19321,x19322)+E(f760(x19323,x19324,x19321,x19325),f760(x19323,x19324,x19322,x19325))
% 28.78/28.54 [1933]~E(x19331,x19332)+E(f760(x19333,x19334,x19335,x19331),f760(x19333,x19334,x19335,x19332))
% 28.78/28.54 [1934]~E(x19341,x19342)+E(f549(x19341,x19343,x19344,x19345,x19346,x19347,x19348),f549(x19342,x19343,x19344,x19345,x19346,x19347,x19348))
% 28.78/28.54 [1935]~E(x19351,x19352)+E(f549(x19353,x19351,x19354,x19355,x19356,x19357,x19358),f549(x19353,x19352,x19354,x19355,x19356,x19357,x19358))
% 28.78/28.54 [1936]~E(x19361,x19362)+E(f549(x19363,x19364,x19361,x19365,x19366,x19367,x19368),f549(x19363,x19364,x19362,x19365,x19366,x19367,x19368))
% 28.78/28.54 [1937]~E(x19371,x19372)+E(f549(x19373,x19374,x19375,x19371,x19376,x19377,x19378),f549(x19373,x19374,x19375,x19372,x19376,x19377,x19378))
% 28.78/28.54 [1938]~E(x19381,x19382)+E(f549(x19383,x19384,x19385,x19386,x19381,x19387,x19388),f549(x19383,x19384,x19385,x19386,x19382,x19387,x19388))
% 28.78/28.54 [1939]~E(x19391,x19392)+E(f549(x19393,x19394,x19395,x19396,x19397,x19391,x19398),f549(x19393,x19394,x19395,x19396,x19397,x19392,x19398))
% 28.78/28.54 [1940]~E(x19401,x19402)+E(f549(x19403,x19404,x19405,x19406,x19407,x19408,x19401),f549(x19403,x19404,x19405,x19406,x19407,x19408,x19402))
% 28.78/28.54 [1941]~E(x19411,x19412)+E(f390(x19411,x19413),f390(x19412,x19413))
% 28.78/28.54 [1942]~E(x19421,x19422)+E(f390(x19423,x19421),f390(x19423,x19422))
% 28.78/28.54 [1943]~E(x19431,x19432)+E(f451(x19431,x19433),f451(x19432,x19433))
% 28.78/28.54 [1944]~E(x19441,x19442)+E(f451(x19443,x19441),f451(x19443,x19442))
% 28.78/28.54 [1945]~E(x19451,x19452)+E(f575(x19451,x19453,x19454,x19455),f575(x19452,x19453,x19454,x19455))
% 28.78/28.54 [1946]~E(x19461,x19462)+E(f575(x19463,x19461,x19464,x19465),f575(x19463,x19462,x19464,x19465))
% 28.78/28.54 [1947]~E(x19471,x19472)+E(f575(x19473,x19474,x19471,x19475),f575(x19473,x19474,x19472,x19475))
% 28.78/28.54 [1948]~E(x19481,x19482)+E(f575(x19483,x19484,x19485,x19481),f575(x19483,x19484,x19485,x19482))
% 28.78/28.54 [1949]~E(x19491,x19492)+E(f845(x19491,x19493,x19494),f845(x19492,x19493,x19494))
% 28.78/28.54 [1950]~E(x19501,x19502)+E(f845(x19503,x19501,x19504),f845(x19503,x19502,x19504))
% 28.78/28.54 [1951]~E(x19511,x19512)+E(f845(x19513,x19514,x19511),f845(x19513,x19514,x19512))
% 28.78/28.54 [1952]~E(x19521,x19522)+E(f333(x19521),f333(x19522))
% 28.78/28.54 [1953]~E(x19531,x19532)+E(f361(x19531,x19533),f361(x19532,x19533))
% 28.78/28.54 [1954]~E(x19541,x19542)+E(f361(x19543,x19541),f361(x19543,x19542))
% 28.78/28.54 [1955]~E(x19551,x19552)+E(f893(x19551,x19553,x19554,x19555,x19556),f893(x19552,x19553,x19554,x19555,x19556))
% 28.78/28.54 [1956]~E(x19561,x19562)+E(f893(x19563,x19561,x19564,x19565,x19566),f893(x19563,x19562,x19564,x19565,x19566))
% 28.78/28.54 [1957]~E(x19571,x19572)+E(f893(x19573,x19574,x19571,x19575,x19576),f893(x19573,x19574,x19572,x19575,x19576))
% 28.78/28.54 [1958]~E(x19581,x19582)+E(f893(x19583,x19584,x19585,x19581,x19586),f893(x19583,x19584,x19585,x19582,x19586))
% 28.78/28.54 [1959]~E(x19591,x19592)+E(f893(x19593,x19594,x19595,x19596,x19591),f893(x19593,x19594,x19595,x19596,x19592))
% 28.78/28.54 [1960]~E(x19601,x19602)+E(f795(x19601,x19603,x19604),f795(x19602,x19603,x19604))
% 28.78/28.54 [1961]~E(x19611,x19612)+E(f795(x19613,x19611,x19614),f795(x19613,x19612,x19614))
% 28.78/28.54 [1962]~E(x19621,x19622)+E(f795(x19623,x19624,x19621),f795(x19623,x19624,x19622))
% 28.78/28.54 [1963]~E(x19631,x19632)+E(f67(x19631,x19633),f67(x19632,x19633))
% 28.78/28.54 [1964]~E(x19641,x19642)+E(f67(x19643,x19641),f67(x19643,x19642))
% 28.78/28.54 [1965]~E(x19651,x19652)+E(f397(x19651,x19653,x19654,x19655),f397(x19652,x19653,x19654,x19655))
% 28.78/28.54 [1966]~E(x19661,x19662)+E(f397(x19663,x19661,x19664,x19665),f397(x19663,x19662,x19664,x19665))
% 28.78/28.54 [1967]~E(x19671,x19672)+E(f397(x19673,x19674,x19671,x19675),f397(x19673,x19674,x19672,x19675))
% 28.78/28.54 [1968]~E(x19681,x19682)+E(f397(x19683,x19684,x19685,x19681),f397(x19683,x19684,x19685,x19682))
% 28.78/28.54 [1969]~E(x19691,x19692)+E(f348(x19691,x19693,x19694),f348(x19692,x19693,x19694))
% 28.78/28.54 [1970]~E(x19701,x19702)+E(f348(x19703,x19701,x19704),f348(x19703,x19702,x19704))
% 28.78/28.54 [1971]~E(x19711,x19712)+E(f348(x19713,x19714,x19711),f348(x19713,x19714,x19712))
% 28.78/28.54 [1972]~E(x19721,x19722)+E(f838(x19721,x19723),f838(x19722,x19723))
% 28.78/28.54 [1973]~E(x19731,x19732)+E(f838(x19733,x19731),f838(x19733,x19732))
% 28.78/28.54 [1974]~E(x19741,x19742)+E(f48(x19741,x19743),f48(x19742,x19743))
% 28.78/28.54 [1975]~E(x19751,x19752)+E(f48(x19753,x19751),f48(x19753,x19752))
% 28.78/28.54 [1976]~E(x19761,x19762)+E(f376(x19761,x19763,x19764),f376(x19762,x19763,x19764))
% 28.78/28.54 [1977]~E(x19771,x19772)+E(f376(x19773,x19771,x19774),f376(x19773,x19772,x19774))
% 28.78/28.54 [1978]~E(x19781,x19782)+E(f376(x19783,x19784,x19781),f376(x19783,x19784,x19782))
% 28.78/28.54 [1979]~E(x19791,x19792)+E(f901(x19791,x19793,x19794,x19795,x19796,x19797),f901(x19792,x19793,x19794,x19795,x19796,x19797))
% 28.78/28.54 [1980]~E(x19801,x19802)+E(f901(x19803,x19801,x19804,x19805,x19806,x19807),f901(x19803,x19802,x19804,x19805,x19806,x19807))
% 28.78/28.54 [1981]~E(x19811,x19812)+E(f901(x19813,x19814,x19811,x19815,x19816,x19817),f901(x19813,x19814,x19812,x19815,x19816,x19817))
% 28.78/28.54 [1982]~E(x19821,x19822)+E(f901(x19823,x19824,x19825,x19821,x19826,x19827),f901(x19823,x19824,x19825,x19822,x19826,x19827))
% 28.78/28.54 [1983]~E(x19831,x19832)+E(f901(x19833,x19834,x19835,x19836,x19831,x19837),f901(x19833,x19834,x19835,x19836,x19832,x19837))
% 28.78/28.54 [1984]~E(x19841,x19842)+E(f901(x19843,x19844,x19845,x19846,x19847,x19841),f901(x19843,x19844,x19845,x19846,x19847,x19842))
% 28.78/28.54 [1985]~E(x19851,x19852)+E(f820(x19851),f820(x19852))
% 28.78/28.54 [1986]~E(x19861,x19862)+E(f759(x19861,x19863,x19864),f759(x19862,x19863,x19864))
% 28.78/28.54 [1987]~E(x19871,x19872)+E(f759(x19873,x19871,x19874),f759(x19873,x19872,x19874))
% 28.78/28.54 [1988]~E(x19881,x19882)+E(f759(x19883,x19884,x19881),f759(x19883,x19884,x19882))
% 28.78/28.54 [1989]~E(x19891,x19892)+E(f701(x19891,x19893,x19894,x19895,x19896),f701(x19892,x19893,x19894,x19895,x19896))
% 28.78/28.54 [1990]~E(x19901,x19902)+E(f701(x19903,x19901,x19904,x19905,x19906),f701(x19903,x19902,x19904,x19905,x19906))
% 28.78/28.54 [1991]~E(x19911,x19912)+E(f701(x19913,x19914,x19911,x19915,x19916),f701(x19913,x19914,x19912,x19915,x19916))
% 28.78/28.54 [1992]~E(x19921,x19922)+E(f701(x19923,x19924,x19925,x19921,x19926),f701(x19923,x19924,x19925,x19922,x19926))
% 28.78/28.54 [1993]~E(x19931,x19932)+E(f701(x19933,x19934,x19935,x19936,x19931),f701(x19933,x19934,x19935,x19936,x19932))
% 28.78/28.54 [1994]~E(x19941,x19942)+E(f543(x19941,x19943,x19944),f543(x19942,x19943,x19944))
% 28.78/28.54 [1995]~E(x19951,x19952)+E(f543(x19953,x19951,x19954),f543(x19953,x19952,x19954))
% 28.78/28.54 [1996]~E(x19961,x19962)+E(f543(x19963,x19964,x19961),f543(x19963,x19964,x19962))
% 28.78/28.54 [1997]~E(x19971,x19972)+E(f229(x19971,x19973),f229(x19972,x19973))
% 28.78/28.54 [1998]~E(x19981,x19982)+E(f229(x19983,x19981),f229(x19983,x19982))
% 28.78/28.54 [1999]~E(x19991,x19992)+E(f187(x19991,x19993,x19994,x19995),f187(x19992,x19993,x19994,x19995))
% 28.78/28.54 [2000]~E(x20001,x20002)+E(f187(x20003,x20001,x20004,x20005),f187(x20003,x20002,x20004,x20005))
% 28.78/28.54 [2001]~E(x20011,x20012)+E(f187(x20013,x20014,x20011,x20015),f187(x20013,x20014,x20012,x20015))
% 28.78/28.54 [2002]~E(x20021,x20022)+E(f187(x20023,x20024,x20025,x20021),f187(x20023,x20024,x20025,x20022))
% 28.78/28.54 [2003]~E(x20031,x20032)+E(f574(x20031,x20033,x20034,x20035),f574(x20032,x20033,x20034,x20035))
% 28.78/28.54 [2004]~E(x20041,x20042)+E(f574(x20043,x20041,x20044,x20045),f574(x20043,x20042,x20044,x20045))
% 28.78/28.54 [2005]~E(x20051,x20052)+E(f574(x20053,x20054,x20051,x20055),f574(x20053,x20054,x20052,x20055))
% 28.78/28.54 [2006]~E(x20061,x20062)+E(f574(x20063,x20064,x20065,x20061),f574(x20063,x20064,x20065,x20062))
% 28.78/28.54 [2007]~E(x20071,x20072)+E(f453(x20071,x20073),f453(x20072,x20073))
% 28.78/28.54 [2008]~E(x20081,x20082)+E(f453(x20083,x20081),f453(x20083,x20082))
% 28.78/28.54 [2009]~E(x20091,x20092)+E(f475(x20091,x20093,x20094),f475(x20092,x20093,x20094))
% 28.78/28.54 [2010]~E(x20101,x20102)+E(f475(x20103,x20101,x20104),f475(x20103,x20102,x20104))
% 28.78/28.54 [2011]~E(x20111,x20112)+E(f475(x20113,x20114,x20111),f475(x20113,x20114,x20112))
% 28.78/28.54 [2012]~E(x20121,x20122)+E(f467(x20121,x20123,x20124,x20125),f467(x20122,x20123,x20124,x20125))
% 28.78/28.54 [2013]~E(x20131,x20132)+E(f467(x20133,x20131,x20134,x20135),f467(x20133,x20132,x20134,x20135))
% 28.78/28.54 [2014]~E(x20141,x20142)+E(f467(x20143,x20144,x20141,x20145),f467(x20143,x20144,x20142,x20145))
% 28.78/28.54 [2015]~E(x20151,x20152)+E(f467(x20153,x20154,x20155,x20151),f467(x20153,x20154,x20155,x20152))
% 28.78/28.54 [2016]~E(x20161,x20162)+E(f848(x20161,x20163,x20164,x20165,x20166,x20167,x20168,x20169),f848(x20162,x20163,x20164,x20165,x20166,x20167,x20168,x20169))
% 28.78/28.54 [2017]~E(x20171,x20172)+E(f848(x20173,x20171,x20174,x20175,x20176,x20177,x20178,x20179),f848(x20173,x20172,x20174,x20175,x20176,x20177,x20178,x20179))
% 28.78/28.54 [2018]~E(x20181,x20182)+E(f848(x20183,x20184,x20181,x20185,x20186,x20187,x20188,x20189),f848(x20183,x20184,x20182,x20185,x20186,x20187,x20188,x20189))
% 28.78/28.54 [2019]~E(x20191,x20192)+E(f848(x20193,x20194,x20195,x20191,x20196,x20197,x20198,x20199),f848(x20193,x20194,x20195,x20192,x20196,x20197,x20198,x20199))
% 28.78/28.54 [2020]~E(x20201,x20202)+E(f848(x20203,x20204,x20205,x20206,x20201,x20207,x20208,x20209),f848(x20203,x20204,x20205,x20206,x20202,x20207,x20208,x20209))
% 28.78/28.54 [2021]~E(x20211,x20212)+E(f848(x20213,x20214,x20215,x20216,x20217,x20211,x20218,x20219),f848(x20213,x20214,x20215,x20216,x20217,x20212,x20218,x20219))
% 28.78/28.54 [2022]~E(x20221,x20222)+E(f848(x20223,x20224,x20225,x20226,x20227,x20228,x20221,x20229),f848(x20223,x20224,x20225,x20226,x20227,x20228,x20222,x20229))
% 28.78/28.54 [2023]~E(x20231,x20232)+E(f848(x20233,x20234,x20235,x20236,x20237,x20238,x20239,x20231),f848(x20233,x20234,x20235,x20236,x20237,x20238,x20239,x20232))
% 28.78/28.54 [2024]~E(x20241,x20242)+E(f591(x20241,x20243,x20244),f591(x20242,x20243,x20244))
% 28.78/28.54 [2025]~E(x20251,x20252)+E(f591(x20253,x20251,x20254),f591(x20253,x20252,x20254))
% 28.78/28.54 [2026]~E(x20261,x20262)+E(f591(x20263,x20264,x20261),f591(x20263,x20264,x20262))
% 28.78/28.54 [2027]~E(x20271,x20272)+E(f502(x20271,x20273,x20274),f502(x20272,x20273,x20274))
% 28.78/28.54 [2028]~E(x20281,x20282)+E(f502(x20283,x20281,x20284),f502(x20283,x20282,x20284))
% 28.78/28.54 [2029]~E(x20291,x20292)+E(f502(x20293,x20294,x20291),f502(x20293,x20294,x20292))
% 28.78/28.54 [2030]~E(x20301,x20302)+E(f35(x20301),f35(x20302))
% 28.78/28.54 [2031]~E(x20311,x20312)+E(f382(x20311,x20313,x20314,x20315,x20316),f382(x20312,x20313,x20314,x20315,x20316))
% 28.78/28.54 [2032]~E(x20321,x20322)+E(f382(x20323,x20321,x20324,x20325,x20326),f382(x20323,x20322,x20324,x20325,x20326))
% 28.78/28.54 [2033]~E(x20331,x20332)+E(f382(x20333,x20334,x20331,x20335,x20336),f382(x20333,x20334,x20332,x20335,x20336))
% 28.78/28.54 [2034]~E(x20341,x20342)+E(f382(x20343,x20344,x20345,x20341,x20346),f382(x20343,x20344,x20345,x20342,x20346))
% 28.78/28.54 [2035]~E(x20351,x20352)+E(f382(x20353,x20354,x20355,x20356,x20351),f382(x20353,x20354,x20355,x20356,x20352))
% 28.78/28.54 [2036]~E(x20361,x20362)+E(f719(x20361,x20363,x20364,x20365),f719(x20362,x20363,x20364,x20365))
% 28.78/28.54 [2037]~E(x20371,x20372)+E(f719(x20373,x20371,x20374,x20375),f719(x20373,x20372,x20374,x20375))
% 28.78/28.54 [2038]~E(x20381,x20382)+E(f719(x20383,x20384,x20381,x20385),f719(x20383,x20384,x20382,x20385))
% 28.78/28.54 [2039]~E(x20391,x20392)+E(f719(x20393,x20394,x20395,x20391),f719(x20393,x20394,x20395,x20392))
% 28.78/28.54 [2040]~E(x20401,x20402)+E(f375(x20401,x20403,x20404),f375(x20402,x20403,x20404))
% 28.78/28.54 [2041]~E(x20411,x20412)+E(f375(x20413,x20411,x20414),f375(x20413,x20412,x20414))
% 28.78/28.54 [2042]~E(x20421,x20422)+E(f375(x20423,x20424,x20421),f375(x20423,x20424,x20422))
% 28.78/28.54 [2043]~E(x20431,x20432)+E(f871(x20431,x20433,x20434),f871(x20432,x20433,x20434))
% 28.78/28.54 [2044]~E(x20441,x20442)+E(f871(x20443,x20441,x20444),f871(x20443,x20442,x20444))
% 28.78/28.54 [2045]~E(x20451,x20452)+E(f871(x20453,x20454,x20451),f871(x20453,x20454,x20452))
% 28.78/28.54 [2046]~E(x20461,x20462)+E(f312(x20461,x20463,x20464,x20465),f312(x20462,x20463,x20464,x20465))
% 28.78/28.54 [2047]~E(x20471,x20472)+E(f312(x20473,x20471,x20474,x20475),f312(x20473,x20472,x20474,x20475))
% 28.78/28.54 [2048]~E(x20481,x20482)+E(f312(x20483,x20484,x20481,x20485),f312(x20483,x20484,x20482,x20485))
% 28.78/28.54 [2049]~E(x20491,x20492)+E(f312(x20493,x20494,x20495,x20491),f312(x20493,x20494,x20495,x20492))
% 28.78/28.54 [2050]~E(x20501,x20502)+E(f452(x20501,x20503),f452(x20502,x20503))
% 28.78/28.54 [2051]~E(x20511,x20512)+E(f452(x20513,x20511),f452(x20513,x20512))
% 28.78/28.54 [2052]~E(x20521,x20522)+E(f369(x20521,x20523,x20524,x20525),f369(x20522,x20523,x20524,x20525))
% 28.78/28.54 [2053]~E(x20531,x20532)+E(f369(x20533,x20531,x20534,x20535),f369(x20533,x20532,x20534,x20535))
% 28.78/28.54 [2054]~E(x20541,x20542)+E(f369(x20543,x20544,x20541,x20545),f369(x20543,x20544,x20542,x20545))
% 28.78/28.54 [2055]~E(x20551,x20552)+E(f369(x20553,x20554,x20555,x20551),f369(x20553,x20554,x20555,x20552))
% 28.78/28.54 [2056]~E(x20561,x20562)+E(f459(x20561,x20563,x20564,x20565,x20566,x20567),f459(x20562,x20563,x20564,x20565,x20566,x20567))
% 28.78/28.54 [2057]~E(x20571,x20572)+E(f459(x20573,x20571,x20574,x20575,x20576,x20577),f459(x20573,x20572,x20574,x20575,x20576,x20577))
% 28.78/28.54 [2058]~E(x20581,x20582)+E(f459(x20583,x20584,x20581,x20585,x20586,x20587),f459(x20583,x20584,x20582,x20585,x20586,x20587))
% 28.78/28.54 [2059]~E(x20591,x20592)+E(f459(x20593,x20594,x20595,x20591,x20596,x20597),f459(x20593,x20594,x20595,x20592,x20596,x20597))
% 28.78/28.54 [2060]~E(x20601,x20602)+E(f459(x20603,x20604,x20605,x20606,x20601,x20607),f459(x20603,x20604,x20605,x20606,x20602,x20607))
% 28.78/28.54 [2061]~E(x20611,x20612)+E(f459(x20613,x20614,x20615,x20616,x20617,x20611),f459(x20613,x20614,x20615,x20616,x20617,x20612))
% 28.78/28.54 [2062]~E(x20621,x20622)+E(f683(x20621,x20623,x20624,x20625),f683(x20622,x20623,x20624,x20625))
% 28.78/28.54 [2063]~E(x20631,x20632)+E(f683(x20633,x20631,x20634,x20635),f683(x20633,x20632,x20634,x20635))
% 28.78/28.54 [2064]~E(x20641,x20642)+E(f683(x20643,x20644,x20641,x20645),f683(x20643,x20644,x20642,x20645))
% 28.78/28.54 [2065]~E(x20651,x20652)+E(f683(x20653,x20654,x20655,x20651),f683(x20653,x20654,x20655,x20652))
% 28.78/28.54 [2066]~E(x20661,x20662)+E(f547(x20661,x20663,x20664,x20665,x20666,x20667,x20668),f547(x20662,x20663,x20664,x20665,x20666,x20667,x20668))
% 28.78/28.54 [2067]~E(x20671,x20672)+E(f547(x20673,x20671,x20674,x20675,x20676,x20677,x20678),f547(x20673,x20672,x20674,x20675,x20676,x20677,x20678))
% 28.78/28.54 [2068]~E(x20681,x20682)+E(f547(x20683,x20684,x20681,x20685,x20686,x20687,x20688),f547(x20683,x20684,x20682,x20685,x20686,x20687,x20688))
% 28.78/28.54 [2069]~E(x20691,x20692)+E(f547(x20693,x20694,x20695,x20691,x20696,x20697,x20698),f547(x20693,x20694,x20695,x20692,x20696,x20697,x20698))
% 28.78/28.54 [2070]~E(x20701,x20702)+E(f547(x20703,x20704,x20705,x20706,x20701,x20707,x20708),f547(x20703,x20704,x20705,x20706,x20702,x20707,x20708))
% 28.78/28.54 [2071]~E(x20711,x20712)+E(f547(x20713,x20714,x20715,x20716,x20717,x20711,x20718),f547(x20713,x20714,x20715,x20716,x20717,x20712,x20718))
% 28.78/28.54 [2072]~E(x20721,x20722)+E(f547(x20723,x20724,x20725,x20726,x20727,x20728,x20721),f547(x20723,x20724,x20725,x20726,x20727,x20728,x20722))
% 28.78/28.54 [2073]~E(x20731,x20732)+E(f651(x20731,x20733,x20734,x20735),f651(x20732,x20733,x20734,x20735))
% 28.78/28.54 [2074]~E(x20741,x20742)+E(f651(x20743,x20741,x20744,x20745),f651(x20743,x20742,x20744,x20745))
% 28.78/28.54 [2075]~E(x20751,x20752)+E(f651(x20753,x20754,x20751,x20755),f651(x20753,x20754,x20752,x20755))
% 28.78/28.54 [2076]~E(x20761,x20762)+E(f651(x20763,x20764,x20765,x20761),f651(x20763,x20764,x20765,x20762))
% 28.78/28.54 [2077]~E(x20771,x20772)+E(f661(x20771,x20773,x20774,x20775),f661(x20772,x20773,x20774,x20775))
% 28.78/28.54 [2078]~E(x20781,x20782)+E(f661(x20783,x20781,x20784,x20785),f661(x20783,x20782,x20784,x20785))
% 28.78/28.54 [2079]~E(x20791,x20792)+E(f661(x20793,x20794,x20791,x20795),f661(x20793,x20794,x20792,x20795))
% 28.78/28.54 [2080]~E(x20801,x20802)+E(f661(x20803,x20804,x20805,x20801),f661(x20803,x20804,x20805,x20802))
% 28.78/28.54 [2081]~E(x20811,x20812)+E(f713(x20811,x20813,x20814),f713(x20812,x20813,x20814))
% 28.78/28.54 [2082]~E(x20821,x20822)+E(f713(x20823,x20821,x20824),f713(x20823,x20822,x20824))
% 28.78/28.54 [2083]~E(x20831,x20832)+E(f713(x20833,x20834,x20831),f713(x20833,x20834,x20832))
% 28.78/28.54 [2084]~E(x20841,x20842)+E(f859(x20841,x20843,x20844,x20845),f859(x20842,x20843,x20844,x20845))
% 28.78/28.54 [2085]~E(x20851,x20852)+E(f859(x20853,x20851,x20854,x20855),f859(x20853,x20852,x20854,x20855))
% 28.78/28.54 [2086]~E(x20861,x20862)+E(f859(x20863,x20864,x20861,x20865),f859(x20863,x20864,x20862,x20865))
% 28.78/28.54 [2087]~E(x20871,x20872)+E(f859(x20873,x20874,x20875,x20871),f859(x20873,x20874,x20875,x20872))
% 28.78/28.54 [2088]~E(x20881,x20882)+E(f496(x20881,x20883,x20884),f496(x20882,x20883,x20884))
% 28.78/28.54 [2089]~E(x20891,x20892)+E(f496(x20893,x20891,x20894),f496(x20893,x20892,x20894))
% 28.78/28.54 [2090]~E(x20901,x20902)+E(f496(x20903,x20904,x20901),f496(x20903,x20904,x20902))
% 28.78/28.54 [2091]~E(x20911,x20912)+E(f492(x20911,x20913,x20914,x20915,x20916),f492(x20912,x20913,x20914,x20915,x20916))
% 28.78/28.54 [2092]~E(x20921,x20922)+E(f492(x20923,x20921,x20924,x20925,x20926),f492(x20923,x20922,x20924,x20925,x20926))
% 28.78/28.54 [2093]~E(x20931,x20932)+E(f492(x20933,x20934,x20931,x20935,x20936),f492(x20933,x20934,x20932,x20935,x20936))
% 28.78/28.54 [2094]~E(x20941,x20942)+E(f492(x20943,x20944,x20945,x20941,x20946),f492(x20943,x20944,x20945,x20942,x20946))
% 28.78/28.54 [2095]~E(x20951,x20952)+E(f492(x20953,x20954,x20955,x20956,x20951),f492(x20953,x20954,x20955,x20956,x20952))
% 28.78/28.54 [2096]~E(x20961,x20962)+E(f357(x20961,x20963,x20964),f357(x20962,x20963,x20964))
% 28.78/28.54 [2097]~E(x20971,x20972)+E(f357(x20973,x20971,x20974),f357(x20973,x20972,x20974))
% 28.78/28.54 [2098]~E(x20981,x20982)+E(f357(x20983,x20984,x20981),f357(x20983,x20984,x20982))
% 28.78/28.54 [2099]~E(x20991,x20992)+E(f754(x20991,x20993,x20994,x20995,x20996,x20997,x20998,x20999),f754(x20992,x20993,x20994,x20995,x20996,x20997,x20998,x20999))
% 28.78/28.54 [2100]~E(x21001,x21002)+E(f754(x21003,x21001,x21004,x21005,x21006,x21007,x21008,x21009),f754(x21003,x21002,x21004,x21005,x21006,x21007,x21008,x21009))
% 28.78/28.54 [2101]~E(x21011,x21012)+E(f754(x21013,x21014,x21011,x21015,x21016,x21017,x21018,x21019),f754(x21013,x21014,x21012,x21015,x21016,x21017,x21018,x21019))
% 28.78/28.54 [2102]~E(x21021,x21022)+E(f754(x21023,x21024,x21025,x21021,x21026,x21027,x21028,x21029),f754(x21023,x21024,x21025,x21022,x21026,x21027,x21028,x21029))
% 28.78/28.54 [2103]~E(x21031,x21032)+E(f754(x21033,x21034,x21035,x21036,x21031,x21037,x21038,x21039),f754(x21033,x21034,x21035,x21036,x21032,x21037,x21038,x21039))
% 28.78/28.54 [2104]~E(x21041,x21042)+E(f754(x21043,x21044,x21045,x21046,x21047,x21041,x21048,x21049),f754(x21043,x21044,x21045,x21046,x21047,x21042,x21048,x21049))
% 28.78/28.54 [2105]~E(x21051,x21052)+E(f754(x21053,x21054,x21055,x21056,x21057,x21058,x21051,x21059),f754(x21053,x21054,x21055,x21056,x21057,x21058,x21052,x21059))
% 28.78/28.54 [2106]~E(x21061,x21062)+E(f754(x21063,x21064,x21065,x21066,x21067,x21068,x21069,x21061),f754(x21063,x21064,x21065,x21066,x21067,x21068,x21069,x21062))
% 28.78/28.54 [2107]~E(x21071,x21072)+E(f866(x21071,x21073,x21074,x21075,x21076,x21077,x21078),f866(x21072,x21073,x21074,x21075,x21076,x21077,x21078))
% 28.78/28.54 [2108]~E(x21081,x21082)+E(f866(x21083,x21081,x21084,x21085,x21086,x21087,x21088),f866(x21083,x21082,x21084,x21085,x21086,x21087,x21088))
% 28.78/28.54 [2109]~E(x21091,x21092)+E(f866(x21093,x21094,x21091,x21095,x21096,x21097,x21098),f866(x21093,x21094,x21092,x21095,x21096,x21097,x21098))
% 28.78/28.54 [2110]~E(x21101,x21102)+E(f866(x21103,x21104,x21105,x21101,x21106,x21107,x21108),f866(x21103,x21104,x21105,x21102,x21106,x21107,x21108))
% 28.78/28.54 [2111]~E(x21111,x21112)+E(f866(x21113,x21114,x21115,x21116,x21111,x21117,x21118),f866(x21113,x21114,x21115,x21116,x21112,x21117,x21118))
% 28.78/28.54 [2112]~E(x21121,x21122)+E(f866(x21123,x21124,x21125,x21126,x21127,x21121,x21128),f866(x21123,x21124,x21125,x21126,x21127,x21122,x21128))
% 28.78/28.54 [2113]~E(x21131,x21132)+E(f866(x21133,x21134,x21135,x21136,x21137,x21138,x21131),f866(x21133,x21134,x21135,x21136,x21137,x21138,x21132))
% 28.78/28.54 [2114]~E(x21141,x21142)+E(f206(x21141,x21143),f206(x21142,x21143))
% 28.78/28.54 [2115]~E(x21151,x21152)+E(f206(x21153,x21151),f206(x21153,x21152))
% 28.78/28.54 [2116]~E(x21161,x21162)+E(f313(x21161,x21163,x21164),f313(x21162,x21163,x21164))
% 28.78/28.54 [2117]~E(x21171,x21172)+E(f313(x21173,x21171,x21174),f313(x21173,x21172,x21174))
% 28.78/28.54 [2118]~E(x21181,x21182)+E(f313(x21183,x21184,x21181),f313(x21183,x21184,x21182))
% 28.78/28.54 [2119]~E(x21191,x21192)+E(f172(x21191),f172(x21192))
% 28.78/28.54 [2120]~E(x21201,x21202)+E(f615(x21201,x21203,x21204,x21205),f615(x21202,x21203,x21204,x21205))
% 28.78/28.54 [2121]~E(x21211,x21212)+E(f615(x21213,x21211,x21214,x21215),f615(x21213,x21212,x21214,x21215))
% 28.78/28.54 [2122]~E(x21221,x21222)+E(f615(x21223,x21224,x21221,x21225),f615(x21223,x21224,x21222,x21225))
% 28.78/28.54 [2123]~E(x21231,x21232)+E(f615(x21233,x21234,x21235,x21231),f615(x21233,x21234,x21235,x21232))
% 28.78/28.54 [2124]~E(x21241,x21242)+E(f455(x21241,x21243,x21244,x21245),f455(x21242,x21243,x21244,x21245))
% 28.78/28.54 [2125]~E(x21251,x21252)+E(f455(x21253,x21251,x21254,x21255),f455(x21253,x21252,x21254,x21255))
% 28.78/28.54 [2126]~E(x21261,x21262)+E(f455(x21263,x21264,x21261,x21265),f455(x21263,x21264,x21262,x21265))
% 28.78/28.54 [2127]~E(x21271,x21272)+E(f455(x21273,x21274,x21275,x21271),f455(x21273,x21274,x21275,x21272))
% 28.78/28.54 [2128]~E(x21281,x21282)+E(f918(x21281,x21283),f918(x21282,x21283))
% 28.78/28.54 [2129]~E(x21291,x21292)+E(f918(x21293,x21291),f918(x21293,x21292))
% 28.78/28.54 [2130]~E(x21301,x21302)+E(f657(x21301,x21303,x21304,x21305),f657(x21302,x21303,x21304,x21305))
% 28.78/28.54 [2131]~E(x21311,x21312)+E(f657(x21313,x21311,x21314,x21315),f657(x21313,x21312,x21314,x21315))
% 28.78/28.54 [2132]~E(x21321,x21322)+E(f657(x21323,x21324,x21321,x21325),f657(x21323,x21324,x21322,x21325))
% 28.78/28.54 [2133]~E(x21331,x21332)+E(f657(x21333,x21334,x21335,x21331),f657(x21333,x21334,x21335,x21332))
% 28.78/28.54 [2134]~E(x21341,x21342)+E(f442(x21341,x21343),f442(x21342,x21343))
% 28.78/28.54 [2135]~E(x21351,x21352)+E(f442(x21353,x21351),f442(x21353,x21352))
% 28.78/28.54 [2136]~E(x21361,x21362)+E(f577(x21361,x21363,x21364,x21365),f577(x21362,x21363,x21364,x21365))
% 28.78/28.54 [2137]~E(x21371,x21372)+E(f577(x21373,x21371,x21374,x21375),f577(x21373,x21372,x21374,x21375))
% 28.78/28.54 [2138]~E(x21381,x21382)+E(f577(x21383,x21384,x21381,x21385),f577(x21383,x21384,x21382,x21385))
% 28.78/28.54 [2139]~E(x21391,x21392)+E(f577(x21393,x21394,x21395,x21391),f577(x21393,x21394,x21395,x21392))
% 28.78/28.54 [2140]~E(x21401,x21402)+E(f290(x21401,x21403,x21404),f290(x21402,x21403,x21404))
% 28.78/28.54 [2141]~E(x21411,x21412)+E(f290(x21413,x21411,x21414),f290(x21413,x21412,x21414))
% 28.78/28.54 [2142]~E(x21421,x21422)+E(f290(x21423,x21424,x21421),f290(x21423,x21424,x21422))
% 28.78/28.54 [2143]~E(x21431,x21432)+E(f387(x21431,x21433,x21434,x21435),f387(x21432,x21433,x21434,x21435))
% 28.78/28.54 [2144]~E(x21441,x21442)+E(f387(x21443,x21441,x21444,x21445),f387(x21443,x21442,x21444,x21445))
% 28.78/28.54 [2145]~E(x21451,x21452)+E(f387(x21453,x21454,x21451,x21455),f387(x21453,x21454,x21452,x21455))
% 28.78/28.54 [2146]~E(x21461,x21462)+E(f387(x21463,x21464,x21465,x21461),f387(x21463,x21464,x21465,x21462))
% 28.78/28.54 [2147]~E(x21471,x21472)+E(f538(x21471,x21473,x21474),f538(x21472,x21473,x21474))
% 28.78/28.54 [2148]~E(x21481,x21482)+E(f538(x21483,x21481,x21484),f538(x21483,x21482,x21484))
% 28.78/28.54 [2149]~E(x21491,x21492)+E(f538(x21493,x21494,x21491),f538(x21493,x21494,x21492))
% 28.78/28.54 [2150]~E(x21501,x21502)+E(f581(x21501,x21503,x21504,x21505,x21506,x21507),f581(x21502,x21503,x21504,x21505,x21506,x21507))
% 28.78/28.54 [2151]~E(x21511,x21512)+E(f581(x21513,x21511,x21514,x21515,x21516,x21517),f581(x21513,x21512,x21514,x21515,x21516,x21517))
% 28.78/28.54 [2152]~E(x21521,x21522)+E(f581(x21523,x21524,x21521,x21525,x21526,x21527),f581(x21523,x21524,x21522,x21525,x21526,x21527))
% 28.78/28.54 [2153]~E(x21531,x21532)+E(f581(x21533,x21534,x21535,x21531,x21536,x21537),f581(x21533,x21534,x21535,x21532,x21536,x21537))
% 28.78/28.54 [2154]~E(x21541,x21542)+E(f581(x21543,x21544,x21545,x21546,x21541,x21547),f581(x21543,x21544,x21545,x21546,x21542,x21547))
% 28.78/28.54 [2155]~E(x21551,x21552)+E(f581(x21553,x21554,x21555,x21556,x21557,x21551),f581(x21553,x21554,x21555,x21556,x21557,x21552))
% 28.78/28.54 [2156]~E(x21561,x21562)+E(f857(x21561,x21563,x21564),f857(x21562,x21563,x21564))
% 28.78/28.54 [2157]~E(x21571,x21572)+E(f857(x21573,x21571,x21574),f857(x21573,x21572,x21574))
% 28.78/28.54 [2158]~E(x21581,x21582)+E(f857(x21583,x21584,x21581),f857(x21583,x21584,x21582))
% 28.78/28.54 [2159]~E(x21591,x21592)+E(f380(x21591,x21593,x21594,x21595),f380(x21592,x21593,x21594,x21595))
% 28.78/28.54 [2160]~E(x21601,x21602)+E(f380(x21603,x21601,x21604,x21605),f380(x21603,x21602,x21604,x21605))
% 28.78/28.54 [2161]~E(x21611,x21612)+E(f380(x21613,x21614,x21611,x21615),f380(x21613,x21614,x21612,x21615))
% 28.78/28.54 [2162]~E(x21621,x21622)+E(f380(x21623,x21624,x21625,x21621),f380(x21623,x21624,x21625,x21622))
% 28.78/28.54 [2163]~E(x21631,x21632)+E(f648(x21631,x21633),f648(x21632,x21633))
% 28.78/28.54 [2164]~E(x21641,x21642)+E(f648(x21643,x21641),f648(x21643,x21642))
% 28.78/28.54 [2165]~E(x21651,x21652)+E(f378(x21651,x21653,x21654),f378(x21652,x21653,x21654))
% 28.78/28.54 [2166]~E(x21661,x21662)+E(f378(x21663,x21661,x21664),f378(x21663,x21662,x21664))
% 28.78/28.54 [2167]~E(x21671,x21672)+E(f378(x21673,x21674,x21671),f378(x21673,x21674,x21672))
% 28.78/28.54 [2168]~E(x21681,x21682)+E(f887(x21681,x21683,x21684,x21685,x21686),f887(x21682,x21683,x21684,x21685,x21686))
% 28.78/28.54 [2169]~E(x21691,x21692)+E(f887(x21693,x21691,x21694,x21695,x21696),f887(x21693,x21692,x21694,x21695,x21696))
% 28.78/28.54 [2170]~E(x21701,x21702)+E(f887(x21703,x21704,x21701,x21705,x21706),f887(x21703,x21704,x21702,x21705,x21706))
% 28.78/28.54 [2171]~E(x21711,x21712)+E(f887(x21713,x21714,x21715,x21711,x21716),f887(x21713,x21714,x21715,x21712,x21716))
% 28.78/28.54 [2172]~E(x21721,x21722)+E(f887(x21723,x21724,x21725,x21726,x21721),f887(x21723,x21724,x21725,x21726,x21722))
% 28.78/28.54 [2173]~E(x21731,x21732)+E(f61(x21731,x21733,x21734),f61(x21732,x21733,x21734))
% 28.78/28.54 [2174]~E(x21741,x21742)+E(f61(x21743,x21741,x21744),f61(x21743,x21742,x21744))
% 28.78/28.54 [2175]~E(x21751,x21752)+E(f61(x21753,x21754,x21751),f61(x21753,x21754,x21752))
% 28.78/28.54 [2176]~E(x21761,x21762)+E(f435(x21761,x21763,x21764),f435(x21762,x21763,x21764))
% 28.78/28.54 [2177]~E(x21771,x21772)+E(f435(x21773,x21771,x21774),f435(x21773,x21772,x21774))
% 28.78/28.54 [2178]~E(x21781,x21782)+E(f435(x21783,x21784,x21781),f435(x21783,x21784,x21782))
% 28.78/28.54 [2179]~E(x21791,x21792)+E(f415(x21791,x21793,x21794,x21795),f415(x21792,x21793,x21794,x21795))
% 28.78/28.54 [2180]~E(x21801,x21802)+E(f415(x21803,x21801,x21804,x21805),f415(x21803,x21802,x21804,x21805))
% 28.78/28.54 [2181]~E(x21811,x21812)+E(f415(x21813,x21814,x21811,x21815),f415(x21813,x21814,x21812,x21815))
% 28.78/28.54 [2182]~E(x21821,x21822)+E(f415(x21823,x21824,x21825,x21821),f415(x21823,x21824,x21825,x21822))
% 28.78/28.54 [2183]~E(x21831,x21832)+E(f832(x21831,x21833,x21834,x21835,x21836,x21837),f832(x21832,x21833,x21834,x21835,x21836,x21837))
% 28.78/28.54 [2184]~E(x21841,x21842)+E(f832(x21843,x21841,x21844,x21845,x21846,x21847),f832(x21843,x21842,x21844,x21845,x21846,x21847))
% 28.78/28.54 [2185]~E(x21851,x21852)+E(f832(x21853,x21854,x21851,x21855,x21856,x21857),f832(x21853,x21854,x21852,x21855,x21856,x21857))
% 28.78/28.54 [2186]~E(x21861,x21862)+E(f832(x21863,x21864,x21865,x21861,x21866,x21867),f832(x21863,x21864,x21865,x21862,x21866,x21867))
% 28.78/28.54 [2187]~E(x21871,x21872)+E(f832(x21873,x21874,x21875,x21876,x21871,x21877),f832(x21873,x21874,x21875,x21876,x21872,x21877))
% 28.78/28.54 [2188]~E(x21881,x21882)+E(f832(x21883,x21884,x21885,x21886,x21887,x21881),f832(x21883,x21884,x21885,x21886,x21887,x21882))
% 28.78/28.54 [2189]~E(x21891,x21892)+E(f287(x21891,x21893,x21894),f287(x21892,x21893,x21894))
% 28.78/28.54 [2190]~E(x21901,x21902)+E(f287(x21903,x21901,x21904),f287(x21903,x21902,x21904))
% 28.78/28.54 [2191]~E(x21911,x21912)+E(f287(x21913,x21914,x21911),f287(x21913,x21914,x21912))
% 28.78/28.54 [2192]~E(x21921,x21922)+E(f639(x21921,x21923,x21924,x21925,x21926),f639(x21922,x21923,x21924,x21925,x21926))
% 28.78/28.54 [2193]~E(x21931,x21932)+E(f639(x21933,x21931,x21934,x21935,x21936),f639(x21933,x21932,x21934,x21935,x21936))
% 28.78/28.54 [2194]~E(x21941,x21942)+E(f639(x21943,x21944,x21941,x21945,x21946),f639(x21943,x21944,x21942,x21945,x21946))
% 28.78/28.54 [2195]~E(x21951,x21952)+E(f639(x21953,x21954,x21955,x21951,x21956),f639(x21953,x21954,x21955,x21952,x21956))
% 28.78/28.54 [2196]~E(x21961,x21962)+E(f639(x21963,x21964,x21965,x21966,x21961),f639(x21963,x21964,x21965,x21966,x21962))
% 28.78/28.54 [2197]~E(x21971,x21972)+E(f464(x21971,x21973,x21974,x21975,x21976,x21977),f464(x21972,x21973,x21974,x21975,x21976,x21977))
% 28.78/28.54 [2198]~E(x21981,x21982)+E(f464(x21983,x21981,x21984,x21985,x21986,x21987),f464(x21983,x21982,x21984,x21985,x21986,x21987))
% 28.78/28.54 [2199]~E(x21991,x21992)+E(f464(x21993,x21994,x21991,x21995,x21996,x21997),f464(x21993,x21994,x21992,x21995,x21996,x21997))
% 28.78/28.54 [2200]~E(x22001,x22002)+E(f464(x22003,x22004,x22005,x22001,x22006,x22007),f464(x22003,x22004,x22005,x22002,x22006,x22007))
% 28.78/28.54 [2201]~E(x22011,x22012)+E(f464(x22013,x22014,x22015,x22016,x22011,x22017),f464(x22013,x22014,x22015,x22016,x22012,x22017))
% 28.78/28.54 [2202]~E(x22021,x22022)+E(f464(x22023,x22024,x22025,x22026,x22027,x22021),f464(x22023,x22024,x22025,x22026,x22027,x22022))
% 28.78/28.54 [2203]~E(x22031,x22032)+E(f339(x22031,x22033,x22034,x22035),f339(x22032,x22033,x22034,x22035))
% 28.78/28.54 [2204]~E(x22041,x22042)+E(f339(x22043,x22041,x22044,x22045),f339(x22043,x22042,x22044,x22045))
% 28.78/28.54 [2205]~E(x22051,x22052)+E(f339(x22053,x22054,x22051,x22055),f339(x22053,x22054,x22052,x22055))
% 28.78/28.54 [2206]~E(x22061,x22062)+E(f339(x22063,x22064,x22065,x22061),f339(x22063,x22064,x22065,x22062))
% 28.78/28.54 [2207]~E(x22071,x22072)+E(f769(x22071,x22073,x22074,x22075,x22076,x22077,x22078),f769(x22072,x22073,x22074,x22075,x22076,x22077,x22078))
% 28.78/28.54 [2208]~E(x22081,x22082)+E(f769(x22083,x22081,x22084,x22085,x22086,x22087,x22088),f769(x22083,x22082,x22084,x22085,x22086,x22087,x22088))
% 28.78/28.54 [2209]~E(x22091,x22092)+E(f769(x22093,x22094,x22091,x22095,x22096,x22097,x22098),f769(x22093,x22094,x22092,x22095,x22096,x22097,x22098))
% 28.78/28.54 [2210]~E(x22101,x22102)+E(f769(x22103,x22104,x22105,x22101,x22106,x22107,x22108),f769(x22103,x22104,x22105,x22102,x22106,x22107,x22108))
% 28.78/28.54 [2211]~E(x22111,x22112)+E(f769(x22113,x22114,x22115,x22116,x22111,x22117,x22118),f769(x22113,x22114,x22115,x22116,x22112,x22117,x22118))
% 28.78/28.54 [2212]~E(x22121,x22122)+E(f769(x22123,x22124,x22125,x22126,x22127,x22121,x22128),f769(x22123,x22124,x22125,x22126,x22127,x22122,x22128))
% 28.78/28.54 [2213]~E(x22131,x22132)+E(f769(x22133,x22134,x22135,x22136,x22137,x22138,x22131),f769(x22133,x22134,x22135,x22136,x22137,x22138,x22132))
% 28.78/28.54 [2214]~E(x22141,x22142)+E(f411(x22141,x22143,x22144),f411(x22142,x22143,x22144))
% 28.78/28.54 [2215]~E(x22151,x22152)+E(f411(x22153,x22151,x22154),f411(x22153,x22152,x22154))
% 28.78/28.54 [2216]~E(x22161,x22162)+E(f411(x22163,x22164,x22161),f411(x22163,x22164,x22162))
% 28.78/28.54 [2217]~E(x22171,x22172)+E(f266(x22171,x22173,x22174),f266(x22172,x22173,x22174))
% 28.78/28.54 [2218]~E(x22181,x22182)+E(f266(x22183,x22181,x22184),f266(x22183,x22182,x22184))
% 28.78/28.54 [2219]~E(x22191,x22192)+E(f266(x22193,x22194,x22191),f266(x22193,x22194,x22192))
% 28.78/28.54 [2220]~E(x22201,x22202)+E(f687(x22201,x22203),f687(x22202,x22203))
% 28.78/28.54 [2221]~E(x22211,x22212)+E(f687(x22213,x22211),f687(x22213,x22212))
% 28.78/28.54 [2222]~E(x22221,x22222)+E(f158(x22221,x22223,x22224),f158(x22222,x22223,x22224))
% 28.78/28.54 [2223]~E(x22231,x22232)+E(f158(x22233,x22231,x22234),f158(x22233,x22232,x22234))
% 28.78/28.54 [2224]~E(x22241,x22242)+E(f158(x22243,x22244,x22241),f158(x22243,x22244,x22242))
% 28.78/28.54 [2225]~E(x22251,x22252)+E(f566(x22251,x22253,x22254,x22255),f566(x22252,x22253,x22254,x22255))
% 28.78/28.54 [2226]~E(x22261,x22262)+E(f566(x22263,x22261,x22264,x22265),f566(x22263,x22262,x22264,x22265))
% 28.78/28.54 [2227]~E(x22271,x22272)+E(f566(x22273,x22274,x22271,x22275),f566(x22273,x22274,x22272,x22275))
% 28.78/28.54 [2228]~E(x22281,x22282)+E(f566(x22283,x22284,x22285,x22281),f566(x22283,x22284,x22285,x22282))
% 28.78/28.54 [2229]~E(x22291,x22292)+E(f823(x22291,x22293),f823(x22292,x22293))
% 28.78/28.54 [2230]~E(x22301,x22302)+E(f823(x22303,x22301),f823(x22303,x22302))
% 28.78/28.54 [2231]~E(x22311,x22312)+E(f916(x22311,x22313,x22314,x22315),f916(x22312,x22313,x22314,x22315))
% 28.78/28.54 [2232]~E(x22321,x22322)+E(f916(x22323,x22321,x22324,x22325),f916(x22323,x22322,x22324,x22325))
% 28.78/28.54 [2233]~E(x22331,x22332)+E(f916(x22333,x22334,x22331,x22335),f916(x22333,x22334,x22332,x22335))
% 28.78/28.54 [2234]~E(x22341,x22342)+E(f916(x22343,x22344,x22345,x22341),f916(x22343,x22344,x22345,x22342))
% 28.78/28.54 [2235]~E(x22351,x22352)+E(f745(x22351,x22353,x22354,x22355),f745(x22352,x22353,x22354,x22355))
% 28.78/28.54 [2236]~E(x22361,x22362)+E(f745(x22363,x22361,x22364,x22365),f745(x22363,x22362,x22364,x22365))
% 28.78/28.54 [2237]~E(x22371,x22372)+E(f745(x22373,x22374,x22371,x22375),f745(x22373,x22374,x22372,x22375))
% 28.78/28.54 [2238]~E(x22381,x22382)+E(f745(x22383,x22384,x22385,x22381),f745(x22383,x22384,x22385,x22382))
% 28.78/28.54 [2239]~E(x22391,x22392)+E(f526(x22391,x22393,x22394),f526(x22392,x22393,x22394))
% 28.78/28.54 [2240]~E(x22401,x22402)+E(f526(x22403,x22401,x22404),f526(x22403,x22402,x22404))
% 28.78/28.54 [2241]~E(x22411,x22412)+E(f526(x22413,x22414,x22411),f526(x22413,x22414,x22412))
% 28.78/28.54 [2242]~E(x22421,x22422)+E(f781(x22421,x22423,x22424),f781(x22422,x22423,x22424))
% 28.78/28.54 [2243]~E(x22431,x22432)+E(f781(x22433,x22431,x22434),f781(x22433,x22432,x22434))
% 28.78/28.54 [2244]~E(x22441,x22442)+E(f781(x22443,x22444,x22441),f781(x22443,x22444,x22442))
% 28.78/28.54 [2245]~E(x22451,x22452)+E(f553(x22451,x22453,x22454,x22455,x22456,x22457),f553(x22452,x22453,x22454,x22455,x22456,x22457))
% 28.78/28.54 [2246]~E(x22461,x22462)+E(f553(x22463,x22461,x22464,x22465,x22466,x22467),f553(x22463,x22462,x22464,x22465,x22466,x22467))
% 28.78/28.54 [2247]~E(x22471,x22472)+E(f553(x22473,x22474,x22471,x22475,x22476,x22477),f553(x22473,x22474,x22472,x22475,x22476,x22477))
% 28.78/28.54 [2248]~E(x22481,x22482)+E(f553(x22483,x22484,x22485,x22481,x22486,x22487),f553(x22483,x22484,x22485,x22482,x22486,x22487))
% 28.78/28.54 [2249]~E(x22491,x22492)+E(f553(x22493,x22494,x22495,x22496,x22491,x22497),f553(x22493,x22494,x22495,x22496,x22492,x22497))
% 28.78/28.54 [2250]~E(x22501,x22502)+E(f553(x22503,x22504,x22505,x22506,x22507,x22501),f553(x22503,x22504,x22505,x22506,x22507,x22502))
% 28.78/28.54 [2251]~E(x22511,x22512)+E(f525(x22511,x22513,x22514),f525(x22512,x22513,x22514))
% 28.78/28.54 [2252]~E(x22521,x22522)+E(f525(x22523,x22521,x22524),f525(x22523,x22522,x22524))
% 28.78/28.54 [2253]~E(x22531,x22532)+E(f525(x22533,x22534,x22531),f525(x22533,x22534,x22532))
% 28.78/28.54 [2254]~E(x22541,x22542)+E(f892(x22541,x22543,x22544,x22545),f892(x22542,x22543,x22544,x22545))
% 28.78/28.54 [2255]~E(x22551,x22552)+E(f892(x22553,x22551,x22554,x22555),f892(x22553,x22552,x22554,x22555))
% 28.78/28.54 [2256]~E(x22561,x22562)+E(f892(x22563,x22564,x22561,x22565),f892(x22563,x22564,x22562,x22565))
% 28.78/28.54 [2257]~E(x22571,x22572)+E(f892(x22573,x22574,x22575,x22571),f892(x22573,x22574,x22575,x22572))
% 28.78/28.54 [2258]~E(x22581,x22582)+E(f614(x22581,x22583,x22584,x22585),f614(x22582,x22583,x22584,x22585))
% 28.78/28.54 [2259]~E(x22591,x22592)+E(f614(x22593,x22591,x22594,x22595),f614(x22593,x22592,x22594,x22595))
% 28.78/28.54 [2260]~E(x22601,x22602)+E(f614(x22603,x22604,x22601,x22605),f614(x22603,x22604,x22602,x22605))
% 28.78/28.54 [2261]~E(x22611,x22612)+E(f614(x22613,x22614,x22615,x22611),f614(x22613,x22614,x22615,x22612))
% 28.78/28.54 [2262]~E(x22621,x22622)+E(f659(x22621,x22623,x22624),f659(x22622,x22623,x22624))
% 28.78/28.54 [2263]~E(x22631,x22632)+E(f659(x22633,x22631,x22634),f659(x22633,x22632,x22634))
% 28.78/28.54 [2264]~E(x22641,x22642)+E(f659(x22643,x22644,x22641),f659(x22643,x22644,x22642))
% 28.78/28.54 [2265]~E(x22651,x22652)+E(f370(x22651),f370(x22652))
% 28.78/28.54 [2266]~E(x22661,x22662)+E(f356(x22661,x22663,x22664),f356(x22662,x22663,x22664))
% 28.78/28.54 [2267]~E(x22671,x22672)+E(f356(x22673,x22671,x22674),f356(x22673,x22672,x22674))
% 28.78/28.54 [2268]~E(x22681,x22682)+E(f356(x22683,x22684,x22681),f356(x22683,x22684,x22682))
% 28.78/28.54 [2269]~E(x22691,x22692)+E(f573(x22691,x22693,x22694,x22695),f573(x22692,x22693,x22694,x22695))
% 28.78/28.54 [2270]~E(x22701,x22702)+E(f573(x22703,x22701,x22704,x22705),f573(x22703,x22702,x22704,x22705))
% 28.78/28.54 [2271]~E(x22711,x22712)+E(f573(x22713,x22714,x22711,x22715),f573(x22713,x22714,x22712,x22715))
% 28.78/28.54 [2272]~E(x22721,x22722)+E(f573(x22723,x22724,x22725,x22721),f573(x22723,x22724,x22725,x22722))
% 28.78/28.54 [2273]~E(x22731,x22732)+E(f373(x22731),f373(x22732))
% 28.78/28.54 [2274]~E(x22741,x22742)+E(f447(x22741,x22743,x22744,x22745,x22746),f447(x22742,x22743,x22744,x22745,x22746))
% 28.78/28.54 [2275]~E(x22751,x22752)+E(f447(x22753,x22751,x22754,x22755,x22756),f447(x22753,x22752,x22754,x22755,x22756))
% 28.78/28.54 [2276]~E(x22761,x22762)+E(f447(x22763,x22764,x22761,x22765,x22766),f447(x22763,x22764,x22762,x22765,x22766))
% 28.78/28.54 [2277]~E(x22771,x22772)+E(f447(x22773,x22774,x22775,x22771,x22776),f447(x22773,x22774,x22775,x22772,x22776))
% 28.78/28.54 [2278]~E(x22781,x22782)+E(f447(x22783,x22784,x22785,x22786,x22781),f447(x22783,x22784,x22785,x22786,x22782))
% 28.78/28.54 [2279]~E(x22791,x22792)+E(f488(x22791,x22793,x22794),f488(x22792,x22793,x22794))
% 28.78/28.54 [2280]~E(x22801,x22802)+E(f488(x22803,x22801,x22804),f488(x22803,x22802,x22804))
% 28.78/28.54 [2281]~E(x22811,x22812)+E(f488(x22813,x22814,x22811),f488(x22813,x22814,x22812))
% 28.78/28.54 [2282]~E(x22821,x22822)+E(f764(x22821,x22823,x22824,x22825,x22826),f764(x22822,x22823,x22824,x22825,x22826))
% 28.78/28.54 [2283]~E(x22831,x22832)+E(f764(x22833,x22831,x22834,x22835,x22836),f764(x22833,x22832,x22834,x22835,x22836))
% 28.78/28.54 [2284]~E(x22841,x22842)+E(f764(x22843,x22844,x22841,x22845,x22846),f764(x22843,x22844,x22842,x22845,x22846))
% 28.78/28.54 [2285]~E(x22851,x22852)+E(f764(x22853,x22854,x22855,x22851,x22856),f764(x22853,x22854,x22855,x22852,x22856))
% 28.78/28.54 [2286]~E(x22861,x22862)+E(f764(x22863,x22864,x22865,x22866,x22861),f764(x22863,x22864,x22865,x22866,x22862))
% 28.78/28.54 [2287]~E(x22871,x22872)+E(f785(x22871,x22873,x22874),f785(x22872,x22873,x22874))
% 28.78/28.54 [2288]~E(x22881,x22882)+E(f785(x22883,x22881,x22884),f785(x22883,x22882,x22884))
% 28.78/28.54 [2289]~E(x22891,x22892)+E(f785(x22893,x22894,x22891),f785(x22893,x22894,x22892))
% 28.78/28.54 [2290]~E(x22901,x22902)+E(f763(x22901,x22903,x22904,x22905,x22906),f763(x22902,x22903,x22904,x22905,x22906))
% 28.78/28.54 [2291]~E(x22911,x22912)+E(f763(x22913,x22911,x22914,x22915,x22916),f763(x22913,x22912,x22914,x22915,x22916))
% 28.78/28.54 [2292]~E(x22921,x22922)+E(f763(x22923,x22924,x22921,x22925,x22926),f763(x22923,x22924,x22922,x22925,x22926))
% 28.78/28.54 [2293]~E(x22931,x22932)+E(f763(x22933,x22934,x22935,x22931,x22936),f763(x22933,x22934,x22935,x22932,x22936))
% 28.78/28.54 [2294]~E(x22941,x22942)+E(f763(x22943,x22944,x22945,x22946,x22941),f763(x22943,x22944,x22945,x22946,x22942))
% 28.78/28.54 [2295]~E(x22951,x22952)+E(f560(x22951,x22953,x22954),f560(x22952,x22953,x22954))
% 28.78/28.54 [2296]~E(x22961,x22962)+E(f560(x22963,x22961,x22964),f560(x22963,x22962,x22964))
% 28.78/28.54 [2297]~E(x22971,x22972)+E(f560(x22973,x22974,x22971),f560(x22973,x22974,x22972))
% 28.78/28.54 [2298]~E(x22981,x22982)+E(f494(x22981,x22983,x22984),f494(x22982,x22983,x22984))
% 28.78/28.54 [2299]~E(x22991,x22992)+E(f494(x22993,x22991,x22994),f494(x22993,x22992,x22994))
% 28.78/28.54 [2300]~E(x23001,x23002)+E(f494(x23003,x23004,x23001),f494(x23003,x23004,x23002))
% 28.78/28.54 [2301]~E(x23011,x23012)+E(f578(x23011,x23013,x23014,x23015),f578(x23012,x23013,x23014,x23015))
% 28.78/28.54 [2302]~E(x23021,x23022)+E(f578(x23023,x23021,x23024,x23025),f578(x23023,x23022,x23024,x23025))
% 28.78/28.54 [2303]~E(x23031,x23032)+E(f578(x23033,x23034,x23031,x23035),f578(x23033,x23034,x23032,x23035))
% 28.78/28.54 [2304]~E(x23041,x23042)+E(f578(x23043,x23044,x23045,x23041),f578(x23043,x23044,x23045,x23042))
% 28.78/28.54 [2305]~E(x23051,x23052)+E(f788(x23051,x23053,x23054),f788(x23052,x23053,x23054))
% 28.78/28.54 [2306]~E(x23061,x23062)+E(f788(x23063,x23061,x23064),f788(x23063,x23062,x23064))
% 28.78/28.54 [2307]~E(x23071,x23072)+E(f788(x23073,x23074,x23071),f788(x23073,x23074,x23072))
% 28.78/28.54 [2308]~E(x23081,x23082)+E(f345(x23081,x23083,x23084),f345(x23082,x23083,x23084))
% 28.78/28.54 [2309]~E(x23091,x23092)+E(f345(x23093,x23091,x23094),f345(x23093,x23092,x23094))
% 28.78/28.54 [2310]~E(x23101,x23102)+E(f345(x23103,x23104,x23101),f345(x23103,x23104,x23102))
% 28.78/28.54 [2311]~E(x23111,x23112)+E(f509(x23111,x23113,x23114),f509(x23112,x23113,x23114))
% 28.78/28.54 [2312]~E(x23121,x23122)+E(f509(x23123,x23121,x23124),f509(x23123,x23122,x23124))
% 28.78/28.54 [2313]~E(x23131,x23132)+E(f509(x23133,x23134,x23131),f509(x23133,x23134,x23132))
% 28.78/28.54 [2314]~E(x23141,x23142)+E(f779(x23141,x23143,x23144),f779(x23142,x23143,x23144))
% 28.78/28.54 [2315]~E(x23151,x23152)+E(f779(x23153,x23151,x23154),f779(x23153,x23152,x23154))
% 28.78/28.54 [2316]~E(x23161,x23162)+E(f779(x23163,x23164,x23161),f779(x23163,x23164,x23162))
% 28.78/28.54 [2317]~E(x23171,x23172)+E(f548(x23171,x23173,x23174,x23175,x23176,x23177),f548(x23172,x23173,x23174,x23175,x23176,x23177))
% 28.78/28.54 [2318]~E(x23181,x23182)+E(f548(x23183,x23181,x23184,x23185,x23186,x23187),f548(x23183,x23182,x23184,x23185,x23186,x23187))
% 28.78/28.54 [2319]~E(x23191,x23192)+E(f548(x23193,x23194,x23191,x23195,x23196,x23197),f548(x23193,x23194,x23192,x23195,x23196,x23197))
% 28.78/28.54 [2320]~E(x23201,x23202)+E(f548(x23203,x23204,x23205,x23201,x23206,x23207),f548(x23203,x23204,x23205,x23202,x23206,x23207))
% 28.78/28.54 [2321]~E(x23211,x23212)+E(f548(x23213,x23214,x23215,x23216,x23211,x23217),f548(x23213,x23214,x23215,x23216,x23212,x23217))
% 28.78/28.54 [2322]~E(x23221,x23222)+E(f548(x23223,x23224,x23225,x23226,x23227,x23221),f548(x23223,x23224,x23225,x23226,x23227,x23222))
% 28.78/28.54 [2323]~E(x23231,x23232)+E(f385(x23231,x23233,x23234,x23235),f385(x23232,x23233,x23234,x23235))
% 28.78/28.54 [2324]~E(x23241,x23242)+E(f385(x23243,x23241,x23244,x23245),f385(x23243,x23242,x23244,x23245))
% 28.78/28.54 [2325]~E(x23251,x23252)+E(f385(x23253,x23254,x23251,x23255),f385(x23253,x23254,x23252,x23255))
% 28.78/28.54 [2326]~E(x23261,x23262)+E(f385(x23263,x23264,x23265,x23261),f385(x23263,x23264,x23265,x23262))
% 28.78/28.54 [2327]~E(x23271,x23272)+E(f600(x23271,x23273,x23274),f600(x23272,x23273,x23274))
% 28.78/28.54 [2328]~E(x23281,x23282)+E(f600(x23283,x23281,x23284),f600(x23283,x23282,x23284))
% 28.78/28.54 [2329]~E(x23291,x23292)+E(f600(x23293,x23294,x23291),f600(x23293,x23294,x23292))
% 28.78/28.54 [2330]~E(x23301,x23302)+E(f216(x23301,x23303,x23304,x23305,x23306),f216(x23302,x23303,x23304,x23305,x23306))
% 28.78/28.54 [2331]~E(x23311,x23312)+E(f216(x23313,x23311,x23314,x23315,x23316),f216(x23313,x23312,x23314,x23315,x23316))
% 28.78/28.54 [2332]~E(x23321,x23322)+E(f216(x23323,x23324,x23321,x23325,x23326),f216(x23323,x23324,x23322,x23325,x23326))
% 28.78/28.54 [2333]~E(x23331,x23332)+E(f216(x23333,x23334,x23335,x23331,x23336),f216(x23333,x23334,x23335,x23332,x23336))
% 28.78/28.54 [2334]~E(x23341,x23342)+E(f216(x23343,x23344,x23345,x23346,x23341),f216(x23343,x23344,x23345,x23346,x23342))
% 28.78/28.54 [2335]~E(x23351,x23352)+E(f428(x23351,x23353,x23354),f428(x23352,x23353,x23354))
% 28.78/28.54 [2336]~E(x23361,x23362)+E(f428(x23363,x23361,x23364),f428(x23363,x23362,x23364))
% 28.78/28.54 [2337]~E(x23371,x23372)+E(f428(x23373,x23374,x23371),f428(x23373,x23374,x23372))
% 28.78/28.54 [2338]~E(x23381,x23382)+E(f684(x23381,x23383,x23384),f684(x23382,x23383,x23384))
% 28.78/28.54 [2339]~E(x23391,x23392)+E(f684(x23393,x23391,x23394),f684(x23393,x23392,x23394))
% 28.78/28.54 [2340]~E(x23401,x23402)+E(f684(x23403,x23404,x23401),f684(x23403,x23404,x23402))
% 28.78/28.54 [2341]~E(x23411,x23412)+E(f528(x23411,x23413,x23414,x23415,x23416,x23417),f528(x23412,x23413,x23414,x23415,x23416,x23417))
% 28.78/28.54 [2342]~E(x23421,x23422)+E(f528(x23423,x23421,x23424,x23425,x23426,x23427),f528(x23423,x23422,x23424,x23425,x23426,x23427))
% 28.78/28.54 [2343]~E(x23431,x23432)+E(f528(x23433,x23434,x23431,x23435,x23436,x23437),f528(x23433,x23434,x23432,x23435,x23436,x23437))
% 28.78/28.54 [2344]~E(x23441,x23442)+E(f528(x23443,x23444,x23445,x23441,x23446,x23447),f528(x23443,x23444,x23445,x23442,x23446,x23447))
% 28.78/28.54 [2345]~E(x23451,x23452)+E(f528(x23453,x23454,x23455,x23456,x23451,x23457),f528(x23453,x23454,x23455,x23456,x23452,x23457))
% 28.78/28.54 [2346]~E(x23461,x23462)+E(f528(x23463,x23464,x23465,x23466,x23467,x23461),f528(x23463,x23464,x23465,x23466,x23467,x23462))
% 28.78/28.54 [2347]~E(x23471,x23472)+E(f330(x23471),f330(x23472))
% 28.78/28.54 [2348]~E(x23481,x23482)+E(f362(x23481,x23483),f362(x23482,x23483))
% 28.78/28.54 [2349]~E(x23491,x23492)+E(f362(x23493,x23491),f362(x23493,x23492))
% 28.78/28.54 [2350]~E(x23501,x23502)+E(f721(x23501,x23503,x23504,x23505,x23506),f721(x23502,x23503,x23504,x23505,x23506))
% 28.78/28.54 [2351]~E(x23511,x23512)+E(f721(x23513,x23511,x23514,x23515,x23516),f721(x23513,x23512,x23514,x23515,x23516))
% 28.78/28.54 [2352]~E(x23521,x23522)+E(f721(x23523,x23524,x23521,x23525,x23526),f721(x23523,x23524,x23522,x23525,x23526))
% 28.78/28.54 [2353]~E(x23531,x23532)+E(f721(x23533,x23534,x23535,x23531,x23536),f721(x23533,x23534,x23535,x23532,x23536))
% 28.78/28.54 [2354]~E(x23541,x23542)+E(f721(x23543,x23544,x23545,x23546,x23541),f721(x23543,x23544,x23545,x23546,x23542))
% 28.78/28.54 [2355]~E(x23551,x23552)+E(f709(x23551,x23553,x23554,x23555,x23556),f709(x23552,x23553,x23554,x23555,x23556))
% 28.78/28.54 [2356]~E(x23561,x23562)+E(f709(x23563,x23561,x23564,x23565,x23566),f709(x23563,x23562,x23564,x23565,x23566))
% 28.78/28.54 [2357]~E(x23571,x23572)+E(f709(x23573,x23574,x23571,x23575,x23576),f709(x23573,x23574,x23572,x23575,x23576))
% 28.78/28.54 [2358]~E(x23581,x23582)+E(f709(x23583,x23584,x23585,x23581,x23586),f709(x23583,x23584,x23585,x23582,x23586))
% 28.78/28.54 [2359]~E(x23591,x23592)+E(f709(x23593,x23594,x23595,x23596,x23591),f709(x23593,x23594,x23595,x23596,x23592))
% 28.78/28.54 [2360]~E(x23601,x23602)+E(f537(x23601,x23603,x23604,x23605,x23606),f537(x23602,x23603,x23604,x23605,x23606))
% 28.78/28.54 [2361]~E(x23611,x23612)+E(f537(x23613,x23611,x23614,x23615,x23616),f537(x23613,x23612,x23614,x23615,x23616))
% 28.78/28.54 [2362]~E(x23621,x23622)+E(f537(x23623,x23624,x23621,x23625,x23626),f537(x23623,x23624,x23622,x23625,x23626))
% 28.78/28.54 [2363]~E(x23631,x23632)+E(f537(x23633,x23634,x23635,x23631,x23636),f537(x23633,x23634,x23635,x23632,x23636))
% 28.78/28.54 [2364]~E(x23641,x23642)+E(f537(x23643,x23644,x23645,x23646,x23641),f537(x23643,x23644,x23645,x23646,x23642))
% 28.78/28.54 [2365]~E(x23651,x23652)+E(f889(x23651,x23653,x23654,x23655),f889(x23652,x23653,x23654,x23655))
% 28.78/28.54 [2366]~E(x23661,x23662)+E(f889(x23663,x23661,x23664,x23665),f889(x23663,x23662,x23664,x23665))
% 28.78/28.54 [2367]~E(x23671,x23672)+E(f889(x23673,x23674,x23671,x23675),f889(x23673,x23674,x23672,x23675))
% 28.78/28.54 [2368]~E(x23681,x23682)+E(f889(x23683,x23684,x23685,x23681),f889(x23683,x23684,x23685,x23682))
% 28.78/28.54 [2369]~E(x23691,x23692)+E(f286(x23691,x23693,x23694),f286(x23692,x23693,x23694))
% 28.78/28.54 [2370]~E(x23701,x23702)+E(f286(x23703,x23701,x23704),f286(x23703,x23702,x23704))
% 28.78/28.54 [2371]~E(x23711,x23712)+E(f286(x23713,x23714,x23711),f286(x23713,x23714,x23712))
% 28.78/28.54 [2372]~E(x23721,x23722)+E(f697(x23721,x23723),f697(x23722,x23723))
% 28.78/28.54 [2373]~E(x23731,x23732)+E(f697(x23733,x23731),f697(x23733,x23732))
% 28.78/28.54 [2374]~E(x23741,x23742)+E(f439(x23741),f439(x23742))
% 28.78/28.54 [2375]~E(x23751,x23752)+E(f702(x23751,x23753,x23754,x23755,x23756),f702(x23752,x23753,x23754,x23755,x23756))
% 28.78/28.54 [2376]~E(x23761,x23762)+E(f702(x23763,x23761,x23764,x23765,x23766),f702(x23763,x23762,x23764,x23765,x23766))
% 28.78/28.54 [2377]~E(x23771,x23772)+E(f702(x23773,x23774,x23771,x23775,x23776),f702(x23773,x23774,x23772,x23775,x23776))
% 28.78/28.54 [2378]~E(x23781,x23782)+E(f702(x23783,x23784,x23785,x23781,x23786),f702(x23783,x23784,x23785,x23782,x23786))
% 28.78/28.54 [2379]~E(x23791,x23792)+E(f702(x23793,x23794,x23795,x23796,x23791),f702(x23793,x23794,x23795,x23796,x23792))
% 28.78/28.54 [2380]~E(x23801,x23802)+E(f374(x23801,x23803),f374(x23802,x23803))
% 28.78/28.54 [2381]~E(x23811,x23812)+E(f374(x23813,x23811),f374(x23813,x23812))
% 28.78/28.54 [2382]~E(x23821,x23822)+E(f556(x23821,x23823,x23824,x23825,x23826),f556(x23822,x23823,x23824,x23825,x23826))
% 28.78/28.54 [2383]~E(x23831,x23832)+E(f556(x23833,x23831,x23834,x23835,x23836),f556(x23833,x23832,x23834,x23835,x23836))
% 28.78/28.54 [2384]~E(x23841,x23842)+E(f556(x23843,x23844,x23841,x23845,x23846),f556(x23843,x23844,x23842,x23845,x23846))
% 28.78/28.54 [2385]~E(x23851,x23852)+E(f556(x23853,x23854,x23855,x23851,x23856),f556(x23853,x23854,x23855,x23852,x23856))
% 28.78/28.54 [2386]~E(x23861,x23862)+E(f556(x23863,x23864,x23865,x23866,x23861),f556(x23863,x23864,x23865,x23866,x23862))
% 28.78/28.54 [2387]~E(x23871,x23872)+E(f393(x23871,x23873,x23874,x23875),f393(x23872,x23873,x23874,x23875))
% 28.78/28.54 [2388]~E(x23881,x23882)+E(f393(x23883,x23881,x23884,x23885),f393(x23883,x23882,x23884,x23885))
% 28.78/28.54 [2389]~E(x23891,x23892)+E(f393(x23893,x23894,x23891,x23895),f393(x23893,x23894,x23892,x23895))
% 28.78/28.54 [2390]~E(x23901,x23902)+E(f393(x23903,x23904,x23905,x23901),f393(x23903,x23904,x23905,x23902))
% 28.78/28.54 [2391]~E(x23911,x23912)+E(f830(x23911,x23913),f830(x23912,x23913))
% 28.78/28.54 [2392]~E(x23921,x23922)+E(f830(x23923,x23921),f830(x23923,x23922))
% 28.78/28.54 [2393]~E(x23931,x23932)+E(f839(x23931,x23933,x23934),f839(x23932,x23933,x23934))
% 28.78/28.54 [2394]~E(x23941,x23942)+E(f839(x23943,x23941,x23944),f839(x23943,x23942,x23944))
% 28.78/28.54 [2395]~E(x23951,x23952)+E(f839(x23953,x23954,x23951),f839(x23953,x23954,x23952))
% 28.78/28.54 [2396]~E(x23961,x23962)+E(f197(x23961,x23963,x23964,x23965),f197(x23962,x23963,x23964,x23965))
% 28.78/28.54 [2397]~E(x23971,x23972)+E(f197(x23973,x23971,x23974,x23975),f197(x23973,x23972,x23974,x23975))
% 28.78/28.54 [2398]~E(x23981,x23982)+E(f197(x23983,x23984,x23981,x23985),f197(x23983,x23984,x23982,x23985))
% 28.78/28.54 [2399]~E(x23991,x23992)+E(f197(x23993,x23994,x23995,x23991),f197(x23993,x23994,x23995,x23992))
% 28.78/28.54 [2400]~E(x24001,x24002)+E(f882(x24001,x24003,x24004),f882(x24002,x24003,x24004))
% 28.78/28.54 [2401]~E(x24011,x24012)+E(f882(x24013,x24011,x24014),f882(x24013,x24012,x24014))
% 28.78/28.54 [2402]~E(x24021,x24022)+E(f882(x24023,x24024,x24021),f882(x24023,x24024,x24022))
% 28.78/28.54 [2403]~E(x24031,x24032)+E(f842(x24031,x24033,x24034,x24035,x24036),f842(x24032,x24033,x24034,x24035,x24036))
% 28.78/28.54 [2404]~E(x24041,x24042)+E(f842(x24043,x24041,x24044,x24045,x24046),f842(x24043,x24042,x24044,x24045,x24046))
% 28.78/28.54 [2405]~E(x24051,x24052)+E(f842(x24053,x24054,x24051,x24055,x24056),f842(x24053,x24054,x24052,x24055,x24056))
% 28.78/28.54 [2406]~E(x24061,x24062)+E(f842(x24063,x24064,x24065,x24061,x24066),f842(x24063,x24064,x24065,x24062,x24066))
% 28.78/28.54 [2407]~E(x24071,x24072)+E(f842(x24073,x24074,x24075,x24076,x24071),f842(x24073,x24074,x24075,x24076,x24072))
% 28.78/28.54 [2408]~E(x24081,x24082)+E(f127(x24081),f127(x24082))
% 28.78/28.54 [2409]~E(x24091,x24092)+E(f484(x24091,x24093),f484(x24092,x24093))
% 28.78/28.54 [2410]~E(x24101,x24102)+E(f484(x24103,x24101),f484(x24103,x24102))
% 28.78/28.54 [2411]~E(x24111,x24112)+E(f409(x24111,x24113,x24114,x24115,x24116),f409(x24112,x24113,x24114,x24115,x24116))
% 28.78/28.54 [2412]~E(x24121,x24122)+E(f409(x24123,x24121,x24124,x24125,x24126),f409(x24123,x24122,x24124,x24125,x24126))
% 28.78/28.54 [2413]~E(x24131,x24132)+E(f409(x24133,x24134,x24131,x24135,x24136),f409(x24133,x24134,x24132,x24135,x24136))
% 28.78/28.54 [2414]~E(x24141,x24142)+E(f409(x24143,x24144,x24145,x24141,x24146),f409(x24143,x24144,x24145,x24142,x24146))
% 28.78/28.54 [2415]~E(x24151,x24152)+E(f409(x24153,x24154,x24155,x24156,x24151),f409(x24153,x24154,x24155,x24156,x24152))
% 28.78/28.54 [2416]~E(x24161,x24162)+E(f416(x24161,x24163),f416(x24162,x24163))
% 28.78/28.54 [2417]~E(x24171,x24172)+E(f416(x24173,x24171),f416(x24173,x24172))
% 28.78/28.54 [2418]~E(x24181,x24182)+E(f921(x24181,x24183,x24184,x24185,x24186),f921(x24182,x24183,x24184,x24185,x24186))
% 28.78/28.54 [2419]~E(x24191,x24192)+E(f921(x24193,x24191,x24194,x24195,x24196),f921(x24193,x24192,x24194,x24195,x24196))
% 28.78/28.54 [2420]~E(x24201,x24202)+E(f921(x24203,x24204,x24201,x24205,x24206),f921(x24203,x24204,x24202,x24205,x24206))
% 28.78/28.54 [2421]~E(x24211,x24212)+E(f921(x24213,x24214,x24215,x24211,x24216),f921(x24213,x24214,x24215,x24212,x24216))
% 28.78/28.54 [2422]~E(x24221,x24222)+E(f921(x24223,x24224,x24225,x24226,x24221),f921(x24223,x24224,x24225,x24226,x24222))
% 28.78/28.54 [2423]~E(x24231,x24232)+E(f743(x24231,x24233,x24234),f743(x24232,x24233,x24234))
% 28.78/28.54 [2424]~E(x24241,x24242)+E(f743(x24243,x24241,x24244),f743(x24243,x24242,x24244))
% 28.78/28.54 [2425]~E(x24251,x24252)+E(f743(x24253,x24254,x24251),f743(x24253,x24254,x24252))
% 28.78/28.54 [2426]~E(x24261,x24262)+E(f736(x24261,x24263,x24264),f736(x24262,x24263,x24264))
% 28.78/28.54 [2427]~E(x24271,x24272)+E(f736(x24273,x24271,x24274),f736(x24273,x24272,x24274))
% 28.78/28.54 [2428]~E(x24281,x24282)+E(f736(x24283,x24284,x24281),f736(x24283,x24284,x24282))
% 28.78/28.54 [2429]~E(x24291,x24292)+E(f739(x24291,x24293,x24294),f739(x24292,x24293,x24294))
% 28.78/28.54 [2430]~E(x24301,x24302)+E(f739(x24303,x24301,x24304),f739(x24303,x24302,x24304))
% 28.78/28.54 [2431]~E(x24311,x24312)+E(f739(x24313,x24314,x24311),f739(x24313,x24314,x24312))
% 28.78/28.54 [2432]~E(x24321,x24322)+E(f555(x24321,x24323,x24324),f555(x24322,x24323,x24324))
% 28.78/28.54 [2433]~E(x24331,x24332)+E(f555(x24333,x24331,x24334),f555(x24333,x24332,x24334))
% 28.78/28.54 [2434]~E(x24341,x24342)+E(f555(x24343,x24344,x24341),f555(x24343,x24344,x24342))
% 28.78/28.54 [2435]~E(x24351,x24352)+E(f489(x24351,x24353),f489(x24352,x24353))
% 28.78/28.54 [2436]~E(x24361,x24362)+E(f489(x24363,x24361),f489(x24363,x24362))
% 28.78/28.54 [2437]~E(x24371,x24372)+E(f238(x24371,x24373,x24374,x24375,x24376,x24377),f238(x24372,x24373,x24374,x24375,x24376,x24377))
% 28.78/28.54 [2438]~E(x24381,x24382)+E(f238(x24383,x24381,x24384,x24385,x24386,x24387),f238(x24383,x24382,x24384,x24385,x24386,x24387))
% 28.78/28.54 [2439]~E(x24391,x24392)+E(f238(x24393,x24394,x24391,x24395,x24396,x24397),f238(x24393,x24394,x24392,x24395,x24396,x24397))
% 28.78/28.54 [2440]~E(x24401,x24402)+E(f238(x24403,x24404,x24405,x24401,x24406,x24407),f238(x24403,x24404,x24405,x24402,x24406,x24407))
% 28.78/28.54 [2441]~E(x24411,x24412)+E(f238(x24413,x24414,x24415,x24416,x24411,x24417),f238(x24413,x24414,x24415,x24416,x24412,x24417))
% 28.78/28.54 [2442]~E(x24421,x24422)+E(f238(x24423,x24424,x24425,x24426,x24427,x24421),f238(x24423,x24424,x24425,x24426,x24427,x24422))
% 28.78/28.54 [2443]~E(x24431,x24432)+E(f762(x24431,x24433,x24434,x24435),f762(x24432,x24433,x24434,x24435))
% 28.78/28.54 [2444]~E(x24441,x24442)+E(f762(x24443,x24441,x24444,x24445),f762(x24443,x24442,x24444,x24445))
% 28.78/28.54 [2445]~E(x24451,x24452)+E(f762(x24453,x24454,x24451,x24455),f762(x24453,x24454,x24452,x24455))
% 28.78/28.54 [2446]~E(x24461,x24462)+E(f762(x24463,x24464,x24465,x24461),f762(x24463,x24464,x24465,x24462))
% 28.78/28.54 [2447]~E(x24471,x24472)+E(f391(x24471,x24473),f391(x24472,x24473))
% 28.78/28.54 [2448]~E(x24481,x24482)+E(f391(x24483,x24481),f391(x24483,x24482))
% 28.78/28.54 [2449]~E(x24491,x24492)+E(f586(x24491,x24493,x24494,x24495,x24496,x24497,x24498,x24499),f586(x24492,x24493,x24494,x24495,x24496,x24497,x24498,x24499))
% 28.78/28.54 [2450]~E(x24501,x24502)+E(f586(x24503,x24501,x24504,x24505,x24506,x24507,x24508,x24509),f586(x24503,x24502,x24504,x24505,x24506,x24507,x24508,x24509))
% 28.78/28.54 [2451]~E(x24511,x24512)+E(f586(x24513,x24514,x24511,x24515,x24516,x24517,x24518,x24519),f586(x24513,x24514,x24512,x24515,x24516,x24517,x24518,x24519))
% 28.78/28.54 [2452]~E(x24521,x24522)+E(f586(x24523,x24524,x24525,x24521,x24526,x24527,x24528,x24529),f586(x24523,x24524,x24525,x24522,x24526,x24527,x24528,x24529))
% 28.78/28.54 [2453]~E(x24531,x24532)+E(f586(x24533,x24534,x24535,x24536,x24531,x24537,x24538,x24539),f586(x24533,x24534,x24535,x24536,x24532,x24537,x24538,x24539))
% 28.78/28.54 [2454]~E(x24541,x24542)+E(f586(x24543,x24544,x24545,x24546,x24547,x24541,x24548,x24549),f586(x24543,x24544,x24545,x24546,x24547,x24542,x24548,x24549))
% 28.78/28.54 [2455]~E(x24551,x24552)+E(f586(x24553,x24554,x24555,x24556,x24557,x24558,x24551,x24559),f586(x24553,x24554,x24555,x24556,x24557,x24558,x24552,x24559))
% 28.78/28.54 [2456]~E(x24561,x24562)+E(f586(x24563,x24564,x24565,x24566,x24567,x24568,x24569,x24561),f586(x24563,x24564,x24565,x24566,x24567,x24568,x24569,x24562))
% 28.78/28.54 [2457]~E(x24571,x24572)+E(f381(x24571,x24573,x24574,x24575),f381(x24572,x24573,x24574,x24575))
% 28.78/28.54 [2458]~E(x24581,x24582)+E(f381(x24583,x24581,x24584,x24585),f381(x24583,x24582,x24584,x24585))
% 28.78/28.54 [2459]~E(x24591,x24592)+E(f381(x24593,x24594,x24591,x24595),f381(x24593,x24594,x24592,x24595))
% 28.78/28.54 [2460]~E(x24601,x24602)+E(f381(x24603,x24604,x24605,x24601),f381(x24603,x24604,x24605,x24602))
% 28.78/28.54 [2461]~E(x24611,x24612)+E(f620(x24611,x24613,x24614),f620(x24612,x24613,x24614))
% 28.78/28.54 [2462]~E(x24621,x24622)+E(f620(x24623,x24621,x24624),f620(x24623,x24622,x24624))
% 28.78/28.54 [2463]~E(x24631,x24632)+E(f620(x24633,x24634,x24631),f620(x24633,x24634,x24632))
% 28.78/28.54 [2464]~E(x24641,x24642)+E(f696(x24641,x24643,x24644),f696(x24642,x24643,x24644))
% 28.78/28.54 [2465]~E(x24651,x24652)+E(f696(x24653,x24651,x24654),f696(x24653,x24652,x24654))
% 28.78/28.54 [2466]~E(x24661,x24662)+E(f696(x24663,x24664,x24661),f696(x24663,x24664,x24662))
% 28.78/28.54 [2467]~E(x24671,x24672)+E(f643(x24671,x24673,x24674,x24675,x24676),f643(x24672,x24673,x24674,x24675,x24676))
% 28.78/28.54 [2468]~E(x24681,x24682)+E(f643(x24683,x24681,x24684,x24685,x24686),f643(x24683,x24682,x24684,x24685,x24686))
% 28.78/28.54 [2469]~E(x24691,x24692)+E(f643(x24693,x24694,x24691,x24695,x24696),f643(x24693,x24694,x24692,x24695,x24696))
% 28.78/28.54 [2470]~E(x24701,x24702)+E(f643(x24703,x24704,x24705,x24701,x24706),f643(x24703,x24704,x24705,x24702,x24706))
% 28.78/28.54 [2471]~E(x24711,x24712)+E(f643(x24713,x24714,x24715,x24716,x24711),f643(x24713,x24714,x24715,x24716,x24712))
% 28.78/28.54 [2472]~E(x24721,x24722)+E(f737(x24721,x24723,x24724),f737(x24722,x24723,x24724))
% 28.78/28.54 [2473]~E(x24731,x24732)+E(f737(x24733,x24731,x24734),f737(x24733,x24732,x24734))
% 28.78/28.54 [2474]~E(x24741,x24742)+E(f737(x24743,x24744,x24741),f737(x24743,x24744,x24742))
% 28.78/28.54 [2475]~E(x24751,x24752)+E(f430(x24751,x24753),f430(x24752,x24753))
% 28.78/28.54 [2476]~E(x24761,x24762)+E(f430(x24763,x24761),f430(x24763,x24762))
% 28.78/28.54 [2477]~E(x24771,x24772)+E(f753(x24771,x24773,x24774,x24775),f753(x24772,x24773,x24774,x24775))
% 28.78/28.54 [2478]~E(x24781,x24782)+E(f753(x24783,x24781,x24784,x24785),f753(x24783,x24782,x24784,x24785))
% 28.78/28.54 [2479]~E(x24791,x24792)+E(f753(x24793,x24794,x24791,x24795),f753(x24793,x24794,x24792,x24795))
% 28.78/28.54 [2480]~E(x24801,x24802)+E(f753(x24803,x24804,x24805,x24801),f753(x24803,x24804,x24805,x24802))
% 28.78/28.54 [2481]~E(x24811,x24812)+E(f870(x24811,x24813,x24814),f870(x24812,x24813,x24814))
% 28.78/28.54 [2482]~E(x24821,x24822)+E(f870(x24823,x24821,x24824),f870(x24823,x24822,x24824))
% 28.78/28.54 [2483]~E(x24831,x24832)+E(f870(x24833,x24834,x24831),f870(x24833,x24834,x24832))
% 28.78/28.54 [2484]~E(x24841,x24842)+E(f670(x24841,x24843,x24844,x24845,x24846),f670(x24842,x24843,x24844,x24845,x24846))
% 28.78/28.54 [2485]~E(x24851,x24852)+E(f670(x24853,x24851,x24854,x24855,x24856),f670(x24853,x24852,x24854,x24855,x24856))
% 28.78/28.54 [2486]~E(x24861,x24862)+E(f670(x24863,x24864,x24861,x24865,x24866),f670(x24863,x24864,x24862,x24865,x24866))
% 28.78/28.54 [2487]~E(x24871,x24872)+E(f670(x24873,x24874,x24875,x24871,x24876),f670(x24873,x24874,x24875,x24872,x24876))
% 28.78/28.54 [2488]~E(x24881,x24882)+E(f670(x24883,x24884,x24885,x24886,x24881),f670(x24883,x24884,x24885,x24886,x24882))
% 28.78/28.54 [2489]~E(x24891,x24892)+E(f700(x24891,x24893,x24894,x24895,x24896),f700(x24892,x24893,x24894,x24895,x24896))
% 28.78/28.54 [2490]~E(x24901,x24902)+E(f700(x24903,x24901,x24904,x24905,x24906),f700(x24903,x24902,x24904,x24905,x24906))
% 28.78/28.54 [2491]~E(x24911,x24912)+E(f700(x24913,x24914,x24911,x24915,x24916),f700(x24913,x24914,x24912,x24915,x24916))
% 28.78/28.54 [2492]~E(x24921,x24922)+E(f700(x24923,x24924,x24925,x24921,x24926),f700(x24923,x24924,x24925,x24922,x24926))
% 28.78/28.54 [2493]~E(x24931,x24932)+E(f700(x24933,x24934,x24935,x24936,x24931),f700(x24933,x24934,x24935,x24936,x24932))
% 28.78/28.54 [2494]~E(x24941,x24942)+E(f585(x24941,x24943,x24944,x24945,x24946),f585(x24942,x24943,x24944,x24945,x24946))
% 28.78/28.54 [2495]~E(x24951,x24952)+E(f585(x24953,x24951,x24954,x24955,x24956),f585(x24953,x24952,x24954,x24955,x24956))
% 28.78/28.54 [2496]~E(x24961,x24962)+E(f585(x24963,x24964,x24961,x24965,x24966),f585(x24963,x24964,x24962,x24965,x24966))
% 28.78/28.54 [2497]~E(x24971,x24972)+E(f585(x24973,x24974,x24975,x24971,x24976),f585(x24973,x24974,x24975,x24972,x24976))
% 28.78/28.54 [2498]~E(x24981,x24982)+E(f585(x24983,x24984,x24985,x24986,x24981),f585(x24983,x24984,x24985,x24986,x24982))
% 28.78/28.54 [2499]~E(x24991,x24992)+E(f571(x24991,x24993,x24994,x24995),f571(x24992,x24993,x24994,x24995))
% 28.78/28.54 [2500]~E(x25001,x25002)+E(f571(x25003,x25001,x25004,x25005),f571(x25003,x25002,x25004,x25005))
% 28.78/28.54 [2501]~E(x25011,x25012)+E(f571(x25013,x25014,x25011,x25015),f571(x25013,x25014,x25012,x25015))
% 28.78/28.54 [2502]~E(x25021,x25022)+E(f571(x25023,x25024,x25025,x25021),f571(x25023,x25024,x25025,x25022))
% 28.78/28.54 [2503]~E(x25031,x25032)+E(f825(x25031,x25033),f825(x25032,x25033))
% 28.78/28.54 [2504]~E(x25041,x25042)+E(f825(x25043,x25041),f825(x25043,x25042))
% 28.78/28.54 [2505]~E(x25051,x25052)+E(f672(x25051,x25053,x25054,x25055,x25056),f672(x25052,x25053,x25054,x25055,x25056))
% 28.78/28.54 [2506]~E(x25061,x25062)+E(f672(x25063,x25061,x25064,x25065,x25066),f672(x25063,x25062,x25064,x25065,x25066))
% 28.78/28.54 [2507]~E(x25071,x25072)+E(f672(x25073,x25074,x25071,x25075,x25076),f672(x25073,x25074,x25072,x25075,x25076))
% 28.78/28.54 [2508]~E(x25081,x25082)+E(f672(x25083,x25084,x25085,x25081,x25086),f672(x25083,x25084,x25085,x25082,x25086))
% 28.78/28.54 [2509]~E(x25091,x25092)+E(f672(x25093,x25094,x25095,x25096,x25091),f672(x25093,x25094,x25095,x25096,x25092))
% 28.78/28.54 [2510]~E(x25101,x25102)+E(f17(x25101,x25103,x25104,x25105),f17(x25102,x25103,x25104,x25105))
% 28.78/28.54 [2511]~E(x25111,x25112)+E(f17(x25113,x25111,x25114,x25115),f17(x25113,x25112,x25114,x25115))
% 28.78/28.54 [2512]~E(x25121,x25122)+E(f17(x25123,x25124,x25121,x25125),f17(x25123,x25124,x25122,x25125))
% 28.78/28.54 [2513]~E(x25131,x25132)+E(f17(x25133,x25134,x25135,x25131),f17(x25133,x25134,x25135,x25132))
% 28.78/28.54 [2514]~E(x25141,x25142)+E(f505(x25141,x25143,x25144,x25145,x25146),f505(x25142,x25143,x25144,x25145,x25146))
% 28.78/28.54 [2515]~E(x25151,x25152)+E(f505(x25153,x25151,x25154,x25155,x25156),f505(x25153,x25152,x25154,x25155,x25156))
% 28.78/28.54 [2516]~E(x25161,x25162)+E(f505(x25163,x25164,x25161,x25165,x25166),f505(x25163,x25164,x25162,x25165,x25166))
% 28.78/28.54 [2517]~E(x25171,x25172)+E(f505(x25173,x25174,x25175,x25171,x25176),f505(x25173,x25174,x25175,x25172,x25176))
% 28.78/28.54 [2518]~E(x25181,x25182)+E(f505(x25183,x25184,x25185,x25186,x25181),f505(x25183,x25184,x25185,x25186,x25182))
% 28.78/28.54 [2519]~E(x25191,x25192)+E(f708(x25191,x25193,x25194,x25195),f708(x25192,x25193,x25194,x25195))
% 28.78/28.54 [2520]~E(x25201,x25202)+E(f708(x25203,x25201,x25204,x25205),f708(x25203,x25202,x25204,x25205))
% 28.78/28.54 [2521]~E(x25211,x25212)+E(f708(x25213,x25214,x25211,x25215),f708(x25213,x25214,x25212,x25215))
% 28.78/28.54 [2522]~E(x25221,x25222)+E(f708(x25223,x25224,x25225,x25221),f708(x25223,x25224,x25225,x25222))
% 28.78/28.54 [2523]~E(x25231,x25232)+E(f572(x25231,x25233,x25234,x25235),f572(x25232,x25233,x25234,x25235))
% 28.78/28.54 [2524]~E(x25241,x25242)+E(f572(x25243,x25241,x25244,x25245),f572(x25243,x25242,x25244,x25245))
% 28.78/28.54 [2525]~E(x25251,x25252)+E(f572(x25253,x25254,x25251,x25255),f572(x25253,x25254,x25252,x25255))
% 28.78/28.54 [2526]~E(x25261,x25262)+E(f572(x25263,x25264,x25265,x25261),f572(x25263,x25264,x25265,x25262))
% 28.78/28.54 [2527]~E(x25271,x25272)+E(f482(x25271,x25273),f482(x25272,x25273))
% 28.78/28.54 [2528]~E(x25281,x25282)+E(f482(x25283,x25281),f482(x25283,x25282))
% 28.78/28.54 [2529]~E(x25291,x25292)+E(f540(x25291,x25293),f540(x25292,x25293))
% 28.78/28.54 [2530]~E(x25301,x25302)+E(f540(x25303,x25301),f540(x25303,x25302))
% 28.78/28.54 [2531]~E(x25311,x25312)+E(f500(x25311,x25313,x25314,x25315,x25316,x25317,x25318,x25319),f500(x25312,x25313,x25314,x25315,x25316,x25317,x25318,x25319))
% 28.78/28.54 [2532]~E(x25321,x25322)+E(f500(x25323,x25321,x25324,x25325,x25326,x25327,x25328,x25329),f500(x25323,x25322,x25324,x25325,x25326,x25327,x25328,x25329))
% 28.78/28.54 [2533]~E(x25331,x25332)+E(f500(x25333,x25334,x25331,x25335,x25336,x25337,x25338,x25339),f500(x25333,x25334,x25332,x25335,x25336,x25337,x25338,x25339))
% 28.78/28.54 [2534]~E(x25341,x25342)+E(f500(x25343,x25344,x25345,x25341,x25346,x25347,x25348,x25349),f500(x25343,x25344,x25345,x25342,x25346,x25347,x25348,x25349))
% 28.78/28.54 [2535]~E(x25351,x25352)+E(f500(x25353,x25354,x25355,x25356,x25351,x25357,x25358,x25359),f500(x25353,x25354,x25355,x25356,x25352,x25357,x25358,x25359))
% 28.78/28.54 [2536]~E(x25361,x25362)+E(f500(x25363,x25364,x25365,x25366,x25367,x25361,x25368,x25369),f500(x25363,x25364,x25365,x25366,x25367,x25362,x25368,x25369))
% 28.78/28.54 [2537]~E(x25371,x25372)+E(f500(x25373,x25374,x25375,x25376,x25377,x25378,x25371,x25379),f500(x25373,x25374,x25375,x25376,x25377,x25378,x25372,x25379))
% 28.78/28.54 [2538]~E(x25381,x25382)+E(f500(x25383,x25384,x25385,x25386,x25387,x25388,x25389,x25381),f500(x25383,x25384,x25385,x25386,x25387,x25388,x25389,x25382))
% 28.78/28.54 [2539]~E(x25391,x25392)+E(f53(x25391,x25393,x25394,x25395),f53(x25392,x25393,x25394,x25395))
% 28.78/28.54 [2540]~E(x25401,x25402)+E(f53(x25403,x25401,x25404,x25405),f53(x25403,x25402,x25404,x25405))
% 28.78/28.54 [2541]~E(x25411,x25412)+E(f53(x25413,x25414,x25411,x25415),f53(x25413,x25414,x25412,x25415))
% 28.78/28.54 [2542]~E(x25421,x25422)+E(f53(x25423,x25424,x25425,x25421),f53(x25423,x25424,x25425,x25422))
% 28.78/28.54 [2543]~E(x25431,x25432)+E(f711(x25431,x25433,x25434),f711(x25432,x25433,x25434))
% 28.78/28.54 [2544]~E(x25441,x25442)+E(f711(x25443,x25441,x25444),f711(x25443,x25442,x25444))
% 28.78/28.54 [2545]~E(x25451,x25452)+E(f711(x25453,x25454,x25451),f711(x25453,x25454,x25452))
% 28.78/28.54 [2546]~E(x25461,x25462)+E(f899(x25461,x25463,x25464,x25465,x25466,x25467,x25468,x25469),f899(x25462,x25463,x25464,x25465,x25466,x25467,x25468,x25469))
% 28.78/28.54 [2547]~E(x25471,x25472)+E(f899(x25473,x25471,x25474,x25475,x25476,x25477,x25478,x25479),f899(x25473,x25472,x25474,x25475,x25476,x25477,x25478,x25479))
% 28.78/28.54 [2548]~E(x25481,x25482)+E(f899(x25483,x25484,x25481,x25485,x25486,x25487,x25488,x25489),f899(x25483,x25484,x25482,x25485,x25486,x25487,x25488,x25489))
% 28.78/28.54 [2549]~E(x25491,x25492)+E(f899(x25493,x25494,x25495,x25491,x25496,x25497,x25498,x25499),f899(x25493,x25494,x25495,x25492,x25496,x25497,x25498,x25499))
% 28.78/28.54 [2550]~E(x25501,x25502)+E(f899(x25503,x25504,x25505,x25506,x25501,x25507,x25508,x25509),f899(x25503,x25504,x25505,x25506,x25502,x25507,x25508,x25509))
% 28.78/28.54 [2551]~E(x25511,x25512)+E(f899(x25513,x25514,x25515,x25516,x25517,x25511,x25518,x25519),f899(x25513,x25514,x25515,x25516,x25517,x25512,x25518,x25519))
% 28.78/28.54 [2552]~E(x25521,x25522)+E(f899(x25523,x25524,x25525,x25526,x25527,x25528,x25521,x25529),f899(x25523,x25524,x25525,x25526,x25527,x25528,x25522,x25529))
% 28.78/28.54 [2553]~E(x25531,x25532)+E(f899(x25533,x25534,x25535,x25536,x25537,x25538,x25539,x25531),f899(x25533,x25534,x25535,x25536,x25537,x25538,x25539,x25532))
% 28.78/28.54 [2554]~E(x25541,x25542)+E(f724(x25541,x25543,x25544),f724(x25542,x25543,x25544))
% 28.78/28.54 [2555]~E(x25551,x25552)+E(f724(x25553,x25551,x25554),f724(x25553,x25552,x25554))
% 28.78/28.54 [2556]~E(x25561,x25562)+E(f724(x25563,x25564,x25561),f724(x25563,x25564,x25562))
% 28.78/28.54 [2557]~E(x25571,x25572)+E(f813(x25571,x25573,x25574,x25575),f813(x25572,x25573,x25574,x25575))
% 28.78/28.54 [2558]~E(x25581,x25582)+E(f813(x25583,x25581,x25584,x25585),f813(x25583,x25582,x25584,x25585))
% 28.78/28.54 [2559]~E(x25591,x25592)+E(f813(x25593,x25594,x25591,x25595),f813(x25593,x25594,x25592,x25595))
% 28.78/28.54 [2560]~E(x25601,x25602)+E(f813(x25603,x25604,x25605,x25601),f813(x25603,x25604,x25605,x25602))
% 28.78/28.54 [2561]~E(x25611,x25612)+E(f905(x25611,x25613,x25614,x25615),f905(x25612,x25613,x25614,x25615))
% 28.78/28.54 [2562]~E(x25621,x25622)+E(f905(x25623,x25621,x25624,x25625),f905(x25623,x25622,x25624,x25625))
% 28.78/28.54 [2563]~E(x25631,x25632)+E(f905(x25633,x25634,x25631,x25635),f905(x25633,x25634,x25632,x25635))
% 28.78/28.54 [2564]~E(x25641,x25642)+E(f905(x25643,x25644,x25645,x25641),f905(x25643,x25644,x25645,x25642))
% 28.78/28.54 [2565]~E(x25651,x25652)+E(f792(x25651,x25653,x25654),f792(x25652,x25653,x25654))
% 28.78/28.54 [2566]~E(x25661,x25662)+E(f792(x25663,x25661,x25664),f792(x25663,x25662,x25664))
% 28.78/28.54 [2567]~E(x25671,x25672)+E(f792(x25673,x25674,x25671),f792(x25673,x25674,x25672))
% 28.78/28.54 [2568]~E(x25681,x25682)+E(f405(x25681,x25683,x25684,x25685),f405(x25682,x25683,x25684,x25685))
% 28.78/28.54 [2569]~E(x25691,x25692)+E(f405(x25693,x25691,x25694,x25695),f405(x25693,x25692,x25694,x25695))
% 28.78/28.54 [2570]~E(x25701,x25702)+E(f405(x25703,x25704,x25701,x25705),f405(x25703,x25704,x25702,x25705))
% 28.78/28.54 [2571]~E(x25711,x25712)+E(f405(x25713,x25714,x25715,x25711),f405(x25713,x25714,x25715,x25712))
% 28.78/28.54 [2572]~E(x25721,x25722)+E(f590(x25721,x25723),f590(x25722,x25723))
% 28.78/28.54 [2573]~E(x25731,x25732)+E(f590(x25733,x25731),f590(x25733,x25732))
% 28.78/28.54 [2574]~E(x25741,x25742)+E(f773(x25741,x25743,x25744),f773(x25742,x25743,x25744))
% 28.78/28.54 [2575]~E(x25751,x25752)+E(f773(x25753,x25751,x25754),f773(x25753,x25752,x25754))
% 28.78/28.54 [2576]~E(x25761,x25762)+E(f773(x25763,x25764,x25761),f773(x25763,x25764,x25762))
% 28.78/28.54 [2577]~E(x25771,x25772)+E(f605(x25771,x25773,x25774,x25775,x25776,x25777),f605(x25772,x25773,x25774,x25775,x25776,x25777))
% 28.78/28.54 [2578]~E(x25781,x25782)+E(f605(x25783,x25781,x25784,x25785,x25786,x25787),f605(x25783,x25782,x25784,x25785,x25786,x25787))
% 28.78/28.54 [2579]~E(x25791,x25792)+E(f605(x25793,x25794,x25791,x25795,x25796,x25797),f605(x25793,x25794,x25792,x25795,x25796,x25797))
% 28.78/28.54 [2580]~E(x25801,x25802)+E(f605(x25803,x25804,x25805,x25801,x25806,x25807),f605(x25803,x25804,x25805,x25802,x25806,x25807))
% 28.78/28.54 [2581]~E(x25811,x25812)+E(f605(x25813,x25814,x25815,x25816,x25811,x25817),f605(x25813,x25814,x25815,x25816,x25812,x25817))
% 28.78/28.54 [2582]~E(x25821,x25822)+E(f605(x25823,x25824,x25825,x25826,x25827,x25821),f605(x25823,x25824,x25825,x25826,x25827,x25822))
% 28.78/28.54 [2583]~E(x25831,x25832)+E(f425(x25831),f425(x25832))
% 28.78/28.54 [2584]~E(x25841,x25842)+E(f513(x25841,x25843,x25844),f513(x25842,x25843,x25844))
% 28.78/28.54 [2585]~E(x25851,x25852)+E(f513(x25853,x25851,x25854),f513(x25853,x25852,x25854))
% 28.78/28.54 [2586]~E(x25861,x25862)+E(f513(x25863,x25864,x25861),f513(x25863,x25864,x25862))
% 28.78/28.54 [2587]~E(x25871,x25872)+E(f818(x25871,x25873,x25874,x25875),f818(x25872,x25873,x25874,x25875))
% 28.78/28.54 [2588]~E(x25881,x25882)+E(f818(x25883,x25881,x25884,x25885),f818(x25883,x25882,x25884,x25885))
% 28.78/28.54 [2589]~E(x25891,x25892)+E(f818(x25893,x25894,x25891,x25895),f818(x25893,x25894,x25892,x25895))
% 28.78/28.54 [2590]~E(x25901,x25902)+E(f818(x25903,x25904,x25905,x25901),f818(x25903,x25904,x25905,x25902))
% 28.78/28.54 [2591]~E(x25911,x25912)+E(f429(x25911,x25913,x25914,x25915,x25916),f429(x25912,x25913,x25914,x25915,x25916))
% 28.78/28.54 [2592]~E(x25921,x25922)+E(f429(x25923,x25921,x25924,x25925,x25926),f429(x25923,x25922,x25924,x25925,x25926))
% 28.78/28.54 [2593]~E(x25931,x25932)+E(f429(x25933,x25934,x25931,x25935,x25936),f429(x25933,x25934,x25932,x25935,x25936))
% 28.78/28.54 [2594]~E(x25941,x25942)+E(f429(x25943,x25944,x25945,x25941,x25946),f429(x25943,x25944,x25945,x25942,x25946))
% 28.78/28.54 [2595]~E(x25951,x25952)+E(f429(x25953,x25954,x25955,x25956,x25951),f429(x25953,x25954,x25955,x25956,x25952))
% 28.78/28.54 [2596]~E(x25961,x25962)+E(f765(x25961,x25963,x25964,x25965,x25966),f765(x25962,x25963,x25964,x25965,x25966))
% 28.78/28.54 [2597]~E(x25971,x25972)+E(f765(x25973,x25971,x25974,x25975,x25976),f765(x25973,x25972,x25974,x25975,x25976))
% 28.78/28.54 [2598]~E(x25981,x25982)+E(f765(x25983,x25984,x25981,x25985,x25986),f765(x25983,x25984,x25982,x25985,x25986))
% 28.78/28.54 [2599]~E(x25991,x25992)+E(f765(x25993,x25994,x25995,x25991,x25996),f765(x25993,x25994,x25995,x25992,x25996))
% 28.78/28.54 [2600]~E(x26001,x26002)+E(f765(x26003,x26004,x26005,x26006,x26001),f765(x26003,x26004,x26005,x26006,x26002))
% 28.78/28.54 [2601]~E(x26011,x26012)+E(f21(x26011,x26013),f21(x26012,x26013))
% 28.78/28.54 [2602]~E(x26021,x26022)+E(f21(x26023,x26021),f21(x26023,x26022))
% 28.78/28.54 [2603]~E(x26031,x26032)+E(f609(x26031,x26033,x26034,x26035,x26036,x26037),f609(x26032,x26033,x26034,x26035,x26036,x26037))
% 28.78/28.54 [2604]~E(x26041,x26042)+E(f609(x26043,x26041,x26044,x26045,x26046,x26047),f609(x26043,x26042,x26044,x26045,x26046,x26047))
% 28.78/28.54 [2605]~E(x26051,x26052)+E(f609(x26053,x26054,x26051,x26055,x26056,x26057),f609(x26053,x26054,x26052,x26055,x26056,x26057))
% 28.78/28.54 [2606]~E(x26061,x26062)+E(f609(x26063,x26064,x26065,x26061,x26066,x26067),f609(x26063,x26064,x26065,x26062,x26066,x26067))
% 28.78/28.54 [2607]~E(x26071,x26072)+E(f609(x26073,x26074,x26075,x26076,x26071,x26077),f609(x26073,x26074,x26075,x26076,x26072,x26077))
% 28.78/28.54 [2608]~E(x26081,x26082)+E(f609(x26083,x26084,x26085,x26086,x26087,x26081),f609(x26083,x26084,x26085,x26086,x26087,x26082))
% 28.78/28.54 [2609]~E(x26091,x26092)+E(f359(x26091,x26093,x26094,x26095),f359(x26092,x26093,x26094,x26095))
% 28.78/28.54 [2610]~E(x26101,x26102)+E(f359(x26103,x26101,x26104,x26105),f359(x26103,x26102,x26104,x26105))
% 28.78/28.54 [2611]~E(x26111,x26112)+E(f359(x26113,x26114,x26111,x26115),f359(x26113,x26114,x26112,x26115))
% 28.78/28.54 [2612]~E(x26121,x26122)+E(f359(x26123,x26124,x26125,x26121),f359(x26123,x26124,x26125,x26122))
% 28.78/28.54 [2613]~E(x26131,x26132)+E(f476(x26131,x26133,x26134),f476(x26132,x26133,x26134))
% 28.78/28.54 [2614]~E(x26141,x26142)+E(f476(x26143,x26141,x26144),f476(x26143,x26142,x26144))
% 28.78/28.54 [2615]~E(x26151,x26152)+E(f476(x26153,x26154,x26151),f476(x26153,x26154,x26152))
% 28.78/28.54 [2616]~E(x26161,x26162)+E(f582(x26161,x26163,x26164,x26165,x26166,x26167),f582(x26162,x26163,x26164,x26165,x26166,x26167))
% 28.78/28.54 [2617]~E(x26171,x26172)+E(f582(x26173,x26171,x26174,x26175,x26176,x26177),f582(x26173,x26172,x26174,x26175,x26176,x26177))
% 28.78/28.54 [2618]~E(x26181,x26182)+E(f582(x26183,x26184,x26181,x26185,x26186,x26187),f582(x26183,x26184,x26182,x26185,x26186,x26187))
% 28.78/28.54 [2619]~E(x26191,x26192)+E(f582(x26193,x26194,x26195,x26191,x26196,x26197),f582(x26193,x26194,x26195,x26192,x26196,x26197))
% 28.78/28.54 [2620]~E(x26201,x26202)+E(f582(x26203,x26204,x26205,x26206,x26201,x26207),f582(x26203,x26204,x26205,x26206,x26202,x26207))
% 28.78/28.54 [2621]~E(x26211,x26212)+E(f582(x26213,x26214,x26215,x26216,x26217,x26211),f582(x26213,x26214,x26215,x26216,x26217,x26212))
% 28.78/28.54 [2622]~E(x26221,x26222)+E(f545(x26221,x26223,x26224,x26225),f545(x26222,x26223,x26224,x26225))
% 28.78/28.54 [2623]~E(x26231,x26232)+E(f545(x26233,x26231,x26234,x26235),f545(x26233,x26232,x26234,x26235))
% 28.78/28.54 [2624]~E(x26241,x26242)+E(f545(x26243,x26244,x26241,x26245),f545(x26243,x26244,x26242,x26245))
% 28.78/28.54 [2625]~E(x26251,x26252)+E(f545(x26253,x26254,x26255,x26251),f545(x26253,x26254,x26255,x26252))
% 28.78/28.54 [2626]~E(x26261,x26262)+E(f675(x26261,x26263,x26264,x26265,x26266),f675(x26262,x26263,x26264,x26265,x26266))
% 28.78/28.54 [2627]~E(x26271,x26272)+E(f675(x26273,x26271,x26274,x26275,x26276),f675(x26273,x26272,x26274,x26275,x26276))
% 28.78/28.54 [2628]~E(x26281,x26282)+E(f675(x26283,x26284,x26281,x26285,x26286),f675(x26283,x26284,x26282,x26285,x26286))
% 28.78/28.54 [2629]~E(x26291,x26292)+E(f675(x26293,x26294,x26295,x26291,x26296),f675(x26293,x26294,x26295,x26292,x26296))
% 28.78/28.54 [2630]~E(x26301,x26302)+E(f675(x26303,x26304,x26305,x26306,x26301),f675(x26303,x26304,x26305,x26306,x26302))
% 28.78/28.54 [2631]~E(x26311,x26312)+E(f558(x26311),f558(x26312))
% 28.78/28.54 [2632]~E(x26321,x26322)+E(f323(x26321,x26323,x26324,x26325),f323(x26322,x26323,x26324,x26325))
% 28.78/28.54 [2633]~E(x26331,x26332)+E(f323(x26333,x26331,x26334,x26335),f323(x26333,x26332,x26334,x26335))
% 28.78/28.54 [2634]~E(x26341,x26342)+E(f323(x26343,x26344,x26341,x26345),f323(x26343,x26344,x26342,x26345))
% 28.78/28.54 [2635]~E(x26351,x26352)+E(f323(x26353,x26354,x26355,x26351),f323(x26353,x26354,x26355,x26352))
% 28.78/28.54 [2636]~E(x26361,x26362)+E(f257(x26361,x26363,x26364),f257(x26362,x26363,x26364))
% 28.78/28.54 [2637]~E(x26371,x26372)+E(f257(x26373,x26371,x26374),f257(x26373,x26372,x26374))
% 28.78/28.54 [2638]~E(x26381,x26382)+E(f257(x26383,x26384,x26381),f257(x26383,x26384,x26382))
% 28.78/28.54 [2639]~E(x26391,x26392)+E(f618(x26391,x26393,x26394,x26395),f618(x26392,x26393,x26394,x26395))
% 28.78/28.54 [2640]~E(x26401,x26402)+E(f618(x26403,x26401,x26404,x26405),f618(x26403,x26402,x26404,x26405))
% 28.78/28.54 [2641]~E(x26411,x26412)+E(f618(x26413,x26414,x26411,x26415),f618(x26413,x26414,x26412,x26415))
% 28.78/28.54 [2642]~E(x26421,x26422)+E(f618(x26423,x26424,x26425,x26421),f618(x26423,x26424,x26425,x26422))
% 28.78/28.54 [2643]~E(x26431,x26432)+E(f271(x26431,x26433,x26434,x26435),f271(x26432,x26433,x26434,x26435))
% 28.78/28.54 [2644]~E(x26441,x26442)+E(f271(x26443,x26441,x26444,x26445),f271(x26443,x26442,x26444,x26445))
% 28.78/28.54 [2645]~E(x26451,x26452)+E(f271(x26453,x26454,x26451,x26455),f271(x26453,x26454,x26452,x26455))
% 28.78/28.54 [2646]~E(x26461,x26462)+E(f271(x26463,x26464,x26465,x26461),f271(x26463,x26464,x26465,x26462))
% 28.78/28.54 [2647]~E(x26471,x26472)+E(f654(x26471,x26473,x26474,x26475,x26476,x26477,x26478),f654(x26472,x26473,x26474,x26475,x26476,x26477,x26478))
% 28.78/28.54 [2648]~E(x26481,x26482)+E(f654(x26483,x26481,x26484,x26485,x26486,x26487,x26488),f654(x26483,x26482,x26484,x26485,x26486,x26487,x26488))
% 28.78/28.54 [2649]~E(x26491,x26492)+E(f654(x26493,x26494,x26491,x26495,x26496,x26497,x26498),f654(x26493,x26494,x26492,x26495,x26496,x26497,x26498))
% 28.78/28.54 [2650]~E(x26501,x26502)+E(f654(x26503,x26504,x26505,x26501,x26506,x26507,x26508),f654(x26503,x26504,x26505,x26502,x26506,x26507,x26508))
% 28.78/28.54 [2651]~E(x26511,x26512)+E(f654(x26513,x26514,x26515,x26516,x26511,x26517,x26518),f654(x26513,x26514,x26515,x26516,x26512,x26517,x26518))
% 28.78/28.54 [2652]~E(x26521,x26522)+E(f654(x26523,x26524,x26525,x26526,x26527,x26521,x26528),f654(x26523,x26524,x26525,x26526,x26527,x26522,x26528))
% 28.78/28.54 [2653]~E(x26531,x26532)+E(f654(x26533,x26534,x26535,x26536,x26537,x26538,x26531),f654(x26533,x26534,x26535,x26536,x26537,x26538,x26532))
% 28.78/28.54 [2654]~E(x26541,x26542)+E(f346(x26541,x26543),f346(x26542,x26543))
% 28.78/28.54 [2655]~E(x26551,x26552)+E(f346(x26553,x26551),f346(x26553,x26552))
% 28.78/28.54 [2656]~E(x26561,x26562)+E(f395(x26561,x26563),f395(x26562,x26563))
% 28.78/28.54 [2657]~E(x26571,x26572)+E(f395(x26573,x26571),f395(x26573,x26572))
% 28.78/28.54 [2658]~E(x26581,x26582)+E(f239(x26581,x26583,x26584),f239(x26582,x26583,x26584))
% 28.78/28.54 [2659]~E(x26591,x26592)+E(f239(x26593,x26591,x26594),f239(x26593,x26592,x26594))
% 28.78/28.54 [2660]~E(x26601,x26602)+E(f239(x26603,x26604,x26601),f239(x26603,x26604,x26602))
% 28.78/28.54 [2661]~E(x26611,x26612)+E(f253(x26611,x26613,x26614,x26615,x26616),f253(x26612,x26613,x26614,x26615,x26616))
% 28.78/28.54 [2662]~E(x26621,x26622)+E(f253(x26623,x26621,x26624,x26625,x26626),f253(x26623,x26622,x26624,x26625,x26626))
% 28.78/28.54 [2663]~E(x26631,x26632)+E(f253(x26633,x26634,x26631,x26635,x26636),f253(x26633,x26634,x26632,x26635,x26636))
% 28.78/28.54 [2664]~E(x26641,x26642)+E(f253(x26643,x26644,x26645,x26641,x26646),f253(x26643,x26644,x26645,x26642,x26646))
% 28.78/28.54 [2665]~E(x26651,x26652)+E(f253(x26653,x26654,x26655,x26656,x26651),f253(x26653,x26654,x26655,x26656,x26652))
% 28.78/28.54 [2666]~E(x26661,x26662)+E(f426(x26661),f426(x26662))
% 28.78/28.54 [2667]~E(x26671,x26672)+E(f217(x26671,x26673,x26674,x26675,x26676),f217(x26672,x26673,x26674,x26675,x26676))
% 28.78/28.54 [2668]~E(x26681,x26682)+E(f217(x26683,x26681,x26684,x26685,x26686),f217(x26683,x26682,x26684,x26685,x26686))
% 28.78/28.54 [2669]~E(x26691,x26692)+E(f217(x26693,x26694,x26691,x26695,x26696),f217(x26693,x26694,x26692,x26695,x26696))
% 28.78/28.54 [2670]~E(x26701,x26702)+E(f217(x26703,x26704,x26705,x26701,x26706),f217(x26703,x26704,x26705,x26702,x26706))
% 28.78/28.54 [2671]~E(x26711,x26712)+E(f217(x26713,x26714,x26715,x26716,x26711),f217(x26713,x26714,x26715,x26716,x26712))
% 28.78/28.54 [2672]~E(x26721,x26722)+E(f706(x26721,x26723,x26724,x26725),f706(x26722,x26723,x26724,x26725))
% 28.78/28.54 [2673]~E(x26731,x26732)+E(f706(x26733,x26731,x26734,x26735),f706(x26733,x26732,x26734,x26735))
% 28.78/28.54 [2674]~E(x26741,x26742)+E(f706(x26743,x26744,x26741,x26745),f706(x26743,x26744,x26742,x26745))
% 28.78/28.54 [2675]~E(x26751,x26752)+E(f706(x26753,x26754,x26755,x26751),f706(x26753,x26754,x26755,x26752))
% 28.78/28.54 [2676]~E(x26761,x26762)+E(f546(x26761,x26763,x26764,x26765,x26766,x26767),f546(x26762,x26763,x26764,x26765,x26766,x26767))
% 28.78/28.54 [2677]~E(x26771,x26772)+E(f546(x26773,x26771,x26774,x26775,x26776,x26777),f546(x26773,x26772,x26774,x26775,x26776,x26777))
% 28.78/28.54 [2678]~E(x26781,x26782)+E(f546(x26783,x26784,x26781,x26785,x26786,x26787),f546(x26783,x26784,x26782,x26785,x26786,x26787))
% 28.78/28.54 [2679]~E(x26791,x26792)+E(f546(x26793,x26794,x26795,x26791,x26796,x26797),f546(x26793,x26794,x26795,x26792,x26796,x26797))
% 28.78/28.54 [2680]~E(x26801,x26802)+E(f546(x26803,x26804,x26805,x26806,x26801,x26807),f546(x26803,x26804,x26805,x26806,x26802,x26807))
% 28.78/28.54 [2681]~E(x26811,x26812)+E(f546(x26813,x26814,x26815,x26816,x26817,x26811),f546(x26813,x26814,x26815,x26816,x26817,x26812))
% 28.78/28.54 [2682]~E(x26821,x26822)+E(f819(x26821,x26823,x26824,x26825,x26826),f819(x26822,x26823,x26824,x26825,x26826))
% 28.78/28.54 [2683]~E(x26831,x26832)+E(f819(x26833,x26831,x26834,x26835,x26836),f819(x26833,x26832,x26834,x26835,x26836))
% 28.78/28.54 [2684]~E(x26841,x26842)+E(f819(x26843,x26844,x26841,x26845,x26846),f819(x26843,x26844,x26842,x26845,x26846))
% 28.78/28.54 [2685]~E(x26851,x26852)+E(f819(x26853,x26854,x26855,x26851,x26856),f819(x26853,x26854,x26855,x26852,x26856))
% 28.78/28.54 [2686]~E(x26861,x26862)+E(f819(x26863,x26864,x26865,x26866,x26861),f819(x26863,x26864,x26865,x26866,x26862))
% 28.78/28.54 [2687]~E(x26871,x26872)+E(f629(x26871,x26873),f629(x26872,x26873))
% 28.78/28.54 [2688]~E(x26881,x26882)+E(f629(x26883,x26881),f629(x26883,x26882))
% 28.78/28.54 [2689]~E(x26891,x26892)+E(f400(x26891,x26893,x26894,x26895),f400(x26892,x26893,x26894,x26895))
% 28.78/28.54 [2690]~E(x26901,x26902)+E(f400(x26903,x26901,x26904,x26905),f400(x26903,x26902,x26904,x26905))
% 28.78/28.54 [2691]~E(x26911,x26912)+E(f400(x26913,x26914,x26911,x26915),f400(x26913,x26914,x26912,x26915))
% 28.78/28.54 [2692]~E(x26921,x26922)+E(f400(x26923,x26924,x26925,x26921),f400(x26923,x26924,x26925,x26922))
% 28.78/28.54 [2693]~E(x26931,x26932)+E(f524(x26931,x26933,x26934),f524(x26932,x26933,x26934))
% 28.78/28.54 [2694]~E(x26941,x26942)+E(f524(x26943,x26941,x26944),f524(x26943,x26942,x26944))
% 28.78/28.54 [2695]~E(x26951,x26952)+E(f524(x26953,x26954,x26951),f524(x26953,x26954,x26952))
% 28.78/28.54 [2696]~E(x26961,x26962)+E(f886(x26961,x26963,x26964,x26965,x26966),f886(x26962,x26963,x26964,x26965,x26966))
% 28.78/28.54 [2697]~E(x26971,x26972)+E(f886(x26973,x26971,x26974,x26975,x26976),f886(x26973,x26972,x26974,x26975,x26976))
% 28.78/28.54 [2698]~E(x26981,x26982)+E(f886(x26983,x26984,x26981,x26985,x26986),f886(x26983,x26984,x26982,x26985,x26986))
% 28.78/28.54 [2699]~E(x26991,x26992)+E(f886(x26993,x26994,x26995,x26991,x26996),f886(x26993,x26994,x26995,x26992,x26996))
% 28.78/28.54 [2700]~E(x27001,x27002)+E(f886(x27003,x27004,x27005,x27006,x27001),f886(x27003,x27004,x27005,x27006,x27002))
% 28.78/28.54 [2701]~E(x27011,x27012)+E(f324(x27011),f324(x27012))
% 28.78/28.54 [2702]~E(x27021,x27022)+E(f383(x27021,x27023,x27024,x27025),f383(x27022,x27023,x27024,x27025))
% 28.78/28.54 [2703]~E(x27031,x27032)+E(f383(x27033,x27031,x27034,x27035),f383(x27033,x27032,x27034,x27035))
% 28.78/28.54 [2704]~E(x27041,x27042)+E(f383(x27043,x27044,x27041,x27045),f383(x27043,x27044,x27042,x27045))
% 28.78/28.54 [2705]~E(x27051,x27052)+E(f383(x27053,x27054,x27055,x27051),f383(x27053,x27054,x27055,x27052))
% 28.78/28.54 [2706]~E(x27061,x27062)+E(f116(x27061),f116(x27062))
% 28.78/28.54 [2707]~E(x27071,x27072)+E(f917(x27071,x27073,x27074,x27075),f917(x27072,x27073,x27074,x27075))
% 28.78/28.54 [2708]~E(x27081,x27082)+E(f917(x27083,x27081,x27084,x27085),f917(x27083,x27082,x27084,x27085))
% 28.78/28.54 [2709]~E(x27091,x27092)+E(f917(x27093,x27094,x27091,x27095),f917(x27093,x27094,x27092,x27095))
% 28.78/28.54 [2710]~E(x27101,x27102)+E(f917(x27103,x27104,x27105,x27101),f917(x27103,x27104,x27105,x27102))
% 28.78/28.54 [2711]~E(x27111,x27112)+E(f228(x27111,x27113),f228(x27112,x27113))
% 28.78/28.54 [2712]~E(x27121,x27122)+E(f228(x27123,x27121),f228(x27123,x27122))
% 28.78/28.54 [2713]~E(x27131,x27132)+E(f36(x27131),f36(x27132))
% 28.78/28.54 [2714]~E(x27141,x27142)+E(f776(x27141,x27143,x27144),f776(x27142,x27143,x27144))
% 28.78/28.54 [2715]~E(x27151,x27152)+E(f776(x27153,x27151,x27154),f776(x27153,x27152,x27154))
% 28.78/28.54 [2716]~E(x27161,x27162)+E(f776(x27163,x27164,x27161),f776(x27163,x27164,x27162))
% 28.78/28.54 [2717]~E(x27171,x27172)+E(f220(x27171,x27173,x27174),f220(x27172,x27173,x27174))
% 28.78/28.54 [2718]~E(x27181,x27182)+E(f220(x27183,x27181,x27184),f220(x27183,x27182,x27184))
% 28.78/28.54 [2719]~E(x27191,x27192)+E(f220(x27193,x27194,x27191),f220(x27193,x27194,x27192))
% 28.78/28.54 [2720]~E(x27201,x27202)+E(f201(x27201,x27203,x27204,x27205),f201(x27202,x27203,x27204,x27205))
% 28.78/28.54 [2721]~E(x27211,x27212)+E(f201(x27213,x27211,x27214,x27215),f201(x27213,x27212,x27214,x27215))
% 28.78/28.54 [2722]~E(x27221,x27222)+E(f201(x27223,x27224,x27221,x27225),f201(x27223,x27224,x27222,x27225))
% 28.78/28.54 [2723]~E(x27231,x27232)+E(f201(x27233,x27234,x27235,x27231),f201(x27233,x27234,x27235,x27232))
% 28.78/28.54 [2724]~E(x27241,x27242)+E(f662(x27241,x27243,x27244,x27245),f662(x27242,x27243,x27244,x27245))
% 28.78/28.54 [2725]~E(x27251,x27252)+E(f662(x27253,x27251,x27254,x27255),f662(x27253,x27252,x27254,x27255))
% 28.78/28.54 [2726]~E(x27261,x27262)+E(f662(x27263,x27264,x27261,x27265),f662(x27263,x27264,x27262,x27265))
% 28.78/28.54 [2727]~E(x27271,x27272)+E(f662(x27273,x27274,x27275,x27271),f662(x27273,x27274,x27275,x27272))
% 28.78/28.54 [2728]~E(x27281,x27282)+E(f285(x27281,x27283),f285(x27282,x27283))
% 28.78/28.54 [2729]~E(x27291,x27292)+E(f285(x27293,x27291),f285(x27293,x27292))
% 28.78/28.54 [2730]~E(x27301,x27302)+E(f801(x27301,x27303,x27304),f801(x27302,x27303,x27304))
% 28.78/28.54 [2731]~E(x27311,x27312)+E(f801(x27313,x27311,x27314),f801(x27313,x27312,x27314))
% 28.78/28.54 [2732]~E(x27321,x27322)+E(f801(x27323,x27324,x27321),f801(x27323,x27324,x27322))
% 28.78/28.54 [2733]~E(x27331,x27332)+E(f462(x27331,x27333,x27334,x27335,x27336),f462(x27332,x27333,x27334,x27335,x27336))
% 28.78/28.54 [2734]~E(x27341,x27342)+E(f462(x27343,x27341,x27344,x27345,x27346),f462(x27343,x27342,x27344,x27345,x27346))
% 28.78/28.54 [2735]~E(x27351,x27352)+E(f462(x27353,x27354,x27351,x27355,x27356),f462(x27353,x27354,x27352,x27355,x27356))
% 28.78/28.54 [2736]~E(x27361,x27362)+E(f462(x27363,x27364,x27365,x27361,x27366),f462(x27363,x27364,x27365,x27362,x27366))
% 28.78/28.54 [2737]~E(x27371,x27372)+E(f462(x27373,x27374,x27375,x27376,x27371),f462(x27373,x27374,x27375,x27376,x27372))
% 28.78/28.54 [2738]~E(x27381,x27382)+E(f530(x27381,x27383,x27384,x27385,x27386),f530(x27382,x27383,x27384,x27385,x27386))
% 28.78/28.54 [2739]~E(x27391,x27392)+E(f530(x27393,x27391,x27394,x27395,x27396),f530(x27393,x27392,x27394,x27395,x27396))
% 28.78/28.54 [2740]~E(x27401,x27402)+E(f530(x27403,x27404,x27401,x27405,x27406),f530(x27403,x27404,x27402,x27405,x27406))
% 28.78/28.54 [2741]~E(x27411,x27412)+E(f530(x27413,x27414,x27415,x27411,x27416),f530(x27413,x27414,x27415,x27412,x27416))
% 28.78/28.54 [2742]~E(x27421,x27422)+E(f530(x27423,x27424,x27425,x27426,x27421),f530(x27423,x27424,x27425,x27426,x27422))
% 28.78/28.54 [2743]~E(x27431,x27432)+E(f195(x27431,x27433,x27434),f195(x27432,x27433,x27434))
% 28.78/28.54 [2744]~E(x27441,x27442)+E(f195(x27443,x27441,x27444),f195(x27443,x27442,x27444))
% 28.78/28.54 [2745]~E(x27451,x27452)+E(f195(x27453,x27454,x27451),f195(x27453,x27454,x27452))
% 28.78/28.54 [2746]~E(x27461,x27462)+E(f589(x27461),f589(x27462))
% 28.78/28.54 [2747]~E(x27471,x27472)+E(f427(x27471),f427(x27472))
% 28.78/28.54 [2748]~E(x27481,x27482)+E(f363(x27481,x27483),f363(x27482,x27483))
% 28.78/28.54 [2749]~E(x27491,x27492)+E(f363(x27493,x27491),f363(x27493,x27492))
% 28.78/28.54 [2750]~E(x27501,x27502)+E(f895(x27501,x27503,x27504),f895(x27502,x27503,x27504))
% 28.78/28.54 [2751]~E(x27511,x27512)+E(f895(x27513,x27511,x27514),f895(x27513,x27512,x27514))
% 28.78/28.54 [2752]~E(x27521,x27522)+E(f895(x27523,x27524,x27521),f895(x27523,x27524,x27522))
% 28.78/28.54 [2753]~E(x27531,x27532)+E(f214(x27531,x27533,x27534),f214(x27532,x27533,x27534))
% 28.78/28.54 [2754]~E(x27541,x27542)+E(f214(x27543,x27541,x27544),f214(x27543,x27542,x27544))
% 28.78/28.54 [2755]~E(x27551,x27552)+E(f214(x27553,x27554,x27551),f214(x27553,x27554,x27552))
% 28.78/28.54 [2756]~E(x27561,x27562)+E(f673(x27561,x27563),f673(x27562,x27563))
% 28.78/28.54 [2757]~E(x27571,x27572)+E(f673(x27573,x27571),f673(x27573,x27572))
% 28.78/28.54 [2758]~E(x27581,x27582)+E(f761(x27581,x27583,x27584,x27585),f761(x27582,x27583,x27584,x27585))
% 28.78/28.54 [2759]~E(x27591,x27592)+E(f761(x27593,x27591,x27594,x27595),f761(x27593,x27592,x27594,x27595))
% 28.78/28.54 [2760]~E(x27601,x27602)+E(f761(x27603,x27604,x27601,x27605),f761(x27603,x27604,x27602,x27605))
% 28.78/28.54 [2761]~E(x27611,x27612)+E(f761(x27613,x27614,x27615,x27611),f761(x27613,x27614,x27615,x27612))
% 28.78/28.54 [2762]~E(x27621,x27622)+E(f199(x27621,x27623,x27624,x27625,x27626,x27627,x27628),f199(x27622,x27623,x27624,x27625,x27626,x27627,x27628))
% 28.78/28.54 [2763]~E(x27631,x27632)+E(f199(x27633,x27631,x27634,x27635,x27636,x27637,x27638),f199(x27633,x27632,x27634,x27635,x27636,x27637,x27638))
% 28.78/28.54 [2764]~E(x27641,x27642)+E(f199(x27643,x27644,x27641,x27645,x27646,x27647,x27648),f199(x27643,x27644,x27642,x27645,x27646,x27647,x27648))
% 28.78/28.54 [2765]~E(x27651,x27652)+E(f199(x27653,x27654,x27655,x27651,x27656,x27657,x27658),f199(x27653,x27654,x27655,x27652,x27656,x27657,x27658))
% 28.78/28.54 [2766]~E(x27661,x27662)+E(f199(x27663,x27664,x27665,x27666,x27661,x27667,x27668),f199(x27663,x27664,x27665,x27666,x27662,x27667,x27668))
% 28.78/28.54 [2767]~E(x27671,x27672)+E(f199(x27673,x27674,x27675,x27676,x27677,x27671,x27678),f199(x27673,x27674,x27675,x27676,x27677,x27672,x27678))
% 28.78/28.54 [2768]~E(x27681,x27682)+E(f199(x27683,x27684,x27685,x27686,x27687,x27688,x27681),f199(x27683,x27684,x27685,x27686,x27687,x27688,x27682))
% 28.78/28.54 [2769]~E(x27691,x27692)+E(f894(x27691,x27693,x27694,x27695),f894(x27692,x27693,x27694,x27695))
% 28.78/28.54 [2770]~E(x27701,x27702)+E(f894(x27703,x27701,x27704,x27705),f894(x27703,x27702,x27704,x27705))
% 28.78/28.54 [2771]~E(x27711,x27712)+E(f894(x27713,x27714,x27711,x27715),f894(x27713,x27714,x27712,x27715))
% 28.78/28.54 [2772]~E(x27721,x27722)+E(f894(x27723,x27724,x27725,x27721),f894(x27723,x27724,x27725,x27722))
% 28.78/28.54 [2773]~E(x27731,x27732)+E(f658(x27731,x27733,x27734),f658(x27732,x27733,x27734))
% 28.78/28.54 [2774]~E(x27741,x27742)+E(f658(x27743,x27741,x27744),f658(x27743,x27742,x27744))
% 28.78/28.54 [2775]~E(x27751,x27752)+E(f658(x27753,x27754,x27751),f658(x27753,x27754,x27752))
% 28.78/28.54 [2776]~E(x27761,x27762)+E(f725(x27761,x27763,x27764),f725(x27762,x27763,x27764))
% 28.78/28.54 [2777]~E(x27771,x27772)+E(f725(x27773,x27771,x27774),f725(x27773,x27772,x27774))
% 28.78/28.54 [2778]~E(x27781,x27782)+E(f725(x27783,x27784,x27781),f725(x27783,x27784,x27782))
% 28.78/28.54 [2779]~E(x27791,x27792)+E(f790(x27791,x27793,x27794,x27795),f790(x27792,x27793,x27794,x27795))
% 28.78/28.54 [2780]~E(x27801,x27802)+E(f790(x27803,x27801,x27804,x27805),f790(x27803,x27802,x27804,x27805))
% 28.78/28.54 [2781]~E(x27811,x27812)+E(f790(x27813,x27814,x27811,x27815),f790(x27813,x27814,x27812,x27815))
% 28.78/28.54 [2782]~E(x27821,x27822)+E(f790(x27823,x27824,x27825,x27821),f790(x27823,x27824,x27825,x27822))
% 28.78/28.54 [2783]~E(x27831,x27832)+E(f647(x27831,x27833,x27834,x27835,x27836),f647(x27832,x27833,x27834,x27835,x27836))
% 28.78/28.54 [2784]~E(x27841,x27842)+E(f647(x27843,x27841,x27844,x27845,x27846),f647(x27843,x27842,x27844,x27845,x27846))
% 28.78/28.54 [2785]~E(x27851,x27852)+E(f647(x27853,x27854,x27851,x27855,x27856),f647(x27853,x27854,x27852,x27855,x27856))
% 28.78/28.54 [2786]~E(x27861,x27862)+E(f647(x27863,x27864,x27865,x27861,x27866),f647(x27863,x27864,x27865,x27862,x27866))
% 28.78/28.54 [2787]~E(x27871,x27872)+E(f647(x27873,x27874,x27875,x27876,x27871),f647(x27873,x27874,x27875,x27876,x27872))
% 28.78/28.54 [2788]~E(x27881,x27882)+E(f766(x27881,x27883,x27884,x27885,x27886),f766(x27882,x27883,x27884,x27885,x27886))
% 28.78/28.54 [2789]~E(x27891,x27892)+E(f766(x27893,x27891,x27894,x27895,x27896),f766(x27893,x27892,x27894,x27895,x27896))
% 28.78/28.54 [2790]~E(x27901,x27902)+E(f766(x27903,x27904,x27901,x27905,x27906),f766(x27903,x27904,x27902,x27905,x27906))
% 28.78/28.54 [2791]~E(x27911,x27912)+E(f766(x27913,x27914,x27915,x27911,x27916),f766(x27913,x27914,x27915,x27912,x27916))
% 28.78/28.54 [2792]~E(x27921,x27922)+E(f766(x27923,x27924,x27925,x27926,x27921),f766(x27923,x27924,x27925,x27926,x27922))
% 28.78/28.54 [2793]~E(x27931,x27932)+E(f221(x27931,x27933,x27934,x27935),f221(x27932,x27933,x27934,x27935))
% 28.78/28.54 [2794]~E(x27941,x27942)+E(f221(x27943,x27941,x27944,x27945),f221(x27943,x27942,x27944,x27945))
% 28.78/28.54 [2795]~E(x27951,x27952)+E(f221(x27953,x27954,x27951,x27955),f221(x27953,x27954,x27952,x27955))
% 28.78/28.54 [2796]~E(x27961,x27962)+E(f221(x27963,x27964,x27965,x27961),f221(x27963,x27964,x27965,x27962))
% 28.78/28.54 [2797]~E(x27971,x27972)+E(f343(x27971,x27973,x27974,x27975,x27976),f343(x27972,x27973,x27974,x27975,x27976))
% 28.78/28.54 [2798]~E(x27981,x27982)+E(f343(x27983,x27981,x27984,x27985,x27986),f343(x27983,x27982,x27984,x27985,x27986))
% 28.78/28.54 [2799]~E(x27991,x27992)+E(f343(x27993,x27994,x27991,x27995,x27996),f343(x27993,x27994,x27992,x27995,x27996))
% 28.78/28.54 [2800]~E(x28001,x28002)+E(f343(x28003,x28004,x28005,x28001,x28006),f343(x28003,x28004,x28005,x28002,x28006))
% 28.78/28.54 [2801]~E(x28011,x28012)+E(f343(x28013,x28014,x28015,x28016,x28011),f343(x28013,x28014,x28015,x28016,x28012))
% 28.78/28.54 [2802]~E(x28021,x28022)+E(f740(x28021,x28023,x28024),f740(x28022,x28023,x28024))
% 28.78/28.54 [2803]~E(x28031,x28032)+E(f740(x28033,x28031,x28034),f740(x28033,x28032,x28034))
% 28.78/28.54 [2804]~E(x28041,x28042)+E(f740(x28043,x28044,x28041),f740(x28043,x28044,x28042))
% 28.78/28.54 [2805]~E(x28051,x28052)+E(f559(x28051,x28053),f559(x28052,x28053))
% 28.78/28.54 [2806]~E(x28061,x28062)+E(f559(x28063,x28061),f559(x28063,x28062))
% 28.78/28.54 [2807]~E(x28071,x28072)+E(f834(x28071,x28073),f834(x28072,x28073))
% 28.78/28.54 [2808]~E(x28081,x28082)+E(f834(x28083,x28081),f834(x28083,x28082))
% 28.78/28.54 [2809]~E(x28091,x28092)+E(f263(x28091,x28093,x28094,x28095),f263(x28092,x28093,x28094,x28095))
% 28.78/28.54 [2810]~E(x28101,x28102)+E(f263(x28103,x28101,x28104,x28105),f263(x28103,x28102,x28104,x28105))
% 28.78/28.54 [2811]~E(x28111,x28112)+E(f263(x28113,x28114,x28111,x28115),f263(x28113,x28114,x28112,x28115))
% 28.78/28.54 [2812]~E(x28121,x28122)+E(f263(x28123,x28124,x28125,x28121),f263(x28123,x28124,x28125,x28122))
% 28.78/28.54 [2813]~E(x28131,x28132)+E(f888(x28131,x28133,x28134,x28135),f888(x28132,x28133,x28134,x28135))
% 28.78/28.54 [2814]~E(x28141,x28142)+E(f888(x28143,x28141,x28144,x28145),f888(x28143,x28142,x28144,x28145))
% 28.78/28.54 [2815]~E(x28151,x28152)+E(f888(x28153,x28154,x28151,x28155),f888(x28153,x28154,x28152,x28155))
% 28.78/28.54 [2816]~E(x28161,x28162)+E(f888(x28163,x28164,x28165,x28161),f888(x28163,x28164,x28165,x28162))
% 28.78/28.54 [2817]~E(x28171,x28172)+E(f203(x28171,x28173,x28174,x28175,x28176,x28177,x28178),f203(x28172,x28173,x28174,x28175,x28176,x28177,x28178))
% 28.78/28.54 [2818]~E(x28181,x28182)+E(f203(x28183,x28181,x28184,x28185,x28186,x28187,x28188),f203(x28183,x28182,x28184,x28185,x28186,x28187,x28188))
% 28.78/28.54 [2819]~E(x28191,x28192)+E(f203(x28193,x28194,x28191,x28195,x28196,x28197,x28198),f203(x28193,x28194,x28192,x28195,x28196,x28197,x28198))
% 28.78/28.54 [2820]~E(x28201,x28202)+E(f203(x28203,x28204,x28205,x28201,x28206,x28207,x28208),f203(x28203,x28204,x28205,x28202,x28206,x28207,x28208))
% 28.78/28.54 [2821]~E(x28211,x28212)+E(f203(x28213,x28214,x28215,x28216,x28211,x28217,x28218),f203(x28213,x28214,x28215,x28216,x28212,x28217,x28218))
% 28.78/28.54 [2822]~E(x28221,x28222)+E(f203(x28223,x28224,x28225,x28226,x28227,x28221,x28228),f203(x28223,x28224,x28225,x28226,x28227,x28222,x28228))
% 28.78/28.54 [2823]~E(x28231,x28232)+E(f203(x28233,x28234,x28235,x28236,x28237,x28238,x28231),f203(x28233,x28234,x28235,x28236,x28237,x28238,x28232))
% 28.78/28.54 [2824]~E(x28241,x28242)+E(f408(x28241,x28243,x28244,x28245,x28246),f408(x28242,x28243,x28244,x28245,x28246))
% 28.78/28.54 [2825]~E(x28251,x28252)+E(f408(x28253,x28251,x28254,x28255,x28256),f408(x28253,x28252,x28254,x28255,x28256))
% 28.78/28.54 [2826]~E(x28261,x28262)+E(f408(x28263,x28264,x28261,x28265,x28266),f408(x28263,x28264,x28262,x28265,x28266))
% 28.78/28.54 [2827]~E(x28271,x28272)+E(f408(x28273,x28274,x28275,x28271,x28276),f408(x28273,x28274,x28275,x28272,x28276))
% 28.78/28.54 [2828]~E(x28281,x28282)+E(f408(x28283,x28284,x28285,x28286,x28281),f408(x28283,x28284,x28285,x28286,x28282))
% 28.78/28.54 [2829]~E(x28291,x28292)+E(f735(x28291,x28293,x28294),f735(x28292,x28293,x28294))
% 28.78/28.54 [2830]~E(x28301,x28302)+E(f735(x28303,x28301,x28304),f735(x28303,x28302,x28304))
% 28.78/28.54 [2831]~E(x28311,x28312)+E(f735(x28313,x28314,x28311),f735(x28313,x28314,x28312))
% 28.78/28.54 [2832]~E(x28321,x28322)+E(f734(x28321,x28323,x28324),f734(x28322,x28323,x28324))
% 28.78/28.54 [2833]~E(x28331,x28332)+E(f734(x28333,x28331,x28334),f734(x28333,x28332,x28334))
% 28.78/28.54 [2834]~E(x28341,x28342)+E(f734(x28343,x28344,x28341),f734(x28343,x28344,x28342))
% 28.78/28.54 [2835]~E(x28351,x28352)+E(f896(x28351,x28353,x28354,x28355),f896(x28352,x28353,x28354,x28355))
% 28.78/28.54 [2836]~E(x28361,x28362)+E(f896(x28363,x28361,x28364,x28365),f896(x28363,x28362,x28364,x28365))
% 28.78/28.54 [2837]~E(x28371,x28372)+E(f896(x28373,x28374,x28371,x28375),f896(x28373,x28374,x28372,x28375))
% 28.78/28.54 [2838]~E(x28381,x28382)+E(f896(x28383,x28384,x28385,x28381),f896(x28383,x28384,x28385,x28382))
% 28.78/28.54 [2839]~E(x28391,x28392)+E(f824(x28391,x28393,x28394,x28395,x28396),f824(x28392,x28393,x28394,x28395,x28396))
% 28.78/28.54 [2840]~E(x28401,x28402)+E(f824(x28403,x28401,x28404,x28405,x28406),f824(x28403,x28402,x28404,x28405,x28406))
% 28.78/28.54 [2841]~E(x28411,x28412)+E(f824(x28413,x28414,x28411,x28415,x28416),f824(x28413,x28414,x28412,x28415,x28416))
% 28.78/28.54 [2842]~E(x28421,x28422)+E(f824(x28423,x28424,x28425,x28421,x28426),f824(x28423,x28424,x28425,x28422,x28426))
% 28.78/28.54 [2843]~E(x28431,x28432)+E(f824(x28433,x28434,x28435,x28436,x28431),f824(x28433,x28434,x28435,x28436,x28432))
% 28.78/28.54 [2844]~E(x28441,x28442)+E(f371(x28441),f371(x28442))
% 28.78/28.54 [2845]~E(x28451,x28452)+E(f758(x28451,x28453),f758(x28452,x28453))
% 28.78/28.54 [2846]~E(x28461,x28462)+E(f758(x28463,x28461),f758(x28463,x28462))
% 28.78/28.54 [2847]~E(x28471,x28472)+E(f914(x28471,x28473,x28474),f914(x28472,x28473,x28474))
% 28.78/28.54 [2848]~E(x28481,x28482)+E(f914(x28483,x28481,x28484),f914(x28483,x28482,x28484))
% 28.78/28.54 [2849]~E(x28491,x28492)+E(f914(x28493,x28494,x28491),f914(x28493,x28494,x28492))
% 28.78/28.54 [2850]~E(x28501,x28502)+E(f632(x28501,x28503,x28504),f632(x28502,x28503,x28504))
% 28.78/28.54 [2851]~E(x28511,x28512)+E(f632(x28513,x28511,x28514),f632(x28513,x28512,x28514))
% 28.78/28.54 [2852]~E(x28521,x28522)+E(f632(x28523,x28524,x28521),f632(x28523,x28524,x28522))
% 28.78/28.54 [2853]~E(x28531,x28532)+E(f564(x28531,x28533),f564(x28532,x28533))
% 28.78/28.54 [2854]~E(x28541,x28542)+E(f564(x28543,x28541),f564(x28543,x28542))
% 28.78/28.54 [2855]~E(x28551,x28552)+E(f900(x28551,x28553,x28554,x28555,x28556),f900(x28552,x28553,x28554,x28555,x28556))
% 28.78/28.54 [2856]~E(x28561,x28562)+E(f900(x28563,x28561,x28564,x28565,x28566),f900(x28563,x28562,x28564,x28565,x28566))
% 28.78/28.54 [2857]~E(x28571,x28572)+E(f900(x28573,x28574,x28571,x28575,x28576),f900(x28573,x28574,x28572,x28575,x28576))
% 28.78/28.54 [2858]~E(x28581,x28582)+E(f900(x28583,x28584,x28585,x28581,x28586),f900(x28583,x28584,x28585,x28582,x28586))
% 28.78/28.54 [2859]~E(x28591,x28592)+E(f900(x28593,x28594,x28595,x28596,x28591),f900(x28593,x28594,x28595,x28596,x28592))
% 28.78/28.54 [2860]~E(x28601,x28602)+E(f483(x28601,x28603),f483(x28602,x28603))
% 28.78/28.54 [2861]~E(x28611,x28612)+E(f483(x28613,x28611),f483(x28613,x28612))
% 28.78/28.54 [2862]~E(x28621,x28622)+E(f840(x28621,x28623,x28624),f840(x28622,x28623,x28624))
% 28.78/28.54 [2863]~E(x28631,x28632)+E(f840(x28633,x28631,x28634),f840(x28633,x28632,x28634))
% 28.78/28.54 [2864]~E(x28641,x28642)+E(f840(x28643,x28644,x28641),f840(x28643,x28644,x28642))
% 28.78/28.54 [2865]~E(x28651,x28652)+E(f419(x28651,x28653),f419(x28652,x28653))
% 28.78/28.54 [2866]~E(x28661,x28662)+E(f419(x28663,x28661),f419(x28663,x28662))
% 28.78/28.54 [2867]~E(x28671,x28672)+E(f329(x28671),f329(x28672))
% 28.78/28.54 [2868]~E(x28681,x28682)+E(f252(x28681,x28683,x28684,x28685,x28686),f252(x28682,x28683,x28684,x28685,x28686))
% 28.78/28.54 [2869]~E(x28691,x28692)+E(f252(x28693,x28691,x28694,x28695,x28696),f252(x28693,x28692,x28694,x28695,x28696))
% 28.78/28.54 [2870]~E(x28701,x28702)+E(f252(x28703,x28704,x28701,x28705,x28706),f252(x28703,x28704,x28702,x28705,x28706))
% 28.78/28.54 [2871]~E(x28711,x28712)+E(f252(x28713,x28714,x28715,x28711,x28716),f252(x28713,x28714,x28715,x28712,x28716))
% 28.78/28.54 [2872]~E(x28721,x28722)+E(f252(x28723,x28724,x28725,x28726,x28721),f252(x28723,x28724,x28725,x28726,x28722))
% 28.78/28.54 [2873]~E(x28731,x28732)+E(f902(x28731,x28733),f902(x28732,x28733))
% 28.78/28.54 [2874]~E(x28741,x28742)+E(f902(x28743,x28741),f902(x28743,x28742))
% 28.78/28.54 [2875]~E(x28751,x28752)+E(f628(x28751,x28753),f628(x28752,x28753))
% 28.78/28.54 [2876]~E(x28761,x28762)+E(f628(x28763,x28761),f628(x28763,x28762))
% 28.78/28.54 [2877]~E(x28771,x28772)+E(f529(x28771,x28773,x28774),f529(x28772,x28773,x28774))
% 28.78/28.54 [2878]~E(x28781,x28782)+E(f529(x28783,x28781,x28784),f529(x28783,x28782,x28784))
% 28.78/28.54 [2879]~E(x28791,x28792)+E(f529(x28793,x28794,x28791),f529(x28793,x28794,x28792))
% 28.78/28.54 [2880]~E(x28801,x28802)+E(f534(x28801,x28803,x28804),f534(x28802,x28803,x28804))
% 28.78/28.54 [2881]~E(x28811,x28812)+E(f534(x28813,x28811,x28814),f534(x28813,x28812,x28814))
% 28.78/28.54 [2882]~E(x28821,x28822)+E(f534(x28823,x28824,x28821),f534(x28823,x28824,x28822))
% 28.78/28.54 [2883]~E(x28831,x28832)+E(f365(x28831,x28833),f365(x28832,x28833))
% 28.78/28.54 [2884]~E(x28841,x28842)+E(f365(x28843,x28841),f365(x28843,x28842))
% 28.78/28.54 [2885]~E(x28851,x28852)+E(f468(x28851,x28853,x28854,x28855,x28856,x28857),f468(x28852,x28853,x28854,x28855,x28856,x28857))
% 28.78/28.54 [2886]~E(x28861,x28862)+E(f468(x28863,x28861,x28864,x28865,x28866,x28867),f468(x28863,x28862,x28864,x28865,x28866,x28867))
% 28.78/28.54 [2887]~E(x28871,x28872)+E(f468(x28873,x28874,x28871,x28875,x28876,x28877),f468(x28873,x28874,x28872,x28875,x28876,x28877))
% 28.78/28.54 [2888]~E(x28881,x28882)+E(f468(x28883,x28884,x28885,x28881,x28886,x28887),f468(x28883,x28884,x28885,x28882,x28886,x28887))
% 28.78/28.54 [2889]~E(x28891,x28892)+E(f468(x28893,x28894,x28895,x28896,x28891,x28897),f468(x28893,x28894,x28895,x28896,x28892,x28897))
% 28.78/28.54 [2890]~E(x28901,x28902)+E(f468(x28903,x28904,x28905,x28906,x28907,x28901),f468(x28903,x28904,x28905,x28906,x28907,x28902))
% 28.78/28.54 [2891]~E(x28911,x28912)+E(f856(x28911,x28913,x28914),f856(x28912,x28913,x28914))
% 28.78/28.54 [2892]~E(x28921,x28922)+E(f856(x28923,x28921,x28924),f856(x28923,x28922,x28924))
% 28.78/28.54 [2893]~E(x28931,x28932)+E(f856(x28933,x28934,x28931),f856(x28933,x28934,x28932))
% 28.78/28.54 [2894]~E(x28941,x28942)+E(f872(x28941,x28943,x28944),f872(x28942,x28943,x28944))
% 28.78/28.54 [2895]~E(x28951,x28952)+E(f872(x28953,x28951,x28954),f872(x28953,x28952,x28954))
% 28.78/28.54 [2896]~E(x28961,x28962)+E(f872(x28963,x28964,x28961),f872(x28963,x28964,x28962))
% 28.78/28.54 [2897]~P1(x28971)+P1(x28972)+~E(x28971,x28972)
% 28.78/28.54 [2898]~P2(x28981)+P2(x28982)+~E(x28981,x28982)
% 28.78/28.54 [2899]~P4(x28991)+P4(x28992)+~E(x28991,x28992)
% 28.78/28.54 [2900]~P90(x29001)+P90(x29002)+~E(x29001,x29002)
% 28.78/28.54 [2901]~P74(x29011)+P74(x29012)+~E(x29011,x29012)
% 28.78/28.54 [2902]~P3(x29021)+P3(x29022)+~E(x29021,x29022)
% 28.78/28.54 [2903]~P6(x29031)+P6(x29032)+~E(x29031,x29032)
% 28.78/28.54 [2904]P152(x29042,x29043,x29044)+~E(x29041,x29042)+~P152(x29041,x29043,x29044)
% 28.78/28.54 [2905]P152(x29053,x29052,x29054)+~E(x29051,x29052)+~P152(x29053,x29051,x29054)
% 28.78/28.54 [2906]P152(x29063,x29064,x29062)+~E(x29061,x29062)+~P152(x29063,x29064,x29061)
% 28.78/28.54 [2907]P151(x29072,x29073,x29074)+~E(x29071,x29072)+~P151(x29071,x29073,x29074)
% 28.78/28.54 [2908]P151(x29083,x29082,x29084)+~E(x29081,x29082)+~P151(x29083,x29081,x29084)
% 28.78/28.54 [2909]P151(x29093,x29094,x29092)+~E(x29091,x29092)+~P151(x29093,x29094,x29091)
% 28.78/28.54 [2910]~P78(x29101)+P78(x29102)+~E(x29101,x29102)
% 28.78/28.54 [2911]~P121(x29111)+P121(x29112)+~E(x29111,x29112)
% 28.78/28.54 [2912]~P72(x29121)+P72(x29122)+~E(x29121,x29122)
% 28.78/28.54 [2913]~P113(x29131)+P113(x29132)+~E(x29131,x29132)
% 28.78/28.54 [2914]~P79(x29141)+P79(x29142)+~E(x29141,x29142)
% 28.78/28.54 [2915]~P84(x29151)+P84(x29152)+~E(x29151,x29152)
% 28.78/28.54 [2916]~P73(x29161)+P73(x29162)+~E(x29161,x29162)
% 28.78/28.54 [2917]~P5(x29171)+P5(x29172)+~E(x29171,x29172)
% 28.78/28.54 [2918]~P77(x29181)+P77(x29182)+~E(x29181,x29182)
% 28.78/28.54 [2919]~P114(x29191)+P114(x29192)+~E(x29191,x29192)
% 28.78/28.54 [2920]P14(x29202,x29203)+~E(x29201,x29202)+~P14(x29201,x29203)
% 28.78/28.54 [2921]P14(x29213,x29212)+~E(x29211,x29212)+~P14(x29213,x29211)
% 28.78/28.54 [2922]~P67(x29221)+P67(x29222)+~E(x29221,x29222)
% 28.78/28.54 [2923]~P98(x29231)+P98(x29232)+~E(x29231,x29232)
% 28.78/28.54 [2924]~P96(x29241)+P96(x29242)+~E(x29241,x29242)
% 28.78/28.54 [2925]~P68(x29251)+P68(x29252)+~E(x29251,x29252)
% 28.78/28.54 [2926]~P69(x29261)+P69(x29262)+~E(x29261,x29262)
% 28.78/28.54 [2927]~P102(x29271)+P102(x29272)+~E(x29271,x29272)
% 28.78/28.54 [2928]~P126(x29281)+P126(x29282)+~E(x29281,x29282)
% 28.78/28.54 [2929]P21(x29292,x29293,x29294,x29295)+~E(x29291,x29292)+~P21(x29291,x29293,x29294,x29295)
% 28.78/28.54 [2930]P21(x29303,x29302,x29304,x29305)+~E(x29301,x29302)+~P21(x29303,x29301,x29304,x29305)
% 28.78/28.54 [2931]P21(x29313,x29314,x29312,x29315)+~E(x29311,x29312)+~P21(x29313,x29314,x29311,x29315)
% 28.78/28.54 [2932]P21(x29323,x29324,x29325,x29322)+~E(x29321,x29322)+~P21(x29323,x29324,x29325,x29321)
% 28.78/28.54 [2933]~P107(x29331)+P107(x29332)+~E(x29331,x29332)
% 28.78/28.54 [2934]P57(x29342,x29343,x29344)+~E(x29341,x29342)+~P57(x29341,x29343,x29344)
% 28.78/28.54 [2935]P57(x29353,x29352,x29354)+~E(x29351,x29352)+~P57(x29353,x29351,x29354)
% 28.78/28.54 [2936]P57(x29363,x29364,x29362)+~E(x29361,x29362)+~P57(x29363,x29364,x29361)
% 28.78/28.54 [2937]P26(x29372,x29373,x29374,x29375)+~E(x29371,x29372)+~P26(x29371,x29373,x29374,x29375)
% 28.78/28.54 [2938]P26(x29383,x29382,x29384,x29385)+~E(x29381,x29382)+~P26(x29383,x29381,x29384,x29385)
% 28.78/28.54 [2939]P26(x29393,x29394,x29392,x29395)+~E(x29391,x29392)+~P26(x29393,x29394,x29391,x29395)
% 28.78/28.54 [2940]P26(x29403,x29404,x29405,x29402)+~E(x29401,x29402)+~P26(x29403,x29404,x29405,x29401)
% 28.78/28.54 [2941]~P108(x29411)+P108(x29412)+~E(x29411,x29412)
% 28.78/28.54 [2942]P18(x29422,x29423,x29424)+~E(x29421,x29422)+~P18(x29421,x29423,x29424)
% 28.78/28.54 [2943]P18(x29433,x29432,x29434)+~E(x29431,x29432)+~P18(x29433,x29431,x29434)
% 28.78/28.54 [2944]P18(x29443,x29444,x29442)+~E(x29441,x29442)+~P18(x29443,x29444,x29441)
% 28.78/28.54 [2945]P23(x29452,x29453,x29454,x29455,x29456)+~E(x29451,x29452)+~P23(x29451,x29453,x29454,x29455,x29456)
% 28.78/28.54 [2946]P23(x29463,x29462,x29464,x29465,x29466)+~E(x29461,x29462)+~P23(x29463,x29461,x29464,x29465,x29466)
% 28.78/28.54 [2947]P23(x29473,x29474,x29472,x29475,x29476)+~E(x29471,x29472)+~P23(x29473,x29474,x29471,x29475,x29476)
% 28.78/28.54 [2948]P23(x29483,x29484,x29485,x29482,x29486)+~E(x29481,x29482)+~P23(x29483,x29484,x29485,x29481,x29486)
% 28.78/28.54 [2949]P23(x29493,x29494,x29495,x29496,x29492)+~E(x29491,x29492)+~P23(x29493,x29494,x29495,x29496,x29491)
% 28.78/28.54 [2950]~P103(x29501)+P103(x29502)+~E(x29501,x29502)
% 28.78/28.54 [2951]~P115(x29511)+P115(x29512)+~E(x29511,x29512)
% 28.78/28.54 [2952]~P106(x29521)+P106(x29522)+~E(x29521,x29522)
% 28.78/28.54 [2953]P51(x29532,x29533,x29534)+~E(x29531,x29532)+~P51(x29531,x29533,x29534)
% 28.78/28.54 [2954]P51(x29543,x29542,x29544)+~E(x29541,x29542)+~P51(x29543,x29541,x29544)
% 28.78/28.54 [2955]P51(x29553,x29554,x29552)+~E(x29551,x29552)+~P51(x29553,x29554,x29551)
% 28.78/28.54 [2956]~P131(x29561)+P131(x29562)+~E(x29561,x29562)
% 28.78/28.54 [2957]~P109(x29571)+P109(x29572)+~E(x29571,x29572)
% 28.78/28.54 [2958]P32(x29582,x29583,x29584)+~E(x29581,x29582)+~P32(x29581,x29583,x29584)
% 28.78/28.54 [2959]P32(x29593,x29592,x29594)+~E(x29591,x29592)+~P32(x29593,x29591,x29594)
% 28.78/28.54 [2960]P32(x29603,x29604,x29602)+~E(x29601,x29602)+~P32(x29603,x29604,x29601)
% 28.78/28.54 [2961]~P104(x29611)+P104(x29612)+~E(x29611,x29612)
% 28.78/28.54 [2962]~P70(x29621)+P70(x29622)+~E(x29621,x29622)
% 28.78/28.54 [2963]~P83(x29631)+P83(x29632)+~E(x29631,x29632)
% 28.78/28.54 [2964]~P99(x29641)+P99(x29642)+~E(x29641,x29642)
% 28.78/28.54 [2965]~P149(x29651)+P149(x29652)+~E(x29651,x29652)
% 28.78/28.54 [2966]~P88(x29661)+P88(x29662)+~E(x29661,x29662)
% 28.78/28.54 [2967]~P76(x29671)+P76(x29672)+~E(x29671,x29672)
% 28.78/28.54 [2968]~P100(x29681)+P100(x29682)+~E(x29681,x29682)
% 28.78/28.54 [2969]~P132(x29691)+P132(x29692)+~E(x29691,x29692)
% 28.78/28.54 [2970]~P116(x29701)+P116(x29702)+~E(x29701,x29702)
% 28.78/28.54 [2971]~P117(x29711)+P117(x29712)+~E(x29711,x29712)
% 28.78/28.54 [2972]~P71(x29721)+P71(x29722)+~E(x29721,x29722)
% 28.78/28.54 [2973]~P129(x29731)+P129(x29732)+~E(x29731,x29732)
% 28.78/28.54 [2974]P27(x29742,x29743,x29744,x29745,x29746)+~E(x29741,x29742)+~P27(x29741,x29743,x29744,x29745,x29746)
% 28.78/28.54 [2975]P27(x29753,x29752,x29754,x29755,x29756)+~E(x29751,x29752)+~P27(x29753,x29751,x29754,x29755,x29756)
% 28.78/28.54 [2976]P27(x29763,x29764,x29762,x29765,x29766)+~E(x29761,x29762)+~P27(x29763,x29764,x29761,x29765,x29766)
% 28.78/28.54 [2977]P27(x29773,x29774,x29775,x29772,x29776)+~E(x29771,x29772)+~P27(x29773,x29774,x29775,x29771,x29776)
% 28.78/28.54 [2978]P27(x29783,x29784,x29785,x29786,x29782)+~E(x29781,x29782)+~P27(x29783,x29784,x29785,x29786,x29781)
% 28.78/28.54 [2979]P54(x29792,x29793)+~E(x29791,x29792)+~P54(x29791,x29793)
% 28.78/28.54 [2980]P54(x29803,x29802)+~E(x29801,x29802)+~P54(x29803,x29801)
% 28.78/28.54 [2981]P56(x29812,x29813)+~E(x29811,x29812)+~P56(x29811,x29813)
% 28.78/28.54 [2982]P56(x29823,x29822)+~E(x29821,x29822)+~P56(x29823,x29821)
% 28.78/28.54 [2983]P39(x29832,x29833)+~E(x29831,x29832)+~P39(x29831,x29833)
% 28.78/28.54 [2984]P39(x29843,x29842)+~E(x29841,x29842)+~P39(x29843,x29841)
% 28.78/28.54 [2985]~P86(x29851)+P86(x29852)+~E(x29851,x29852)
% 28.78/28.54 [2986]~P93(x29861)+P93(x29862)+~E(x29861,x29862)
% 28.78/28.54 [2987]P9(x29872,x29873,x29874)+~E(x29871,x29872)+~P9(x29871,x29873,x29874)
% 28.78/28.54 [2988]P9(x29883,x29882,x29884)+~E(x29881,x29882)+~P9(x29883,x29881,x29884)
% 28.78/28.54 [2989]P9(x29893,x29894,x29892)+~E(x29891,x29892)+~P9(x29893,x29894,x29891)
% 28.78/28.54 [2990]~P65(x29901)+P65(x29902)+~E(x29901,x29902)
% 28.78/28.54 [2991]P34(x29912,x29913,x29914)+~E(x29911,x29912)+~P34(x29911,x29913,x29914)
% 28.78/28.54 [2992]P34(x29923,x29922,x29924)+~E(x29921,x29922)+~P34(x29923,x29921,x29924)
% 28.78/28.54 [2993]P34(x29933,x29934,x29932)+~E(x29931,x29932)+~P34(x29933,x29934,x29931)
% 28.78/28.54 [2994]~P75(x29941)+P75(x29942)+~E(x29941,x29942)
% 28.78/28.54 [2995]~P87(x29951)+P87(x29952)+~E(x29951,x29952)
% 28.78/28.54 [2996]P12(x29962,x29963,x29964,x29965)+~E(x29961,x29962)+~P12(x29961,x29963,x29964,x29965)
% 28.78/28.54 [2997]P12(x29973,x29972,x29974,x29975)+~E(x29971,x29972)+~P12(x29973,x29971,x29974,x29975)
% 28.78/28.54 [2998]P12(x29983,x29984,x29982,x29985)+~E(x29981,x29982)+~P12(x29983,x29984,x29981,x29985)
% 28.78/28.54 [2999]P12(x29993,x29994,x29995,x29992)+~E(x29991,x29992)+~P12(x29993,x29994,x29995,x29991)
% 28.78/28.54 [3000]P53(x30002,x30003,x30004,x30005,x30006,x30007)+~E(x30001,x30002)+~P53(x30001,x30003,x30004,x30005,x30006,x30007)
% 28.78/28.54 [3001]P53(x30013,x30012,x30014,x30015,x30016,x30017)+~E(x30011,x30012)+~P53(x30013,x30011,x30014,x30015,x30016,x30017)
% 28.78/28.54 [3002]P53(x30023,x30024,x30022,x30025,x30026,x30027)+~E(x30021,x30022)+~P53(x30023,x30024,x30021,x30025,x30026,x30027)
% 28.78/28.54 [3003]P53(x30033,x30034,x30035,x30032,x30036,x30037)+~E(x30031,x30032)+~P53(x30033,x30034,x30035,x30031,x30036,x30037)
% 28.78/28.54 [3004]P53(x30043,x30044,x30045,x30046,x30042,x30047)+~E(x30041,x30042)+~P53(x30043,x30044,x30045,x30046,x30041,x30047)
% 28.78/28.54 [3005]P53(x30053,x30054,x30055,x30056,x30057,x30052)+~E(x30051,x30052)+~P53(x30053,x30054,x30055,x30056,x30057,x30051)
% 28.78/28.54 [3006]~P143(x30061)+P143(x30062)+~E(x30061,x30062)
% 28.78/28.54 [3007]P38(x30072,x30073)+~E(x30071,x30072)+~P38(x30071,x30073)
% 28.78/28.54 [3008]P38(x30083,x30082)+~E(x30081,x30082)+~P38(x30083,x30081)
% 28.78/28.54 [3009]P36(x30092,x30093,x30094)+~E(x30091,x30092)+~P36(x30091,x30093,x30094)
% 28.78/28.54 [3010]P36(x30103,x30102,x30104)+~E(x30101,x30102)+~P36(x30103,x30101,x30104)
% 28.78/28.54 [3011]P36(x30113,x30114,x30112)+~E(x30111,x30112)+~P36(x30113,x30114,x30111)
% 28.78/28.54 [3012]P41(x30122,x30123,x30124)+~E(x30121,x30122)+~P41(x30121,x30123,x30124)
% 28.78/28.54 [3013]P41(x30133,x30132,x30134)+~E(x30131,x30132)+~P41(x30133,x30131,x30134)
% 28.78/28.54 [3014]P41(x30143,x30144,x30142)+~E(x30141,x30142)+~P41(x30143,x30144,x30141)
% 28.78/28.54 [3015]~P42(x30151)+P42(x30152)+~E(x30151,x30152)
% 28.78/28.54 [3016]~P142(x30161)+P142(x30162)+~E(x30161,x30162)
% 28.78/28.54 [3017]~P144(x30171)+P144(x30172)+~E(x30171,x30172)
% 28.78/28.54 [3018]~P118(x30181)+P118(x30182)+~E(x30181,x30182)
% 28.78/28.54 [3019]P8(x30192,x30193)+~E(x30191,x30192)+~P8(x30191,x30193)
% 28.78/28.54 [3020]P8(x30203,x30202)+~E(x30201,x30202)+~P8(x30203,x30201)
% 28.78/28.54 [3021]P35(x30212,x30213,x30214,x30215,x30216)+~E(x30211,x30212)+~P35(x30211,x30213,x30214,x30215,x30216)
% 28.78/28.54 [3022]P35(x30223,x30222,x30224,x30225,x30226)+~E(x30221,x30222)+~P35(x30223,x30221,x30224,x30225,x30226)
% 28.78/28.54 [3023]P35(x30233,x30234,x30232,x30235,x30236)+~E(x30231,x30232)+~P35(x30233,x30234,x30231,x30235,x30236)
% 28.78/28.54 [3024]P35(x30243,x30244,x30245,x30242,x30246)+~E(x30241,x30242)+~P35(x30243,x30244,x30245,x30241,x30246)
% 28.78/28.54 [3025]P35(x30253,x30254,x30255,x30256,x30252)+~E(x30251,x30252)+~P35(x30253,x30254,x30255,x30256,x30251)
% 28.78/28.54 [3026]~P130(x30261)+P130(x30262)+~E(x30261,x30262)
% 28.78/28.54 [3027]~P89(x30271)+P89(x30272)+~E(x30271,x30272)
% 28.78/28.54 [3028]~P66(x30281)+P66(x30282)+~E(x30281,x30282)
% 28.78/28.54 [3029]P29(x30292,x30293)+~E(x30291,x30292)+~P29(x30291,x30293)
% 28.78/28.54 [3030]P29(x30303,x30302)+~E(x30301,x30302)+~P29(x30303,x30301)
% 28.78/28.54 [3031]~P148(x30311)+P148(x30312)+~E(x30311,x30312)
% 28.78/28.54 [3032]~P92(x30321)+P92(x30322)+~E(x30321,x30322)
% 28.78/28.54 [3033]~P80(x30331)+P80(x30332)+~E(x30331,x30332)
% 28.78/28.54 [3034]~P134(x30341)+P134(x30342)+~E(x30341,x30342)
% 28.78/28.54 [3035]~P7(x30351)+P7(x30352)+~E(x30351,x30352)
% 28.78/28.54 [3036]~P81(x30361)+P81(x30362)+~E(x30361,x30362)
% 28.78/28.54 [3037]P45(x30372,x30373)+~E(x30371,x30372)+~P45(x30371,x30373)
% 28.78/28.54 [3038]P45(x30383,x30382)+~E(x30381,x30382)+~P45(x30383,x30381)
% 28.78/28.54 [3039]~P125(x30391)+P125(x30392)+~E(x30391,x30392)
% 28.78/28.54 [3040]P24(x30402,x30403,x30404,x30405,x30406,x30407)+~E(x30401,x30402)+~P24(x30401,x30403,x30404,x30405,x30406,x30407)
% 28.78/28.54 [3041]P24(x30413,x30412,x30414,x30415,x30416,x30417)+~E(x30411,x30412)+~P24(x30413,x30411,x30414,x30415,x30416,x30417)
% 28.78/28.54 [3042]P24(x30423,x30424,x30422,x30425,x30426,x30427)+~E(x30421,x30422)+~P24(x30423,x30424,x30421,x30425,x30426,x30427)
% 28.78/28.54 [3043]P24(x30433,x30434,x30435,x30432,x30436,x30437)+~E(x30431,x30432)+~P24(x30433,x30434,x30435,x30431,x30436,x30437)
% 28.78/28.54 [3044]P24(x30443,x30444,x30445,x30446,x30442,x30447)+~E(x30441,x30442)+~P24(x30443,x30444,x30445,x30446,x30441,x30447)
% 28.78/28.54 [3045]P24(x30453,x30454,x30455,x30456,x30457,x30452)+~E(x30451,x30452)+~P24(x30453,x30454,x30455,x30456,x30457,x30451)
% 28.78/28.54 [3046]P59(x30462,x30463,x30464)+~E(x30461,x30462)+~P59(x30461,x30463,x30464)
% 28.78/28.54 [3047]P59(x30473,x30472,x30474)+~E(x30471,x30472)+~P59(x30473,x30471,x30474)
% 28.78/28.54 [3048]P59(x30483,x30484,x30482)+~E(x30481,x30482)+~P59(x30483,x30484,x30481)
% 28.78/28.54 [3049]P20(x30492,x30493,x30494)+~E(x30491,x30492)+~P20(x30491,x30493,x30494)
% 28.78/28.54 [3050]P20(x30503,x30502,x30504)+~E(x30501,x30502)+~P20(x30503,x30501,x30504)
% 28.78/28.54 [3051]P20(x30513,x30514,x30512)+~E(x30511,x30512)+~P20(x30513,x30514,x30511)
% 28.78/28.54 [3052]P62(x30522,x30523)+~E(x30521,x30522)+~P62(x30521,x30523)
% 28.78/28.54 [3053]P62(x30533,x30532)+~E(x30531,x30532)+~P62(x30533,x30531)
% 28.78/28.54 [3054]P49(x30542,x30543,x30544)+~E(x30541,x30542)+~P49(x30541,x30543,x30544)
% 28.78/28.54 [3055]P49(x30553,x30552,x30554)+~E(x30551,x30552)+~P49(x30553,x30551,x30554)
% 28.78/28.54 [3056]P49(x30563,x30564,x30562)+~E(x30561,x30562)+~P49(x30563,x30564,x30561)
% 28.78/28.54 [3057]P15(x30572,x30573,x30574)+~E(x30571,x30572)+~P15(x30571,x30573,x30574)
% 28.78/28.54 [3058]P15(x30583,x30582,x30584)+~E(x30581,x30582)+~P15(x30583,x30581,x30584)
% 28.78/28.54 [3059]P15(x30593,x30594,x30592)+~E(x30591,x30592)+~P15(x30593,x30594,x30591)
% 28.78/28.54 [3060]~P91(x30601)+P91(x30602)+~E(x30601,x30602)
% 28.78/28.54 [3061]~P37(x30611)+P37(x30612)+~E(x30611,x30612)
% 28.78/28.54 [3062]~P145(x30621)+P145(x30622)+~E(x30621,x30622)
% 28.78/28.54 [3063]~P146(x30631)+P146(x30632)+~E(x30631,x30632)
% 28.78/28.54 [3064]P33(x30642,x30643,x30644,x30645)+~E(x30641,x30642)+~P33(x30641,x30643,x30644,x30645)
% 28.78/28.54 [3065]P33(x30653,x30652,x30654,x30655)+~E(x30651,x30652)+~P33(x30653,x30651,x30654,x30655)
% 28.78/28.54 [3066]P33(x30663,x30664,x30662,x30665)+~E(x30661,x30662)+~P33(x30663,x30664,x30661,x30665)
% 28.78/28.54 [3067]P33(x30673,x30674,x30675,x30672)+~E(x30671,x30672)+~P33(x30673,x30674,x30675,x30671)
% 28.78/28.54 [3068]P64(x30682,x30683)+~E(x30681,x30682)+~P64(x30681,x30683)
% 28.78/28.54 [3069]P64(x30693,x30692)+~E(x30691,x30692)+~P64(x30693,x30691)
% 28.78/28.54 [3070]~P122(x30701)+P122(x30702)+~E(x30701,x30702)
% 28.78/28.54 [3071]~P124(x30711)+P124(x30712)+~E(x30711,x30712)
% 28.78/28.54 [3072]P50(x30722,x30723)+~E(x30721,x30722)+~P50(x30721,x30723)
% 28.78/28.54 [3073]P50(x30733,x30732)+~E(x30731,x30732)+~P50(x30733,x30731)
% 28.78/28.54 [3074]P60(x30742,x30743,x30744)+~E(x30741,x30742)+~P60(x30741,x30743,x30744)
% 28.78/28.54 [3075]P60(x30753,x30752,x30754)+~E(x30751,x30752)+~P60(x30753,x30751,x30754)
% 28.78/28.54 [3076]P60(x30763,x30764,x30762)+~E(x30761,x30762)+~P60(x30763,x30764,x30761)
% 28.78/28.54 [3077]~P101(x30771)+P101(x30772)+~E(x30771,x30772)
% 28.78/28.54 [3078]P61(x30782,x30783,x30784,x30785,x30786)+~E(x30781,x30782)+~P61(x30781,x30783,x30784,x30785,x30786)
% 28.78/28.54 [3079]P61(x30793,x30792,x30794,x30795,x30796)+~E(x30791,x30792)+~P61(x30793,x30791,x30794,x30795,x30796)
% 28.78/28.54 [3080]P61(x30803,x30804,x30802,x30805,x30806)+~E(x30801,x30802)+~P61(x30803,x30804,x30801,x30805,x30806)
% 28.78/28.54 [3081]P61(x30813,x30814,x30815,x30812,x30816)+~E(x30811,x30812)+~P61(x30813,x30814,x30815,x30811,x30816)
% 28.78/28.54 [3082]P61(x30823,x30824,x30825,x30826,x30822)+~E(x30821,x30822)+~P61(x30823,x30824,x30825,x30826,x30821)
% 28.78/28.54 [3083]~P128(x30831)+P128(x30832)+~E(x30831,x30832)
% 28.78/28.54 [3084]~P110(x30841)+P110(x30842)+~E(x30841,x30842)
% 28.78/28.54 [3085]P63(x30852,x30853,x30854,x30855)+~E(x30851,x30852)+~P63(x30851,x30853,x30854,x30855)
% 28.78/28.54 [3086]P63(x30863,x30862,x30864,x30865)+~E(x30861,x30862)+~P63(x30863,x30861,x30864,x30865)
% 28.78/28.54 [3087]P63(x30873,x30874,x30872,x30875)+~E(x30871,x30872)+~P63(x30873,x30874,x30871,x30875)
% 28.78/28.54 [3088]P63(x30883,x30884,x30885,x30882)+~E(x30881,x30882)+~P63(x30883,x30884,x30885,x30881)
% 28.78/28.54 [3089]P28(x30892,x30893)+~E(x30891,x30892)+~P28(x30891,x30893)
% 28.78/28.54 [3090]P28(x30903,x30902)+~E(x30901,x30902)+~P28(x30903,x30901)
% 28.78/28.54 [3091]~P97(x30911)+P97(x30912)+~E(x30911,x30912)
% 28.78/28.54 [3092]~P123(x30921)+P123(x30922)+~E(x30921,x30922)
% 28.78/28.54 [3093]~P119(x30931)+P119(x30932)+~E(x30931,x30932)
% 28.78/28.54 [3094]P55(x30942,x30943)+~E(x30941,x30942)+~P55(x30941,x30943)
% 28.78/28.54 [3095]P55(x30953,x30952)+~E(x30951,x30952)+~P55(x30953,x30951)
% 28.78/28.54 [3096]~P120(x30961)+P120(x30962)+~E(x30961,x30962)
% 28.78/28.54 [3097]P22(x30972,x30973,x30974,x30975)+~E(x30971,x30972)+~P22(x30971,x30973,x30974,x30975)
% 28.78/28.54 [3098]P22(x30983,x30982,x30984,x30985)+~E(x30981,x30982)+~P22(x30983,x30981,x30984,x30985)
% 28.78/28.54 [3099]P22(x30993,x30994,x30992,x30995)+~E(x30991,x30992)+~P22(x30993,x30994,x30991,x30995)
% 28.78/28.54 [3100]P22(x31003,x31004,x31005,x31002)+~E(x31001,x31002)+~P22(x31003,x31004,x31005,x31001)
% 28.78/28.54 [3101]P13(x31012,x31013,x31014,x31015,x31016,x31017)+~E(x31011,x31012)+~P13(x31011,x31013,x31014,x31015,x31016,x31017)
% 28.78/28.54 [3102]P13(x31023,x31022,x31024,x31025,x31026,x31027)+~E(x31021,x31022)+~P13(x31023,x31021,x31024,x31025,x31026,x31027)
% 28.78/28.54 [3103]P13(x31033,x31034,x31032,x31035,x31036,x31037)+~E(x31031,x31032)+~P13(x31033,x31034,x31031,x31035,x31036,x31037)
% 28.78/28.54 [3104]P13(x31043,x31044,x31045,x31042,x31046,x31047)+~E(x31041,x31042)+~P13(x31043,x31044,x31045,x31041,x31046,x31047)
% 28.78/28.54 [3105]P13(x31053,x31054,x31055,x31056,x31052,x31057)+~E(x31051,x31052)+~P13(x31053,x31054,x31055,x31056,x31051,x31057)
% 28.78/28.54 [3106]P13(x31063,x31064,x31065,x31066,x31067,x31062)+~E(x31061,x31062)+~P13(x31063,x31064,x31065,x31066,x31067,x31061)
% 28.78/28.54 [3107]~P133(x31071)+P133(x31072)+~E(x31071,x31072)
% 28.78/28.54 [3108]~P147(x31081)+P147(x31082)+~E(x31081,x31082)
% 28.78/28.54 [3109]~P138(x31091)+P138(x31092)+~E(x31091,x31092)
% 28.78/28.54 [3110]P48(x31102,x31103,x31104)+~E(x31101,x31102)+~P48(x31101,x31103,x31104)
% 28.78/28.54 [3111]P48(x31113,x31112,x31114)+~E(x31111,x31112)+~P48(x31113,x31111,x31114)
% 28.78/28.54 [3112]P48(x31123,x31124,x31122)+~E(x31121,x31122)+~P48(x31123,x31124,x31121)
% 28.78/28.54 [3113]P16(x31132,x31133,x31134)+~E(x31131,x31132)+~P16(x31131,x31133,x31134)
% 28.78/28.54 [3114]P16(x31143,x31142,x31144)+~E(x31141,x31142)+~P16(x31143,x31141,x31144)
% 28.78/28.54 [3115]P16(x31153,x31154,x31152)+~E(x31151,x31152)+~P16(x31153,x31154,x31151)
% 28.78/28.54 [3116]P40(x31162,x31163)+~E(x31161,x31162)+~P40(x31161,x31163)
% 28.78/28.54 [3117]P40(x31173,x31172)+~E(x31171,x31172)+~P40(x31173,x31171)
% 28.78/28.54 [3118]~P150(x31181)+P150(x31182)+~E(x31181,x31182)
% 28.78/28.54 [3119]P25(x31192,x31193,x31194,x31195,x31196,x31197)+~E(x31191,x31192)+~P25(x31191,x31193,x31194,x31195,x31196,x31197)
% 28.78/28.54 [3120]P25(x31203,x31202,x31204,x31205,x31206,x31207)+~E(x31201,x31202)+~P25(x31203,x31201,x31204,x31205,x31206,x31207)
% 28.78/28.54 [3121]P25(x31213,x31214,x31212,x31215,x31216,x31217)+~E(x31211,x31212)+~P25(x31213,x31214,x31211,x31215,x31216,x31217)
% 28.78/28.54 [3122]P25(x31223,x31224,x31225,x31222,x31226,x31227)+~E(x31221,x31222)+~P25(x31223,x31224,x31225,x31221,x31226,x31227)
% 28.78/28.54 [3123]P25(x31233,x31234,x31235,x31236,x31232,x31237)+~E(x31231,x31232)+~P25(x31233,x31234,x31235,x31236,x31231,x31237)
% 28.78/28.54 [3124]P25(x31243,x31244,x31245,x31246,x31247,x31242)+~E(x31241,x31242)+~P25(x31243,x31244,x31245,x31246,x31247,x31241)
% 28.78/28.54 [3125]P19(x31252,x31253,x31254)+~E(x31251,x31252)+~P19(x31251,x31253,x31254)
% 28.78/28.54 [3126]P19(x31263,x31262,x31264)+~E(x31261,x31262)+~P19(x31263,x31261,x31264)
% 28.78/28.54 [3127]P19(x31273,x31274,x31272)+~E(x31271,x31272)+~P19(x31273,x31274,x31271)
% 28.78/28.54 [3128]P44(x31282,x31283,x31284,x31285,x31286,x31287)+~E(x31281,x31282)+~P44(x31281,x31283,x31284,x31285,x31286,x31287)
% 28.78/28.54 [3129]P44(x31293,x31292,x31294,x31295,x31296,x31297)+~E(x31291,x31292)+~P44(x31293,x31291,x31294,x31295,x31296,x31297)
% 28.78/28.54 [3130]P44(x31303,x31304,x31302,x31305,x31306,x31307)+~E(x31301,x31302)+~P44(x31303,x31304,x31301,x31305,x31306,x31307)
% 28.78/28.54 [3131]P44(x31313,x31314,x31315,x31312,x31316,x31317)+~E(x31311,x31312)+~P44(x31313,x31314,x31315,x31311,x31316,x31317)
% 28.78/28.54 [3132]P44(x31323,x31324,x31325,x31326,x31322,x31327)+~E(x31321,x31322)+~P44(x31323,x31324,x31325,x31326,x31321,x31327)
% 28.78/28.54 [3133]P44(x31333,x31334,x31335,x31336,x31337,x31332)+~E(x31331,x31332)+~P44(x31333,x31334,x31335,x31336,x31337,x31331)
% 28.78/28.54 [3134]P31(x31342,x31343,x31344)+~E(x31341,x31342)+~P31(x31341,x31343,x31344)
% 28.78/28.54 [3135]P31(x31353,x31352,x31354)+~E(x31351,x31352)+~P31(x31353,x31351,x31354)
% 28.78/28.54 [3136]P31(x31363,x31364,x31362)+~E(x31361,x31362)+~P31(x31363,x31364,x31361)
% 28.78/28.54 [3137]P17(x31372,x31373)+~E(x31371,x31372)+~P17(x31371,x31373)
% 28.78/28.54 [3138]P17(x31383,x31382)+~E(x31381,x31382)+~P17(x31383,x31381)
% 28.78/28.54 [3139]~P94(x31391)+P94(x31392)+~E(x31391,x31392)
% 28.78/28.54 [3140]~P139(x31401)+P139(x31402)+~E(x31401,x31402)
% 28.78/28.54 [3141]~P105(x31411)+P105(x31412)+~E(x31411,x31412)
% 28.78/28.54 [3142]P52(x31422,x31423,x31424,x31425)+~E(x31421,x31422)+~P52(x31421,x31423,x31424,x31425)
% 28.78/28.54 [3143]P52(x31433,x31432,x31434,x31435)+~E(x31431,x31432)+~P52(x31433,x31431,x31434,x31435)
% 28.78/28.54 [3144]P52(x31443,x31444,x31442,x31445)+~E(x31441,x31442)+~P52(x31443,x31444,x31441,x31445)
% 28.78/28.54 [3145]P52(x31453,x31454,x31455,x31452)+~E(x31451,x31452)+~P52(x31453,x31454,x31455,x31451)
% 28.78/28.54 [3146]~P141(x31461)+P141(x31462)+~E(x31461,x31462)
% 28.78/28.54 [3147]~P111(x31471)+P111(x31472)+~E(x31471,x31472)
% 28.78/28.54 [3148]P58(x31482,x31483)+~E(x31481,x31482)+~P58(x31481,x31483)
% 28.78/28.54 [3149]P58(x31493,x31492)+~E(x31491,x31492)+~P58(x31493,x31491)
% 28.78/28.54 [3150]~P140(x31501)+P140(x31502)+~E(x31501,x31502)
% 28.78/28.54 [3151]P30(x31512,x31513,x31514)+~E(x31511,x31512)+~P30(x31511,x31513,x31514)
% 28.78/28.54 [3152]P30(x31523,x31522,x31524)+~E(x31521,x31522)+~P30(x31523,x31521,x31524)
% 28.78/28.54 [3153]P30(x31533,x31534,x31532)+~E(x31531,x31532)+~P30(x31533,x31534,x31531)
% 28.78/28.54 [3154]~P112(x31541)+P112(x31542)+~E(x31541,x31542)
% 28.78/28.54 [3155]P43(x31552,x31553,x31554,x31555)+~E(x31551,x31552)+~P43(x31551,x31553,x31554,x31555)
% 28.78/28.54 [3156]P43(x31563,x31562,x31564,x31565)+~E(x31561,x31562)+~P43(x31563,x31561,x31564,x31565)
% 28.78/28.54 [3157]P43(x31573,x31574,x31572,x31575)+~E(x31571,x31572)+~P43(x31573,x31574,x31571,x31575)
% 28.78/28.54 [3158]P43(x31583,x31584,x31585,x31582)+~E(x31581,x31582)+~P43(x31583,x31584,x31585,x31581)
% 28.78/28.54 [3159]~P95(x31591)+P95(x31592)+~E(x31591,x31592)
% 28.78/28.54 [3160]~P127(x31601)+P127(x31602)+~E(x31601,x31602)
% 28.78/28.54 [3161]~P85(x31611)+P85(x31612)+~E(x31611,x31612)
% 28.78/28.54 [3162]~P82(x31621)+P82(x31622)+~E(x31621,x31622)
% 28.78/28.54 [3163]P11(x31632,x31633,x31634,x31635,x31636)+~E(x31631,x31632)+~P11(x31631,x31633,x31634,x31635,x31636)
% 28.78/28.54 [3164]P11(x31643,x31642,x31644,x31645,x31646)+~E(x31641,x31642)+~P11(x31643,x31641,x31644,x31645,x31646)
% 28.78/28.54 [3165]P11(x31653,x31654,x31652,x31655,x31656)+~E(x31651,x31652)+~P11(x31653,x31654,x31651,x31655,x31656)
% 28.78/28.54 [3166]P11(x31663,x31664,x31665,x31662,x31666)+~E(x31661,x31662)+~P11(x31663,x31664,x31665,x31661,x31666)
% 28.78/28.54 [3167]P11(x31673,x31674,x31675,x31676,x31672)+~E(x31671,x31672)+~P11(x31673,x31674,x31675,x31676,x31671)
% 28.78/28.54 [3168]~P136(x31681)+P136(x31682)+~E(x31681,x31682)
% 28.78/28.54 [3169]~P137(x31691)+P137(x31692)+~E(x31691,x31692)
% 28.78/28.54 [3170]~P135(x31701)+P135(x31702)+~E(x31701,x31702)
% 28.78/28.54 [3171]P10(x31712,x31713,x31714)+~E(x31711,x31712)+~P10(x31711,x31713,x31714)
% 28.78/28.54 [3172]P10(x31723,x31722,x31724)+~E(x31721,x31722)+~P10(x31723,x31721,x31724)
% 28.78/28.54 [3173]P10(x31733,x31734,x31732)+~E(x31731,x31732)+~P10(x31733,x31734,x31731)
% 28.78/28.54 [3174]~P46(x31741)+P46(x31742)+~E(x31741,x31742)
% 28.78/28.54 [3175]P47(x31752,x31753)+~E(x31751,x31752)+~P47(x31751,x31753)
% 28.78/28.54 [3176]P47(x31763,x31762)+~E(x31761,x31762)+~P47(x31763,x31761)
% 28.78/28.54
% 28.78/28.54 %-------------------------------------------
% 28.78/28.55 cnf(10536,plain,
% 28.78/28.55 ($false),
% 28.78/28.55 inference(scs_inference,[],[4730,3465,3898,7417]),
% 28.78/28.55 ['proof']).
% 28.78/28.55 % SZS output end Proof
% 28.78/28.55 % Total time :22.760000s
%------------------------------------------------------------------------------